Results of Algebraic and Analytic Methods: Difference between revisions
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! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica | ! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica | ||
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| [ | | [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\binom{n}{k} = \frac{n!}{(n-k)!k!}</math>]] || <code>binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k))</code> || <code>Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!]</code> || Successful || Successful || - || - | ||
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| [ | | [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</math>]] || <code>(factorial(n))/(factorial(n - k)*factorial(k))=binomial(n,n - k)</code> || <code>Divide[(n)!,(n - k)!*(k)!]=Binomial[n,n - k]</code> || Successful || Successful || - || - | ||
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| [ | | [https://dlmf.nist.gov/1.2.E6 1.2.E6] || [[Item:Q35|<math>\binom{z}{k} = \frac{z(z-1)\cdots(z-k+1)}{k!}</math>]] || <code>binomial(z,k)=(z*(z - 1)..(z - k + 1))/(factorial(k))</code> || <code>Binomial[z,k]=Divide[z*(z - 1) ... (z - k + 1),(k)!]</code> || Successful || Successful || - || - | ||
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| [ | | [https://dlmf.nist.gov/1.2.E7 1.2.E7] || [[Item:Q36|<math>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</math>]] || <code>binomial(z + 1,k)=binomial(z,k)+binomial(z,k - 1)</code> || <code>Binomial[z + 1,k]=Binomial[z,k]+Binomial[z,k - 1]</code> || Successful || Successful || - || - | ||
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| [ | | [https://dlmf.nist.gov/1.2.E8 1.2.E8] || [[Item:Q37|<math>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</math>]] || <code>sum(binomial(z + k,k), k = 0..m)=binomial(z + m + 1,m)</code> || <code>Sum[Binomial[z + k,k], {k, 0, m}]=Binomial[z + m + 1,m]</code> || Successful || Successful || - || - | ||
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| [ | | [https://dlmf.nist.gov/1.4.E8 1.4.E8] || [[Item:Q87|<math>f^{(2)}(x) = \deriv[2]{f}{x}</math>]] || <code>(f)^(2)*(x)= diff(f, [x$(2)])</code> || <code>(f)^(2)*(x)= D[f, {x, 2}]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>0.+7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>0.+11.99999999*I <- {f = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>0.-7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>0.-11.99999999*I <- {f = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>0.+7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>0.+11.99999999*I <- {f = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>0.-7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>0.-11.99999999*I <- {f = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, 12.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, -12.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, 12.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, -12.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br></div></div> | ||
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| [ | | [https://dlmf.nist.gov/1.4.E8 1.4.E8] || [[Item:Q87|<math>\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)</math>]] || <code>diff(f, [x$(2)])= diff(diff(f, x), x)</code> || <code>D[f, {x, 2}]= D[D[f, x], x]</code> || Successful || Successful || - || - | ||
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| [ | | [https://dlmf.nist.gov/1.4.E9 1.4.E9] || [[Item:Q88|<math>f^{(n)} = f^{(n)}(x)</math>]] || <code>(f)^(n)= (f)^(n)*(x)</code> || <code>(f)^(n)= (f)^(n)*(x)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.414213562-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-2.828427124-2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-0.-7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245-5.656854245*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>11.31370849-11.31370849*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br><code>-1.414213562+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>-2.828427124+2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-0.+7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245+5.656854245*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>11.31370849+11.31370849*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>1.414213562+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>2.828427124+2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-0.-7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245+5.656854245*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>-11.31370849+11.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>1.414213562-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>2.828427124-2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-0.+7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245-5.656854245*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>-11.31370849-11.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br></div></div> | ||
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| [ | | [https://dlmf.nist.gov/1.4.E9 1.4.E9] || [[Item:Q88|<math>f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)</math>]] || <code>(f)^(n)*(x)= diff((f)^(n - 1)*(x), x)</code> || <code>(f)^(n)*(x)= D[(f)^(n - 1)*(x), x]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.414213562+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>1.828427124+2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>3.242640686+4.242640686*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br><code>-1.414213562+6.585786434*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-1.414213562+10.58578643*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245+1.656854247*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 1}</code><br><code>-11.31370849+7.313708492*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>-16.97056274+12.97056274*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br><code>.414213562-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 1}</code><br><code>1.828427124-2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>3.242640686-4.242640686*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 1}</code><br><code>-1.414213562-6.585786434*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-1.414213562-10.58578643*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245-1.656854247*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 1}</code><br><code>-11.31370849-7.313708492*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>-16.97056274-12.97056274*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>-2.414213562-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 1}</code><br><code>-3.828427124-2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>-5.242640686-4.242640686*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 1}</code><br><code>1.414213562+9.414213558*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>1.414213562+13.41421355*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245-9.656854243*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 1}</code><br><code>11.31370849-15.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>16.97056274-20.97056274*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>-2.414213562+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>-3.828427124+2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-5.242640686+4.242640686*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br><code>1.414213562-9.414213558*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>1.414213562-13.41421355*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245+9.656854243*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 1}</code><br><code>11.31370849+15.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>16.97056274+20.97056274*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[1.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[3.2426406871192857, 4.242640687119286] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, 2.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[-1.4142135623730951, 6.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[-1.4142135623730951, 10.585786437626904] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, 1.6568542494923806] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[-11.313708498984761, 7.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-16.970562748477143, 12.970562748477143] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[1.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[3.2426406871192857, -4.242640687119286] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, -2.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[-1.4142135623730951, -6.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[-1.4142135623730951, -10.585786437626904] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, -1.6568542494923806] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[-11.313708498984761, -7.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-16.970562748477143, -12.970562748477143] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[-3.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-5.242640687119286, -4.242640687119286] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, 5.414213562373095] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[1.4142135623730951, 9.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[1.4142135623730951, 13.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, -9.65685424949238] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[11.313708498984761, -15.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[16.970562748477143, -20.970562748477143] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[-3.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-5.242640687119286, 4.242640687119286] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, -5.414213562373095] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[1.4142135623730951, -9.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[1.4142135623730951, -13.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, 9.65685424949238] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[11.313708498984761, 15.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[16.970562748477143, 20.970562748477143] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.4.E16 1.4.E16] || [[Item:Q95|<math>\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}</math>]] || <code>int(f*g, x)=(int(f, x))* g - int((int(f, x))* diff(g, x), x)</code> || <code>Integrate[f*g, x]=(Integrate[f, x])* g - Integrate[(Integrate[f, x])* D[g, x], x]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.4.E37 1.4.E37] || [[Item:Q116|<math>R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t}</math>]] || <code>R[n]=(1)/(factorial(n))*int((x - t)^(n)* (f)^(n + 1)*(t), t = a..x)</code> || <code>Subscript[R, n]=Divide[1,(n)!]*Integrate[(x - t)^(n)* (f)^(n + 1)*(t), {t, a, x}]</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5.E4 1.5.E4] || [[Item:Q121|<math>\pderiv{f}{y} = D_{y}f</math>]] || <code>diff(f, y)= D[y]*f</code> || <code>D[f, y]= Subscript[D, y]*f</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-3.999999998-0.*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>-0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>3.999999998-0.*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-3.999999998-0.*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>3.999999998-0.*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>-0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>3.999999998-0.*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.999999998-0.*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>3.999999998-0.*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.999999998-0.*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.0 <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>4.0 <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.0 <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>4.0 <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>4.0 <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.0 <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>4.0 <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.0 <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5.E4 1.5.E4] || [[Item:Q121|<math>D_{y}f = f_{y}</math>]] || <code>D[y]*f = f[y]</code> || <code>Subscript[D, y]*f = Subscript[f, y]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562+5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562+5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>2.585786436-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.585786436+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>5.414213560+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>5.414213560-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562-5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562-2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.414213560-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.414213560+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.585786436+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.585786436-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>2.585786436-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.585786436+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>5.414213560+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>5.414213560-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562-5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.414213560-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.414213560+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.585786436+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.585786436-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562+2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562+5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562+5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562+2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562-5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562-2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.414213560-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.414213560+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.585786436+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.585786436-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562+2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562+2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>2.585786436-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.585786436+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>5.414213560+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>5.414213560-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.414213560-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.414213560+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.585786436+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.585786436-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562+2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562+5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562+5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562+2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>2.585786436-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.585786436+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>5.414213560+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>5.414213560-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.414213562-2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5#Ex3 1.5#Ex3] || [[Item:Q128|<math>x = r\cos@@{\phi}</math>]] || <code>x = r*cos(phi)</code> || <code>x = r*Cos[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-2.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>4.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>5.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.777253510-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>4.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>5.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.777253510+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>4.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>5.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.777253510-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>4.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>5.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.777253510+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5#Ex4 1.5#Ex4] || [[Item:Q129|<math>y = r\sin@@{\phi}</math>]] || <code>y = r*sin(phi)</code> || <code>y = r*Sin[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>.384024424-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-2.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-1.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>3.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>4.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>5.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>4.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>5.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>6.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-2.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-1.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-1.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>.384024424+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>4.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>5.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>6.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>3.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>4.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>5.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>3.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>4.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>5.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>4.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>5.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>6.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-1.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>.384024424-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-2.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-1.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>4.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>5.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>6.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>3.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>4.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>5.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-2.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-1.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-1.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>.384024424+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5.E13 1.5.E13] || [[Item:Q132|<math>\pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}</math>]] || <code>diff(f, [x$(2)])+ diff(f, [y$(2)])= diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])</code> || <code>D[f, {x, 2}]+ D[f, {y, 2}]= D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5#Ex5 1.5#Ex5] || [[Item:Q133|<math>x = r\cos@@{\phi}</math>]] || <code>x = r*cos(phi)</code> || <code>x = r*Cos[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-2.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>4.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>5.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.777253510-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>4.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>5.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.777253510+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>4.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>5.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.777253510-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>4.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>5.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.777253510+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5#Ex6 1.5#Ex6] || [[Item:Q134|<math>y = r\sin@@{\phi}</math>]] || <code>y = r*sin(phi)</code> || <code>y = r*Sin[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>.384024424-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-2.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-1.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>3.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>4.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>5.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>4.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>5.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>6.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-2.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-1.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-1.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>.384024424+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>4.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>5.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>6.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>3.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>4.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>5.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>3.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>4.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>5.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>4.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>5.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>6.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-1.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>.384024424-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-2.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-1.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>4.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>5.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>6.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>3.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>4.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>5.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-2.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-1.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-1.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>.384024424+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5#Ex8 1.5#Ex8] || [[Item:Q137|<math>x = \rho\sin@@{\theta}\cos@@{\phi}</math>]] || <code>x = rho*sin(theta)*cos(phi)</code> || <code>x = \[Rho]*Sin[\[Theta]]*Cos[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-6.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-5.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-4.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-5.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-4.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-3.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>8.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>9.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>10.52013032-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>7.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>8.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>9.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>4.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>6.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>7.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>8.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-4.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-3.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>8.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>9.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>10.52013032-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>7.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>8.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>9.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-6.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-5.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-4.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-5.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-4.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-3.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-4.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-3.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-2.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>6.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>7.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>8.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>6.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>7.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>8.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>4.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-4.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-3.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-2.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-5.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-4.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-3.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-6.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-5.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-4.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>7.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>8.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>9.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>8.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>9.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>10.52013032+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-4.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-3.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>6.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>7.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>8.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>7.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>8.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>9.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>8.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>9.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>10.52013032+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-5.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-4.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-3.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-6.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-5.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-4.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-6.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-5.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-4.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-5.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-4.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-3.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>8.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>9.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>10.52013032-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>7.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>8.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>9.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>4.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>6.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>7.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>8.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-4.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-3.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>8.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>9.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>10.52013032-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>7.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>8.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>9.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-6.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-5.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-4.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-5.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-4.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-3.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-4.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-3.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-2.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>6.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>7.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>8.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>6.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>7.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>8.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>4.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-4.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-3.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-2.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-5.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-4.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-3.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-6.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-5.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-4.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>7.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>8.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>9.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>8.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>9.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>10.52013032+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-4.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-3.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>6.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>7.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>8.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>7.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>8.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>9.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>8.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>9.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>10.52013032+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-5.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-4.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-3.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-6.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-5.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-4.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5#Ex9 1.5#Ex9] || [[Item:Q138|<math>y = \rho\sin@@{\theta}\sin@@{\phi}</math>]] || <code>y = rho*sin(theta)*sin(phi)</code> || <code>y = \[Rho]*Sin[\[Theta]]*Sin[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-3.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-2.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-1.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-5.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-4.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-3.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>5.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>6.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>7.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>7.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>8.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>9.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-7.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-6.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-5.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-5.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-4.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-3.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>9.254122865-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>10.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>11.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>7.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>8.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>9.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>5.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>6.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>7.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>7.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>8.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>9.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-3.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-2.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-1.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-5.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-4.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-3.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>9.254122865-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>10.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>11.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>7.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>8.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>9.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-7.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-6.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-5.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-5.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-4.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-3.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-5.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-4.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-3.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-7.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-6.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-5.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>7.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>8.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>9.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>9.254122865+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>10.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>11.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-5.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-4.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-3.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-3.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-2.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-1.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>7.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>8.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>9.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>5.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>6.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>7.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>7.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>8.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>9.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>9.254122865+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>10.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>11.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-5.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-4.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-3.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-7.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-6.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-5.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>7.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>8.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>9.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>5.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>6.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>7.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-5.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-4.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-3.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-3.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-2.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-1.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>5.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>6.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>7.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>7.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>8.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>9.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-3.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-2.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-1.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-5.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-4.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-3.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>9.254122865-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>10.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>11.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>7.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>8.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>9.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-7.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-6.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-5.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-5.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-4.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-3.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-3.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-2.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-1.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-5.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-4.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-3.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>5.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>6.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>7.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>7.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>8.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>9.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-7.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-6.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-5.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-5.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-4.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-3.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>9.254122865-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>10.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>11.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>7.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>8.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>9.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>7.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>8.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>9.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>9.254122865+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>10.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>11.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-5.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-4.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-3.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-7.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-6.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-5.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>7.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>8.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>9.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>5.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>6.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>7.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-5.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-4.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-3.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-3.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-2.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-1.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-5.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-4.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-3.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-7.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-6.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-5.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>7.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>8.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>9.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>9.254122865+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>10.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>11.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-5.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-4.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-3.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-3.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-2.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-1.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>7.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>8.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>9.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>5.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>6.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>7.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5#Ex10 1.5#Ex10] || [[Item:Q139|<math>z = \rho\cos@@{\theta}</math>]] || <code>z = rho*cos(theta)</code> || <code>z = \[Rho]*Cos[\[Theta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.769276062+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.769276062+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-4.597703186+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.597703186+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>3.636960052-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>3.636960052-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.808532928-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.808532928-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.769276062+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.769276062+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-4.597703186+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.597703186+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>3.636960052-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>3.636960052-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.808532928-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.808532928-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>3.636960052+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>3.636960052+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.808532928+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.808532928+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.769276062-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.769276062-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-4.597703186-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.597703186-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>3.636960052+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>3.636960052+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>.808532928+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>.808532928+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.769276062-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.769276062-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-4.597703186-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-4.597703186-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>4.597703186-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>4.597703186-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>1.769276062-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>1.769276062-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.808532928+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.808532928+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.636960052+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.636960052+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>4.597703186-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>4.597703186-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>1.769276062-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>1.769276062-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.808532928+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.808532928+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.636960052+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.636960052+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.808532928-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.808532928-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.636960052-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.636960052-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>4.597703186+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>4.597703186+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>1.769276062+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>1.769276062+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-.808532928-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-.808532928-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.636960052-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.636960052-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>4.597703186+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>4.597703186+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>1.769276062+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>1.769276062+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5.E17 1.5.E17] || [[Item:Q140|<math>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)</math>]] || <code>diff(f, [x$(2)])+ diff(f, [y$(2)])+ diff(f, [z$(2)])=(1)/((rho)^(2))*diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))*diff(f, [phi$(2)]), rho)+(1)/((rho)^(2)* sin(theta))*diff(sin(theta)*diff(f, theta), theta)</code> || <code>D[f, {x, 2}]+ D[f, {y, 2}]+ D[f, {z, 2}]=Divide[1,(\[Rho])^(2)]*D[((\[Rho])^(2)* D[f, \[Rho]])+Divide[1,(\[Rho])^(2)* (Sin[\[Theta]])^(2)]*D[f, {\[Phi], 2}], \[Rho]]+Divide[1,(\[Rho])^(2)* Sin[\[Theta]]]*D[Sin[\[Theta]]*D[f, \[Theta]], \[Theta]]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5.E19 1.5.E19] || [[Item:Q142|<math>\pderiv{f}{x} = \pderiv{f}{y}</math>]] || <code>diff(f, x)= diff(f, y)</code> || <code>D[f, x]= D[f, y]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.5.E23 1.5.E23] || [[Item:Q146|<math>\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon</math>]] || <code>abs(int(diff(f, x), y = c[1]..d))< epsilon</code> || <code>Abs[Integrate[D[f, x], {y, Subscript[c, 1], d}]]< \[Epsilon]</code> || Failure || Failure || Skip || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.6#Ex15 1.6#Ex15] || [[Item:Q194|<math>\LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2}</math>]] || <code>LeviCivita[1, 2, 3]= LeviCivita[3, 1, 2]</code> || <code>Part[LeviCivitaTensor[3,List], 1, 2, 3]= Part[LeviCivitaTensor[3,List], 3, 1, 2]</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}</code><br><code>2.828427124+2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}</code><br><code>2.828427124 <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.828427124 <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}</code><br><code>2.828427124-2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124-2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124 <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124 <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124+2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}</code><br><code>2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}</code><br></div></div> || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.6#Ex15 1.6#Ex15] || [[Item:Q194|<math>\LeviCivitasym{3}{1}{2} = 1</math>]] || <code>LeviCivita[3, 1, 2]= 1</code> || <code>Part[LeviCivitaTensor[3,List], 3, 1, 2]= 1</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.414213562+1.414213562*I <- {LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}</code><br><code>.414213562-1.414213562*I <- {LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.414213562-1.414213562*I <- {LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}</code><br><code>-2.414213562+1.414213562*I <- {LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.6#Ex16 1.6#Ex16] || [[Item:Q195|<math>\LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1}</math>]] || <code>LeviCivita[2, 1, 3]= LeviCivita[3, 2, 1]</code> || <code>Part[LeviCivitaTensor[3,List], 2, 1, 3]= Part[LeviCivitaTensor[3,List], 3, 2, 1]</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}</code><br><code>2.828427124+2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}</code><br><code>2.828427124 <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.828427124 <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}</code><br><code>2.828427124-2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124-2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124 <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}</code><br><code>-2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124 <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.828427124+2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}</code><br><code>2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}</code><br></div></div> || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.6#Ex16 1.6#Ex16] || [[Item:Q195|<math>\LeviCivitasym{3}{2}{1} = -1</math>]] || <code>LeviCivita[3, 2, 1]= - 1</code> || <code>Part[LeviCivitaTensor[3,List], 3, 2, 1]= - 1</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.414213562+1.414213562*I <- {LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}</code><br><code>2.414213562-1.414213562*I <- {LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}</code><br><code>-.414213562-1.414213562*I <- {LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}</code><br><code>-.414213562+1.414213562*I <- {LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.6#Ex17 1.6#Ex17] || [[Item:Q196|<math>\LeviCivitasym{2}{2}{1} = 0</math>]] || <code>LeviCivita[2, 2, 1]= 0</code> || <code>Part[LeviCivitaTensor[3,List], 2, 2, 1]= 0</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.414213562+1.414213562*I <- {LeviCivita[2,2,1] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414213562-1.414213562*I <- {LeviCivita[2,2,1] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.414213562-1.414213562*I <- {LeviCivita[2,2,1] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.414213562+1.414213562*I <- {LeviCivita[2,2,1] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.6.E16 1.6.E16] || [[Item:Q197|<math>\LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m}</math>]] || <code>LeviCivita[j, k, ell]*LeviCivita[ell, m, n]= KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m]</code> || <code>Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Part[LeviCivitaTensor[3,List], \[ScriptL], m, n]= KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m]</code> || Failure || Failure || Skip || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.6.E46 1.6.E46] || [[Item:Q227|<math>\mathbf{T}_{u} = \pderiv{x}{u}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{u}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{u}(u_{0},v_{0})\mathbf{k}</math>]] || <code>T[u]= diff(x, u)*(u[0], v[0])* I + diff(y, u)*(u[0], v[0])* j + diff(z, u)*(u[0], v[0])* k</code> || <code>Subscript[T, u]= D[x, u]*(Subscript[u, 0], Subscript[v, 0])* I + D[y, u]*(Subscript[u, 0], Subscript[v, 0])* j + D[z, u]*(Subscript[u, 0], Subscript[v, 0])* k</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.414213562+1.414213562*I <- {T[u] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414213562-1.414213562*I <- {T[u] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.414213562-1.414213562*I <- {T[u] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.414213562+1.414213562*I <- {T[u] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.6.E47 1.6.E47] || [[Item:Q228|<math>\mathbf{T}_{v} = \pderiv{x}{v}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{v}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{v}(u_{0},v_{0})\mathbf{k}</math>]] || <code>T[v]= diff(x, v)*(u[0], v[0])* I + diff(y, v)*(u[0], v[0])* j + diff(z, v)*(u[0], v[0])* k</code> || <code>Subscript[T, v]= D[x, v]*(Subscript[u, 0], Subscript[v, 0])* I + D[y, v]*(Subscript[u, 0], Subscript[v, 0])* j + D[z, v]*(Subscript[u, 0], Subscript[v, 0])* k</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.414213562+1.414213562*I <- {T[v] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414213562-1.414213562*I <- {T[v] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.414213562-1.414213562*I <- {T[v] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.414213562+1.414213562*I <- {T[v] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.8.E16 1.8.E16] || [[Item:Q270|<math>\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}</math>]] || <code>sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity)=sqrt((Pi)/(omega))*(1 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/ omega)*cos(2*n*Pi*x), n = 1..infinity))</code> || <code>Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}]=Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/ \[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}])</code> || Failure || Successful || Skip || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex1 1.9#Ex1] || [[Item:Q272|<math>\realpart@@{z} = x</math>]] || <code>Re(z)= x</code> || <code>Re[z]= x</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.414213562 <- {z = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.585786438 <- {z = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-1.585786438 <- {z = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>.414213562 <- {z = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.585786438 <- {z = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-1.585786438 <- {z = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-3.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-4.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-3.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-4.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.41421356237309515 <- {Rule[x, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-0.5857864376269049 <- {Rule[x, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-1.5857864376269049 <- {Rule[x, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>0.41421356237309515 <- {Rule[x, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-0.5857864376269049 <- {Rule[x, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-1.5857864376269049 <- {Rule[x, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.414213562373095 <- {Rule[x, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-3.414213562373095 <- {Rule[x, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.414213562373095 <- {Rule[x, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.414213562373095 <- {Rule[x, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-3.414213562373095 <- {Rule[x, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.414213562373095 <- {Rule[x, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex2 1.9#Ex2] || [[Item:Q273|<math>\imagpart@@{z} = y</math>]] || <code>Im(z)= y</code> || <code>Im[z]= y</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.414213562 <- {z = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-.585786438 <- {z = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-1.585786438 <- {z = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-2.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-3.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-4.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-2.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-3.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-4.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>.414213562 <- {z = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-.585786438 <- {z = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-1.585786438 <- {z = -2^(1/2)+I*2^(1/2), y = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.41421356237309515 <- {Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-0.5857864376269049 <- {Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-1.5857864376269049 <- {Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.414213562373095 <- {Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-3.414213562373095 <- {Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.414213562373095 <- {Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.414213562373095 <- {Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-3.414213562373095 <- {Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.414213562373095 <- {Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>0.41421356237309515 <- {Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-0.5857864376269049 <- {Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-1.5857864376269049 <- {Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex3 1.9#Ex3] || [[Item:Q274|<math>x = r\cos@@{\theta}</math>]] || <code>x = r*cos(theta)</code> || <code>x = r*Cos[\[Theta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-2.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>4.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>5.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>3.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>4.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>5.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>3.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>4.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>5.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-2.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-1.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>3.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>4.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>5.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-2.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-1.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>4.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-1.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.777253510+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.777253510+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br><code>-1.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>.777253510-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>4.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>5.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>6.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>-.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>.777253510-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>4.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>5.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>6.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex4 1.9#Ex4] || [[Item:Q275|<math>y = r\sin@@{\theta}</math>]] || <code>y = r*sin(theta)</code> || <code>y = r*Sin[\[Theta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.615975576-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-.615975576-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>.384024424-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-2.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-1.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>3.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>4.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>5.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>4.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>5.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>6.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-2.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-1.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-1.615975576+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-.615975576+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>.384024424+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>4.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>5.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>6.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>3.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>4.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>5.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>3.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>4.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>5.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>4.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>5.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>6.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-1.615975576-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-.615975576-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>.384024424-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-2.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-1.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br><code>4.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>5.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>6.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>3.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}</code><br><code>4.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}</code><br><code>5.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-2.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}</code><br><code>-1.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}</code><br><code>-.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}</code><br><code>-1.615975576+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-.615975576+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}</code><br><code>.384024424+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E6 1.9.E6] || [[Item:Q278|<math>\omega = \atan@{|y/x|}\in\left[0,\tfrac{1}{2}\pi\right]</math>]] || <code>omega = arctan(abs(y/ x))in[0 ,(1)/(2)*Pi]</code> || <code>\[Omega]= ArcTan[Abs[y/ x]]\[Element][0 ,Divide[1,2]*Pi]</code> || Failure || Failure || Error || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex6 1.9#Ex6] || [[Item:Q280|<math>\phase@@{z} = \theta+2n\pi</math>]] || <code>argument(z)= theta + 2*n*Pi</code> || <code>Arg[z]= \[Theta]+ 2*n*Pi</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-6.912000706-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}</code><br><code>-13.19518602-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-19.47837132-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}</code><br><code>-8.482797034-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}</code><br><code>-14.76598234-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-21.04916764-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}</code><br><code>-10.05359336-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}</code><br><code>-16.33677867-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-22.61996397-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}</code><br><code>-5.341204380-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}</code><br><code>-11.62438969-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-17.90757499-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}</code><br><code>-6.912000706+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}</code><br><code>-13.19518602+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-19.47837132+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}</code><br><code>-8.482797034+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}</code><br><code>-14.76598234+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-21.04916764+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}</code><br><code>-10.05359336+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}</code><br><code>-16.33677867+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-22.61996397+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}</code><br><code>-5.341204380+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}</code><br><code>-11.62438969+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-17.90757499+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}</code><br><code>-4.083573582+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}</code><br><code>-10.36675890+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-16.64994420+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}</code><br><code>-5.654369910+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}</code><br><code>-11.93755522+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-18.22074052+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}</code><br><code>-7.225166236+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}</code><br><code>-13.50835155+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-19.79153685+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}</code><br><code>-2.512777256+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}</code><br><code>-8.795962568+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-15.07914787+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}</code><br><code>-4.083573582-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}</code><br><code>-10.36675890-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-16.64994420-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}</code><br><code>-5.654369910-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}</code><br><code>-11.93755522-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-18.22074052-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}</code><br><code>-7.225166236-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}</code><br><code>-13.50835155-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}</code><br><code>-19.79153685-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}</code><br><code>-2.512777256-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}</code><br><code>-8.795962568-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}</code><br><code>-15.07914787-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-6.912000706155233, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-13.195186013334819, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-19.478371320514405, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.912000706155233, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-13.195186013334819, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-19.478371320514405, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.083573581409043, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-10.366758888588627, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-16.649944195768214, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.083573581409043, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-10.366758888588627, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-16.649944195768214, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.48279703295013, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-14.765982340129717, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-21.049167647309304, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.48279703295013, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-14.765982340129717, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-21.049167647309304, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.65436990820394, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-11.937555215383526, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-18.220740522563112, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.65436990820394, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-11.937555215383526, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-18.220740522563112, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-10.053593359745026, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-16.336778666924612, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-22.6199639741042, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-10.053593359745026, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-16.336778666924612, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-22.6199639741042, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.225166234998835, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-13.50835154217842, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-19.791536849358007, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.225166234998835, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-13.50835154217842, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-19.791536849358007, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.341204379360336, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-11.624389686539924, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-17.90757499371951, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.341204379360336, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-11.624389686539924, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-17.90757499371951, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5127772546141465, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.795962561793733, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-15.079147868973319, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.5127772546141465, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.795962561793733, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-15.079147868973319, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex7 1.9#Ex7] || [[Item:Q281|<math>|\realpart@@{z}| <= |z|</math>]] || <code>abs(Re(z))< =abs(z)</code> || <code>Abs[Re[z]]< =Abs[z]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex8 1.9#Ex8] || [[Item:Q282|<math>|\imagpart@@{z}| <= |z|</math>]] || <code>abs(Im(z))< =abs(z)</code> || <code>Abs[Im[z]]< =Abs[z]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E10 1.9.E10] || [[Item:Q284|<math>e^{i\theta} = \cos@@{\theta}+i\sin@@{\theta}</math>]] || <code>exp(I*theta)= cos(theta)+ I*sin(theta)</code> || <code>Exp[I*\[Theta]]= Cos[\[Theta]]+ I*Sin[\[Theta]]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E11 1.9.E11] || [[Item:Q285|<math>\conj{z} = x-iy</math>]] || <code>conjugate(z)= x - I*y</code> || <code>Conjugate[z]= x - I*y</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.414213562-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>.414213562+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>.414213562+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>-.585786438-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>-.585786438+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>-.585786438+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>-1.585786438-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>-1.585786438+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>-1.585786438+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br><code>.414213562+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>.414213562+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>.414213562+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>-.585786438+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>-.585786438+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>-.585786438+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>-1.585786438+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>-1.585786438+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>-1.585786438+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>-2.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>-2.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>-2.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>-3.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>-3.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>-3.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>-4.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>-4.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>-4.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>-2.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>-2.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>-2.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>-3.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>-3.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>-3.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>-4.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>-4.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>-4.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.41421356237309515, -0.41421356237309515] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.41421356237309515, 0.5857864376269049] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.41421356237309515, 1.5857864376269049] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.5857864376269049, -0.41421356237309515] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.5857864376269049, 0.5857864376269049] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.5857864376269049, 1.5857864376269049] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5857864376269049, -0.41421356237309515] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5857864376269049, 0.5857864376269049] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5857864376269049, 1.5857864376269049] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.41421356237309515, 2.414213562373095] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.41421356237309515, 3.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.41421356237309515, 4.414213562373095] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.5857864376269049, 2.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.5857864376269049, 3.414213562373095] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.5857864376269049, 4.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5857864376269049, 2.414213562373095] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5857864376269049, 3.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.5857864376269049, 4.414213562373095] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.414213562373095, 2.414213562373095] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.414213562373095, 3.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.414213562373095, 4.414213562373095] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.414213562373095, 2.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.414213562373095, 3.414213562373095] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.414213562373095, 4.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.414213562373095, 2.414213562373095] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.414213562373095, 3.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.414213562373095, 4.414213562373095] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.414213562373095, -0.41421356237309515] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.414213562373095, 0.5857864376269049] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.414213562373095, 1.5857864376269049] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.414213562373095, -0.41421356237309515] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.414213562373095, 0.5857864376269049] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.414213562373095, 1.5857864376269049] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.414213562373095, -0.41421356237309515] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.414213562373095, 0.5857864376269049] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.414213562373095, 1.5857864376269049] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E12 1.9.E12] || [[Item:Q286|<math>|\conj{z}| = |z|</math>]] || <code>abs(conjugate(z))=abs(z)</code> || <code>Abs[Conjugate[z]]=Abs[z]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E13 1.9.E13] || [[Item:Q287|<math>\phase@@{\conj{z}} = -\phase@@{z}</math>]] || <code>argument(conjugate(z))= - argument(z)</code> || <code>Arg[Conjugate[z]]= - Arg[z]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E14 1.9.E14] || [[Item:Q288|<math>z_{1}+ z_{2} = x_{1}+ x_{2}+\iunit(y_{1}+ y_{2})</math>]] || <code>z[1]+ z[2]= x[1]+ x[2]+ I*(y[1]+ y[2])</code> || <code>Subscript[z, 1]+ Subscript[z, 2]= Subscript[x, 1]+ Subscript[x, 2]+ I*(Subscript[y, 1]+ Subscript[y, 2])</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E14 1.9.E14] || [[Item:Q288|<math>z_{1}- z_{2} = x_{1}- x_{2}+\iunit(y_{1}- y_{2})</math>]] || <code>z[1]- z[2]= x[1]- x[2]+ I*(y[1]- y[2])</code> || <code>Subscript[z, 1]- Subscript[z, 2]= Subscript[x, 1]- Subscript[x, 2]+ I*(Subscript[y, 1]- Subscript[y, 2])</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E16 1.9.E16] || [[Item:Q290|<math>\frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}</math>]] || <code>(z[1])/(z[2])=(z[1]*conjugate(z)[2])/((abs(z[2]))^(2))</code> || <code>Divide[Subscript[z, 1],Subscript[z, 2]]=Divide[Subscript[z, 1]*Subscript[Conjugate[z], 2],(Abs[Subscript[z, 2]])^(2)]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E16 1.9.E16] || [[Item:Q290|<math>\frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}</math>]] || <code>(x[1]*x[2]+ y[1]*y[2]+ I*(x[2]*y[1]- x[1]*y[2]))/(x(x[2])^(2)+ y(y[2])^(2))</code> || <code>Divide[Subscript[x, 1]*Subscript[x, 2]+ Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 2]*Subscript[y, 1]- Subscript[x, 1]*Subscript[y, 2]),x(Subscript[x, 2])^(2)+ y(Subscript[y, 2])^(2)]</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E18 1.9.E18] || [[Item:Q292|<math>\phase@{z_{1}z_{2}} = \phase@@{z_{1}}+\phase@@{z_{2}}</math>]] || <code>argument(z[1]*z[2])= argument(z[1])+ argument(z[2])</code> || <code>Arg[Subscript[z, 1]*Subscript[z, 2]]= Arg[Subscript[z, 1]]+ Arg[Subscript[z, 2]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>6.283185308 <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}</code><br><code>6.283185308 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)-I*2^(1/2)}</code><br><code>6.283185307 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}</code><br><code>-6.283185307 <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E19 1.9.E19] || [[Item:Q293|<math>\abs{\frac{z_{1}}{z_{2}}} = \frac{|z_{1}|}{|z_{2}|}</math>]] || <code>abs((z[1])/(z[2]))=(abs(z[1]))/(abs(z[2]))</code> || <code>Abs[Divide[Subscript[z, 1],Subscript[z, 2]]]=Divide[Abs[Subscript[z, 1]],Abs[Subscript[z, 2]]]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E20 1.9.E20] || [[Item:Q294|<math>\phase@@{\frac{z_{1}}{z_{2}}} = \phase@@{z_{1}}-\phase@@{z_{2}}</math>]] || <code>argument((z[1])/(z[2]))= argument(z[1])- argument(z[2])</code> || <code>Arg[Divide[Subscript[z, 1],Subscript[z, 2]]]= Arg[Subscript[z, 1]]- Arg[Subscript[z, 2]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>6.283185308 <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}</code><br><code>6.283185308 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2)}</code><br><code>6.283185307 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}</code><br><code>-6.283185307 <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E22 1.9.E22] || [[Item:Q296|<math>\cos@@{n\theta}+i\sin@@{n\theta} = (\cos@@{\theta}+i\sin@@{\theta})^{n}</math>]] || <code>cos(n*theta)+ I*sin(n*theta)=(cos(theta)+ I*sin(theta))^(n)</code> || <code>Cos[n*\[Theta]]+ I*Sin[n*\[Theta]]=(Cos[\[Theta]]+ I*Sin[\[Theta]])^(n)</code> || Successful || Failure || - || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E23 1.9.E23] || [[Item:Q297|<math>\abs{\abs{z_{1}}-\abs{z_{2}}} <= \abs{z_{1}+z_{2}}</math>]] || <code>abs(abs(z[1])- abs(z[2]))< = abs(z[1]+ z[2])</code> || <code>Abs[Abs[Subscript[z, 1]]- Abs[Subscript[z, 2]]]< = Abs[Subscript[z, 1]+ Subscript[z, 2]]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E23 1.9.E23] || [[Item:Q297|<math>\abs{z_{1}+z_{2}} <= \abs{z_{1}}+\abs{z_{2}}</math>]] || <code>abs(z[1]+ z[2])< = abs(z[1])+ abs(z[2])</code> || <code>Abs[Subscript[z, 1]+ Subscript[z, 2]]< = Abs[Subscript[z, 1]]+ Abs[Subscript[z, 2]]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex9 1.9#Ex9] || [[Item:Q299|<math>\pderiv{u}{x} = \pderiv{v}{y}</math>]] || <code>diff(u, x)= diff(v, y)</code> || <code>D[u, x]= D[v, y]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9#Ex10 1.9#Ex10] || [[Item:Q300|<math>\pderiv{u}{y} = -\pderiv{v}{x}</math>]] || <code>diff(u, y)= - diff(v, x)</code> || <code>D[u, y]= - D[v, x]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E26 1.9.E26] || [[Item:Q301|<math>\pderiv[2]{u}{x}+\pderiv[2]{u}{y} = \pderiv[2]{v}{x}+\pderiv[2]{v}{y}</math>]] || <code>diff(u, [x$(2)])+ diff(u, [y$(2)])= diff(v, [x$(2)])+ diff(v, [y$(2)])</code> || <code>D[u, {x, 2}]+ D[u, {y, 2}]= D[v, {x, 2}]+ D[v, {y, 2}]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E26 1.9.E26] || [[Item:Q301|<math>\pderiv[2]{v}{x}+\pderiv[2]{v}{y} = 0</math>]] || <code>diff(v, [x$(2)])+ diff(v, [y$(2)])= 0</code> || <code>D[v, {x, 2}]+ D[v, {y, 2}]= 0</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E27 1.9.E27] || [[Item:Q302|<math>\pderiv[2]{u}{r}+\frac{1}{r}\pderiv{u}{r}+\frac{1}{r^{2}}\pderiv[2]{u}{\theta} = 0</math>]] || <code>diff(u, [r$(2)])+(1)/(r)*diff(u, r)+(1)/((r)^(2))*diff(u, [theta$(2)])= 0</code> || <code>D[u, {r, 2}]+Divide[1,r]*D[u, r]+Divide[1,(r)^(2)]*D[u, {\[Theta], 2}]= 0</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E33 1.9.E33] || [[Item:Q308|<math>u(z) = \frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})\diff{\phi}</math>]] || <code>u*(z)=(1)/(2*Pi)*int(u*(z + r*exp(I*phi)), phi = 0..2*Pi)</code> || <code>u*(z)=Divide[1,2*Pi]*Integrate[u*(z + r*Exp[I*\[Phi]]), {\[Phi], 0, 2*Pi}]</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E34 1.9.E34] || [[Item:Q309|<math>u(re^{i\theta}) = \frac{1}{2\pi}\int^{2\pi}_{0}\frac{(R^{2}-r^{2})h(Re^{i\phi})\diff{\phi}}{R^{2}-2Rr\cos@{\phi-\theta}+r^{2}}</math>]] || <code>u*(r*exp(I*theta))=(1)/(2*Pi)*int((((R)^(2)- (r)^(2))* h*(R*exp(I*phi)))/((R)^(2)- 2*R*r*cos(phi - theta)+ (r)^(2)), phi = 0..2*Pi)</code> || <code>u*(r*Exp[I*\[Theta]])=Divide[1,2*Pi]*Integrate[Divide[((R)^(2)- (r)^(2))* h*(R*Exp[I*\[Phi]]),(R)^(2)- 2*R*r*Cos[\[Phi]- \[Theta]]+ (r)^(2)], {\[Phi], 0, 2*Pi}]</code> || Error || Failure || - || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E63 1.9.E63] || [[Item:Q345|<math>f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}</math>]] || <code>(f)^(m)*(z)= sum(pochhammer(n + 1, m)*a[n + m]*(z - z[0])^(n), n = 0..infinity)</code> || <code>(f)^(m)*(z)= Sum[Pochhammer[n + 1, m]*Subscript[a, n + m]*(z - Subscript[z, 0])^(n), {n, 0, Infinity}]</code> || Failure || Failure || Skip || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.9.E71 1.9.E71] || [[Item:Q355|<math>\int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\diff{t} = \sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\diff{t}</math>]] || <code>int(sum(f[n]*(t), n = 0..infinity), t = a..b)= sum(int(f[n]*(t), t = a..b), n = 0..infinity)</code> || <code>Integrate[Sum[Subscript[f, n]*(t), {n, 0, Infinity}], {t, a, b}]= Sum[Integrate[Subscript[f, n]*(t), {t, a, b}], {n, 0, Infinity}]</code> || Successful || Failure || - || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.10.E20 1.10.E20] || [[Item:Q375|<math>|\ln@{1+a_{n}(z)}| <= M_{n}</math>]] || <code>abs(ln(1 + a[n]*(z)))< = M[n]</code> || <code>Abs[Log[1 + Subscript[a, n]*(z)]]< = Subscript[M, n]</code> || Failure || Failure || Skip || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.12.E26 1.12.E26] || [[Item:Q459|<math>-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}</math>]] || <code>-(1)/(2)*Pi + delta < argument(b[n])</code> || <code>-Divide[1,2]*Pi + \[Delta]< Arg[Subscript[b, n]]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.12.E26 1.12.E26] || [[Item:Q459|<math>\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta</math>]] || <code>argument(b[n])<(1)/(2)*Pi - delta</code> || <code>Arg[Subscript[b, n]]<Divide[1,2]*Pi - \[Delta]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.12.E27 1.12.E27] || [[Item:Q460|<math>-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}</math>]] || <code>-(1)/(2)*Pi + delta < argument(C[n])</code> || <code>-Divide[1,2]*Pi + \[Delta]< Arg[Subscript[C, n]]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.12.E27 1.12.E27] || [[Item:Q460|<math>\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta</math>]] || <code>argument(C[n])<(1)/(2)*Pi - delta</code> || <code>Arg[Subscript[C, n]]<Divide[1,2]*Pi - \[Delta]</code> || Failure || Failure || Successful || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.13.E11 1.13.E11] || [[Item:Q475|<math>\deriv[2]{W}{\xi}+F(\xi)\deriv{W}{\xi}+G(\xi)W = 0</math>]] || <code>diff(W, [xi$(2)])+ F*(xi)* diff(W, xi)+ G*(xi)* W = 0</code> || <code>D[W, {\[Xi], 2}]+ F*(\[Xi])* D[W, \[Xi]]+ G*(\[Xi])* W = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.13.E14 1.13.E14] || [[Item:Q480|<math>\deriv[2]{W}{z}-H(z)W = 0</math>]] || <code>diff(W, [z$(2)])- H*(z)* W = 0</code> || <code>D[W, {z, 2}]- H*(z)* W = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br><code>-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.13#Ex8 1.13#Ex8] || [[Item:Q490|<math>\deriv[2]{U}{z}+IU = 0</math>]] || <code>diff(U, [z$(2)])+ I*U = 0</code> || <code>D[U, {z, 2}]+ I*U = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.414213562+1.414213562*I <- {U = 2^(1/2)+I*2^(1/2)}</code><br><code>1.414213562+1.414213562*I <- {U = 2^(1/2)-I*2^(1/2)}</code><br><code>1.414213562-1.414213562*I <- {U = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.414213562-1.414213562*I <- {U = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[U, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[U, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.13#Ex9 1.13#Ex9] || [[Item:Q491|<math>\deriv[2]{V}{z}+JV = 0</math>]] || <code>diff(V, [z$(2)])+ J*V = 0</code> || <code>D[V, {z, 2}]+ J*V = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.+3.999999998*I <- {J = 2^(1/2)+I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}</code><br><code>3.999999998+0.*I <- {J = 2^(1/2)+I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {J = 2^(1/2)+I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}</code><br><code>-3.999999998+0.*I <- {J = 2^(1/2)+I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}</code><br><code>3.999999998+0.*I <- {J = 2^(1/2)-I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {J = 2^(1/2)-I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}</code><br><code>-3.999999998+0.*I <- {J = 2^(1/2)-I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}</code><br><code>0.+3.999999998*I <- {J = 2^(1/2)-I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {J = -2^(1/2)-I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}</code><br><code>-3.999999998+0.*I <- {J = -2^(1/2)-I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}</code><br><code>0.+3.999999998*I <- {J = -2^(1/2)-I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}</code><br><code>3.999999998+0.*I <- {J = -2^(1/2)-I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}</code><br><code>-3.999999998+0.*I <- {J = -2^(1/2)+I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}</code><br><code>0.+3.999999998*I <- {J = -2^(1/2)+I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}</code><br><code>3.999999998+0.*I <- {J = -2^(1/2)+I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {J = -2^(1/2)+I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, 4.0] <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>4.0 <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -4.0] <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.0 <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>4.0 <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -4.0] <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.0 <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.0] <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -4.0] <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.0 <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.0] <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>4.0 <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.0 <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.0] <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>4.0 <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -4.0] <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.14.E6 1.14.E6] || [[Item:Q498|<math>(f*g)(t) = \frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}F(x)G(x)e^{-itx}\diff{x}</math>]] || <code>(f * g)*(t)=(1)/(sqrt(2*Pi))*int(F*(x)* G*(x)* exp(- I*t*x), x = - infinity..infinity)</code> || <code>(f * g)*(t)=Divide[1,Sqrt[2*Pi]]*Integrate[F*(x)* G*(x)* Exp[- I*t*x], {x, - Infinity, Infinity}]</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.15.E13 1.15.E13] || [[Item:Q555|<math>\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1</math>]] || <code>(1)/(2*Pi)*int(P*(r , theta), theta = 0..2*Pi)= 1</code> || <code>Divide[1,2*Pi]*Integrate[P*(r , \[Theta]), {\[Theta], 0, 2*Pi}]= 1</code> || Error || Failure || - || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.15.E16 1.15.E16] || [[Item:Q558|<math>\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1</math>]] || <code>(1)/(2*Pi)*int(K[n]*(theta), theta = 0..2*Pi)= 1</code> || <code>Divide[1,2*Pi]*Integrate[Subscript[K, n]*(\[Theta]), {\[Theta], 0, 2*Pi}]= 1</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[3.442882938158366, 4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.442882938158366, -4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.442882938158366, -4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.442882938158366, 4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.15.E34 1.15.E34] || [[Item:Q576|<math>\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1</math>]] || <code>(1)/(2*Pi)*int(P*(x , y), x = - infinity..infinity)= 1</code> || <code>Divide[1,2*Pi]*Integrate[P*(x , y), {x, - Infinity, Infinity}]= 1</code> || Error || Failure || - || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.15.E36 1.15.E36] || [[Item:Q578|<math>h(x,y) = \frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}e^{-y|t|}e^{-ixt}F(t)\diff{t}</math>]] || <code>h*(x , y)=(1)/(sqrt(2*Pi))*int(exp(- y*abs(t))*exp(- I*x*t)*F*(t), t = - infinity..infinity)</code> || <code>h*(x , y)=Divide[1,Sqrt[2*Pi]]*Integrate[Exp[- y*Abs[t]]*Exp[- I*x*t]*F*(t), {t, - Infinity, Infinity}]</code> || Failure || Failure || Skip || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.15.E39 1.15.E39] || [[Item:Q581|<math>\Phi(z) = \Phi(x+iy)</math>]] || <code>Phi*(z)= Phi*(x + I*y)</code> || <code>\[CapitalPhi]*(z)= \[CapitalPhi]*(x + I*y)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.+1.171572874*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>1.414213562-.242640688*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>2.828427124-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>-1.414213562-.242640688*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>0.-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>1.414213562-3.071067812*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>-2.828427124-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>-1.414213562-3.071067812*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>0.-4.485281374*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br><code>3.999999998-2.828427124*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>5.414213560-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>6.828427122-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>2.585786436-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>3.999999998-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>5.414213560-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>1.171572874-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>2.585786436-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>3.999999998-8.485281372*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>0.-6.828427122*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>1.414213562-8.242640684*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>2.828427124-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>-1.414213562-8.242640684*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>0.-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>1.414213562-11.07106781*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>-2.828427124-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>-1.414213562-11.07106781*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>0.-12.48528137*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>-3.999999998-2.828427124*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>-2.585786436-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>-1.171572874-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>-5.414213560-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>-3.999999998-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>-2.585786436-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>-6.828427122-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>-5.414213560-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>-3.999999998-8.485281372*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br><code>1.171572874+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>-.242640688-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>-1.656854250-2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>-.242640688+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>-1.656854250+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>-3.071067812-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>-1.656854250+2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>-3.071067812+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>-4.485281374+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br><code>-2.828427124-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>-4.242640686-5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>-5.656854248-6.828427122*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>-4.242640686-2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>-5.656854248-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>-7.071067810-5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>-5.656854248-1.171572874*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>-7.071067810-2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>-8.485281372-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>-6.828427122+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>-8.242640684-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>-9.656854246-2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>-8.242640684+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>-9.656854246+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>-11.07106781-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>-9.656854246+2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>-11.07106781+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>-12.48528137+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>-2.828427124+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>-4.242640686+2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>-5.656854248+1.171572874*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>-4.242640686+5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>-5.656854248+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>-7.071067810+2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>-5.656854248+6.828427122*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>-7.071067810+5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>-8.485281372+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br><code>0.-1.171572874*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>-1.414213562+.242640688*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>-2.828427124+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>1.414213562+.242640688*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>0.+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>-1.414213562+3.071067812*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>2.828427124+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>1.414213562+3.071067812*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>0.+4.485281374*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br><code>-3.999999998+2.828427124*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>-5.414213560+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>-6.828427122+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>-2.585786436+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>-3.999999998+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>-5.414213560+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>-1.171572874+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>-2.585786436+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>-3.999999998+8.485281372*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>0.+6.828427122*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>-1.414213562+8.242640684*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>-2.828427124+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>1.414213562+8.242640684*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>0.+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>-1.414213562+11.07106781*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>2.828427124+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>1.414213562+11.07106781*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>0.+12.48528137*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>3.999999998+2.828427124*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>2.585786436+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>1.171572874+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>5.414213560+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>3.999999998+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>2.585786436+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>6.828427122+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>5.414213560+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>3.999999998+8.485281372*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br><code>-1.171572874+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>.242640688+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>1.656854250+2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>.242640688-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>1.656854250+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>3.071067812+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>1.656854250-2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>3.071067812-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>4.485281374+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br><code>2.828427124+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>4.242640686+5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>5.656854248+6.828427122*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>4.242640686+2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>5.656854248+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>7.071067810+5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>5.656854248+1.171572874*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>7.071067810+2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>8.485281372+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>6.828427122+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}</code><br><code>8.242640684+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}</code><br><code>9.656854246+2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}</code><br><code>8.242640684-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}</code><br><code>9.656854246+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}</code><br><code>11.07106781+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}</code><br><code>9.656854246-2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}</code><br><code>11.07106781-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}</code><br><code>12.48528137+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}</code><br><code>2.828427124-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}</code><br><code>4.242640686-2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}</code><br><code>5.656854248-1.171572874*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}</code><br><code>4.242640686-5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}</code><br><code>5.656854248-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}</code><br><code>7.071067810-2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}</code><br><code>5.656854248-6.828427122*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}</code><br><code>7.071067810-5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}</code><br><code>8.485281372-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, 1.1715728752538097] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -0.24264068711928566] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8284271247461903, -1.6568542494923806] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -0.24264068711928566] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -1.6568542494923806] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -3.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8284271247461903, -1.6568542494923806] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -3.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -4.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>1.1715728752538097 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.24264068711928566, -1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6568542494923806, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.24264068711928566, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-1.6568542494923806 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.0710678118654755, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6568542494923806, 2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-3.0710678118654755, 1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-4.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -1.1715728752538097] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 0.24264068711928566] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8284271247461903, 1.6568542494923806] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, 0.24264068711928566] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 1.6568542494923806] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 3.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8284271247461903, 1.6568542494923806] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, 3.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-1.1715728752538097 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24264068711928566, 1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6568542494923806, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.24264068711928566, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>1.6568542494923806 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.0710678118654755, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6568542494923806, -2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[3.0710678118654755, -1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>4.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.0, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.414213562373095, -4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.82842712474619, -5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.585786437626905, -4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.0, -5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.414213562373095, -7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1715728752538097, -5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.585786437626905, -7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.0, -8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8284271247461903, -4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.242640687119286, -5.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -6.82842712474619] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.242640687119286, -2.585786437626905] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.0710678118654755, -5.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, -1.1715728752538097] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.0710678118654755, -2.585786437626905] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.485281374238571, -4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.0, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.414213562373095, 4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.82842712474619, 5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.585786437626905, 4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.0, 5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.414213562373095, 7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1715728752538097, 5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.585786437626905, 7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.0, 8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8284271247461903, 4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.242640687119286, 5.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 6.82842712474619] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.242640687119286, 2.585786437626905] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.0710678118654755, 5.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, 1.1715728752538097] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.0710678118654755, 2.585786437626905] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.485281374238571, 4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -6.82842712474619] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -8.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8284271247461903, -9.65685424949238] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -8.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -9.65685424949238] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, -11.071067811865476] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8284271247461903, -9.65685424949238] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, -11.071067811865476] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -12.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-6.82842712474619 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.242640687119286, -1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-9.65685424949238, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.242640687119286, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-9.65685424949238 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-11.071067811865476, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-9.65685424949238, 2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-11.071067811865476, 1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>-12.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 6.82842712474619] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 8.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8284271247461903, 9.65685424949238] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, 8.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 9.65685424949238] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.4142135623730951, 11.071067811865476] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8284271247461903, 9.65685424949238] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.4142135623730951, 11.071067811865476] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 12.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>6.82842712474619 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.242640687119286, 1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.65685424949238, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.242640687119286, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>9.65685424949238 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.071067811865476, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.65685424949238, -2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.071067811865476, -1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>12.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.0, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.585786437626905, -4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1715728752538097, -5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.414213562373095, -4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.0, -5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.585786437626905, -7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-6.82842712474619, -5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.414213562373095, -7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.0, -8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8284271247461903, 4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.242640687119286, 2.585786437626905] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 1.1715728752538097] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-4.242640687119286, 5.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.0710678118654755, 2.585786437626905] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-5.656854249492381, 6.82842712474619] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-7.0710678118654755, 5.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-8.485281374238571, 4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.0, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.585786437626905, 4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1715728752538097, 5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.414213562373095, 4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.0, 5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.585786437626905, 7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[6.82842712474619, 5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.414213562373095, 7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.0, 8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8284271247461903, -4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.242640687119286, -2.585786437626905] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -1.1715728752538097] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.242640687119286, -5.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.0710678118654755, -2.585786437626905] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[5.656854249492381, -6.82842712474619] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[7.0710678118654755, -5.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[8.485281374238571, -4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.15.E42 1.15.E42] || [[Item:Q584|<math>\int^{\infty}_{-\infty}K_{R}(s)\diff{s} = 1</math>]] || <code>int(K[R]*(s), s = - infinity..infinity)= 1</code> || <code>Integrate[Subscript[K, R]*(s), {s, - Infinity, Infinity}]= 1</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.15.E44 1.15.E44] || [[Item:Q586|<math>\sigma_{R}(\theta) = \frac{1}{\sqrt{2\pi}}\int^{R}_{-R}\left(1-\frac{|t|}{R}\right)e^{-i\theta t}F(t)\diff{t}</math>]] || <code>sigma[R]*(theta)=(1)/(sqrt(2*Pi))*int((1 -(abs(t))/(R))* exp(- I*theta*t)*F*(t), t = - R..R)</code> || <code>Subscript[\[Sigma], R]*(\[Theta])=Divide[1,Sqrt[2*Pi]]*Integrate[(1 -Divide[Abs[t],R])* Exp[- I*\[Theta]*t]*F*(t), {t, - R, R}]</code> || Failure || Failure || Skip || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.16.E19 1.16.E19] || [[Item:Q619|<math>x^{\alpha}_{+} = x^{\alpha}\HeavisideH@{x}</math>]] || <code>(x[+])^(alpha)= (x)^(alpha)* Heaviside(x)</code> || <code>(Subscript[x, +])^(\[Alpha])= (x)^(\[Alpha])* HeavisideTheta[x]</code> || Error || Failure || - || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.16#Ex1 1.16#Ex1] || [[Item:Q630|<math>F(\mathbf{x}) = F</math>]] || <code>F*(x)= F</code> || <code>F*(x)= F</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.414213562+1.414213562*I <- {F = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>2.828427124+2.828427124*I <- {F = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>1.414213562-1.414213562*I <- {F = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>2.828427124-2.828427124*I <- {F = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.414213562-1.414213562*I <- {F = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>-2.828427124-2.828427124*I <- {F = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>-1.414213562+1.414213562*I <- {F = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-2.828427124+2.828427124*I <- {F = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[F, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[F, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[F, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[F, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[F, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[F, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.16#Ex2 1.16#Ex2] || [[Item:Q632|<math>D_{\boldsymbol{{\alpha}}} = \iunit^{-|\boldsymbol{{\alpha}}|}D^{\boldsymbol{{\alpha}}}</math>]] || <code>D[alpha]= (I)^(-abs(alpha))* (D)^(alpha)</code> || <code>Subscript[D, \[Alpha]]= (I)^(-Abs[\[Alpha]])* (D)^(\[Alpha])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.9779681321+2.175809568*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>.9779681321-.6526175556*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.850458992-.6526175556*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.850458992+2.175809568*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>9.438272386+2.467033025*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>9.438272386-.361394099*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>6.609845262-.361394099*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>6.609845262+2.467033025*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>.8479100469+.4255625275*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>.8479100469-2.402864596*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.980517077-2.402864596*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.980517077+.4255625275*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.536729595+1.398138497*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.536729595-1.430288627*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.291697529-1.430288627*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.291697529+1.398138497*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>9.438272386+.361394099*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>9.438272386-2.467033025*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>6.609845262-2.467033025*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>6.609845262+.361394099*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>.9779681321+.6526175556*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>.9779681321-2.175809568*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.850458992-2.175809568*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.850458992+.6526175556*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.536729595+1.430288627*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.536729595-1.398138497*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.291697529-1.398138497*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.291697529+1.430288627*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>.8479100469+2.402864596*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>.8479100469-.4255625275*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.980517077-.4255625275*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.980517077+2.402864596*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>-51.12384670-51.57661382*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>-51.12384670-54.40504094*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-53.95227382-54.40504094*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-53.95227382-51.57661382*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.377148458+1.501888445*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.377148458-1.326538679*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.451278666-1.326538679*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.451278666+1.501888445*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.404778314+1.423730122*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.404778314-1.404697002*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.423648810-1.404697002*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.423648810+1.423730122*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.676538322-8.262170665*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.676538322-11.09059779*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.504965446-11.09059779*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.504965446-8.262170665*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.377148458+1.326538679*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.377148458-1.501888445*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.451278666-1.501888445*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.451278666+1.326538679*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>-51.12384670+54.40504094*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>-51.12384670+51.57661382*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-53.95227382+51.57661382*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-53.95227382+54.40504094*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>-2.676538322+11.09059779*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>-2.676538322+8.262170665*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-5.504965446+8.262170665*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.504965446+11.09059779*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br><code>1.404778314+1.404697002*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}</code><br><code>1.404778314-1.423730122*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.423648810-1.423730122*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.423648810+1.404697002*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.16.E32 1.16.E32] || [[Item:Q634|<math>P(\mathbf{D}) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{D}^{\alpha}</math>]] || <code>P*(D)= sum(c[alpha]*(D)^(alpha), alpha = - infinity..infinity)</code> || <code>P*(D)= Sum[Subscript[c, \[Alpha]]*(D)^(\[Alpha]), {\[Alpha], - Infinity, Infinity}]</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.16.E40 1.16.E40] || [[Item:Q648|<math>\int^{\infty}_{-\infty}\Diracdelta@{t}\expe^{\iunit xt}\diff{t} = 1</math>]] || <code>int(Dirac(t)*exp(I*x*t), t = - infinity..infinity)= 1</code> || <code>Integrate[DiracDelta[t]*Exp[I*x*t], {t, - Infinity, Infinity}]= 1</code> || Successful || Successful || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.16.E43 1.16.E43] || [[Item:Q651|<math>\frac{1}{2\cpi}\int^{\infty}_{-\infty}\expe^{\iunit xt}\diff{t} = \Diracdelta@{x}</math>]] || <code>(1)/(2*Pi)*int(exp(I*x*t), t = - infinity..infinity)= Dirac(x)</code> || <code>Divide[1,2*Pi]*Integrate[Exp[I*x*t], {t, - Infinity, Infinity}]= DiracDelta[x]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.16.E44 1.16.E44] || [[Item:Q652|<math>\sign@{x} = 2\HeavisideH@{x}-1</math>]] || <code>signum(x)= 2*Heaviside(x)- 1</code> || <code>Sign[x]= 2*HeavisideTheta[x]- 1</code> || Failure || Failure || Skip || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E1 1.17.E1] || [[Item:Q660|<math>\Diracdelta@{x} = 0</math>]] || <code>Dirac(x)= 0</code> || <code>DiracDelta[x]= 0</code> || Error || Failure || - || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E2 1.17.E2] || [[Item:Q661|<math>\int_{-\infty}^{\infty}\Diracdelta@{x-a}\phi(x)\diff{x} = \phi(a)</math>]] || <code>int(Dirac(x - a)*phi*(x), x = - infinity..infinity)= phi*(a)</code> || <code>Integrate[DiracDelta[x - a]*\[Phi]*(x), {x, - Infinity, Infinity}]= \[Phi]*(a)</code> || Successful || Failure || - || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E6 1.17.E6] || [[Item:Q665|<math>\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \phi(a)</math>]] || <code>limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi*(x), x = - infinity..infinity), n = infinity)= phi*(a)</code> || <code>Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi]*(x), {x, - Infinity, Infinity}], n -> Infinity]= \[Phi]*(a)</code> || Successful || Failure || - || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E7 1.17.E7] || [[Item:Q666|<math>\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \tfrac{1}{2}\phi(a-)+\tfrac{1}{2}\phi(a+)</math>]] || <code>limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi*(x), x = - infinity..infinity), n = infinity)=(1)/(2)*phi*(a -)+(1)/(2)*phi*(a +)</code> || <code>Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi]*(x), {x, - Infinity, Infinity}], n -> Infinity]=Divide[1,2]*\[Phi]*(a -)+Divide[1,2]*\[Phi]*(a +)</code> || Error || Failure || - || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E8 1.17.E8] || [[Item:Q667|<math>\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left(\int_{-\infty}^{\infty}\phi(x)e^{itx}\diff{x}\right)\diff{t} = \phi(a)</math>]] || <code>(1)/(2*Pi)*int(exp(- I*a*t)*(int(phi*(x)* exp(I*t*x), x = - infinity..infinity)), t = - infinity..infinity)= phi*(a)</code> || <code>Divide[1,2*Pi]*Integrate[Exp[- I*a*t]*(Integrate[\[Phi]*(x)* Exp[I*t*x], {x, - Infinity, Infinity}]), {t, - Infinity, Infinity}]= \[Phi]*(a)</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E9 1.17.E9] || [[Item:Q668|<math>\int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}\right)\phi(x)\diff{x} = \phi(a)</math>]] || <code>int(((1)/(2*Pi)*int(exp(I*(x - a)* t), t = - infinity..infinity))* phi*(x), x = - infinity..infinity)= phi*(a)</code> || <code>Integrate[(Divide[1,2*Pi]*Integrate[Exp[I*(x - a)* t], {t, - Infinity, Infinity}])* \[Phi]*(x), {x, - Infinity, Infinity}]= \[Phi]*(a)</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E10 1.17.E10] || [[Item:Q669|<math>\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\diff{t} = \sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}</math>]] || <code>(1)/(2*Pi)*int(exp(- (t)^(2)/(4*n))*exp(I*(x - a)* t), t = - infinity..infinity)=sqrt((n)/(Pi))*exp(- n*(x - a)^(2))</code> || <code>Divide[1,2*Pi]*Integrate[Exp[- (t)^(2)/(4*n)]*Exp[I*(x - a)* t], {t, - Infinity, Infinity}]=Sqrt[Divide[n,Pi]]*Exp[- n*(x - a)^(2)]</code> || Failure || Failure || Skip || Skip | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E12 1.17.E12] || [[Item:Q671|<math>\Diracdelta@{x-a} = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}</math>]] || <code>Dirac(x - a)=(1)/(2*Pi)*int(exp(I*(x - a)* t), t = - infinity..infinity)</code> || <code>DiracDelta[x - a]=Divide[1,2*Pi]*Integrate[Exp[I*(x - a)* t], {t, - Infinity, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E13 1.17.E13] || [[Item:Q672|<math>\Diracdelta@{x-a} = x\int_{0}^{\infty}t\BesselJ{\nu}@{xt}\BesselJ{\nu}@{at}\diff{t}</math>]] || <code>Dirac(x - a)= x*int(t*BesselJ(nu, x*t)*BesselJ(nu, a*t), t = 0..infinity)</code> || <code>DiracDelta[x - a]= x*Integrate[t*BesselJ[\[Nu], x*t]*BesselJ[\[Nu], a*t], {t, 0, Infinity}]</code> || Failure || Failure || Skip || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E14 1.17.E14] || [[Item:Q673|<math>\Diracdelta@{x-a} = \frac{2xa}{\pi}\int_{0}^{\infty}t^{2}\sphBesselJ{\ell}@{xt}\sphBesselJ{\ell}@{at}\diff{t}</math>]] || <code>Error</code> || <code>DiracDelta[x - a]=Divide[2*x*a,Pi]*Integrate[(t)^(2)* SphericalBesselJ[\[ScriptL], x*t]*SphericalBesselJ[\[ScriptL], a*t], {t, 0, Infinity}]</code> || Error || Failure || - || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E17 1.17.E17] || [[Item:Q676|<math>\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}\left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\diff{x}\right) = \phi(a)</math>]] || <code>(1)/(2*Pi)*sum(exp(- I*k*a)*(int(phi*(x)* exp(I*k*x), x = - Pi..Pi)), k = - infinity..infinity)= phi*(a)</code> || <code>Divide[1,2*Pi]*Sum[Exp[- I*k*a]*(Integrate[\[Phi]*(x)* Exp[I*k*x], {x, - Pi, Pi}]), {k, - Infinity, Infinity}]= \[Phi]*(a)</code> || Error || Failure || - || Successful | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E18 1.17.E18] || [[Item:Q677|<math>\int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}\right)\diff{x} = \phi(a)</math>]] || <code>int(phi*(x)*((1)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity)), x = - Pi..Pi)= phi*(a)</code> || <code>Integrate[\[Phi]*(x)*(Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}]), {x, - Pi, Pi}]= \[Phi]*(a)</code> || Failure || Failure || Skip || Error | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E21 1.17.E21] || [[Item:Q680|<math>\Diracdelta@{x-a} = \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}</math>]] || <code>Dirac(x - a)=(1)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity)</code> || <code>DiracDelta[x - a]=Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E22 1.17.E22] || [[Item:Q681|<math>\Diracdelta@{x-a} = \sum_{k=0}^{\infty}(k+\tfrac{1}{2})\LegendrepolyP{k}@{x}\LegendrepolyP{k}@{a}</math>]] || <code>Dirac(x - a)= sum((k +(1)/(2))* LegendreP(k, x)*LegendreP(k, a), k = 0..infinity)</code> || <code>DiracDelta[x - a]= Sum[(k +Divide[1,2])* LegendreP[k, x]*LegendreP[k, a], {k, 0, Infinity}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, 2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>2.8284271247461903 <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>2.8284271247461903 <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.8284271247461903 <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>-2.8284271247461903 <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br></div></div> | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E23 1.17.E23] || [[Item:Q682|<math>\Diracdelta@{x-a} = e^{-(x+a)/2}\sum_{k=0}^{\infty}\LaguerrepolyL[]{k}@{x}\LaguerrepolyL[]{k}@{a}</math>]] || <code>Dirac(x - a)= exp(-(x + a)/ 2)*sum(LaguerreL(k, x)*LaguerreL(k, a), k = 0..infinity)</code> || <code>Error</code> || Failure || Error || - || - | ||
|- | |- | ||
| [ | | [https://dlmf.nist.gov/1.17.E24 1.17.E24] || [[Item:Q683|<math>\Diracdelta@{x-a} = \frac{e^{-(x^{2}+a^{2})/2}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{\HermitepolyH{k}@{x}\HermitepolyH{k}@{a}}{2^{k}k!}</math>]] || <code>Dirac(x - a)=(exp(-((x)^(2)+ (a)^(2))/ 2))/(sqrt(Pi))*sum((HermiteH(k, x)*HermiteH(k, a))/((2)^(k)* factorial(k)), k = 0..infinity)</code> || <code>DiracDelta[x - a]=Divide[Exp[-((x)^(2)+ (a)^(2))/ 2],Sqrt[Pi]]*Sum[Divide[HermiteH[k, x]*HermiteH[k, a],(2)^(k)* (k)!], {k, 0, Infinity}]</code> || Error || Failure || - || Skip | ||
|- | |- | ||
|} | |} | ||
Latest revision as of 13:21, 19 January 2020
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}} | binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k)) |
Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!] |
Successful | Successful | - | - |
| 1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{n!}{(n-k)!k!} = \binom{n}{n-k}} | (factorial(n))/(factorial(n - k)*factorial(k))=binomial(n,n - k) |
Divide[(n)!,(n - k)!*(k)!]=Binomial[n,n - k] |
Successful | Successful | - | - |
| 1.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{z}{k} = \frac{z(z-1)\cdots(z-k+1)}{k!}} | binomial(z,k)=(z*(z - 1)..(z - k + 1))/(factorial(k)) |
Binomial[z,k]=Divide[z*(z - 1) ... (z - k + 1),(k)!] |
Successful | Successful | - | - |
| 1.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}} | binomial(z + 1,k)=binomial(z,k)+binomial(z,k - 1) |
Binomial[z + 1,k]=Binomial[z,k]+Binomial[z,k - 1] |
Successful | Successful | - | - |
| 1.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}} | sum(binomial(z + k,k), k = 0..m)=binomial(z + m + 1,m) |
Sum[Binomial[z + k,k], {k, 0, m}]=Binomial[z + m + 1,m] |
Successful | Successful | - | - |
| 1.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(2)}(x) = \deriv[2]{f}{x}} | (f)^(2)*(x)= diff(f, [x$(2)]) |
(f)^(2)*(x)= D[f, {x, 2}] |
Failure | Failure | Fail 0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), x = 1}0.+7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), x = 2}0.+11.99999999*I <- {f = 2^(1/2)+I*2^(1/2), x = 3}0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), x = 1}0.-7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), x = 2}0.-11.99999999*I <- {f = 2^(1/2)-I*2^(1/2), x = 3}0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), x = 1}0.+7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), x = 2}0.+11.99999999*I <- {f = -2^(1/2)-I*2^(1/2), x = 3}0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), x = 1}0.-7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), x = 2}0.-11.99999999*I <- {f = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.0, 12.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.0, -12.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.0, 12.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[0.0, -12.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} |
| 1.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)} | diff(f, [x$(2)])= diff(diff(f, x), x) |
D[f, {x, 2}]= D[D[f, x], x] |
Successful | Successful | - | - |
| 1.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(n)} = f^{(n)}(x)} | (f)^(n)= (f)^(n)*(x) |
(f)^(n)= (f)^(n)*(x) |
Failure | Failure | Fail -1.414213562-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}-2.828427124-2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}-0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}-0.-7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}5.656854245-5.656854245*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}11.31370849-11.31370849*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}-1.414213562+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}-2.828427124+2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}-0.+7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}5.656854245+5.656854245*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}11.31370849+11.31370849*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}1.414213562+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}2.828427124+2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}-0.-7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}-5.656854245+5.656854245*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}-11.31370849+11.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}1.414213562-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}2.828427124-2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}-0.+7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}-5.656854245-5.656854245*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}-11.31370849-11.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3} |
Fail
Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[-11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[-11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]} |
| 1.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)} | (f)^(n)*(x)= diff((f)^(n - 1)*(x), x) |
(f)^(n)*(x)= D[(f)^(n - 1)*(x), x] |
Failure | Failure | Fail .414213562+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 1}1.828427124+2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}3.242640686+4.242640686*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}-1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 1}-1.414213562+6.585786434*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}-1.414213562+10.58578643*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}-5.656854245+1.656854247*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 1}-11.31370849+7.313708492*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}-16.97056274+12.97056274*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}.414213562-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 1}1.828427124-2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}3.242640686-4.242640686*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 1}-1.414213562-6.585786434*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}-1.414213562-10.58578643*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}-5.656854245-1.656854247*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 1}-11.31370849-7.313708492*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}-16.97056274-12.97056274*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}-2.414213562-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 1}-3.828427124-2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}-5.242640686-4.242640686*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 1}1.414213562+9.414213558*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}1.414213562+13.41421355*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}5.656854245-9.656854243*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 1}11.31370849-15.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}16.97056274-20.97056274*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}-2.414213562+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 1}-3.828427124+2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}-5.242640686+4.242640686*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 1}1.414213562-9.414213558*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}1.414213562-13.41421355*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}5.656854245+9.656854243*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 1}11.31370849+15.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}16.97056274+20.97056274*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3} |
Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}Complex[1.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[3.2426406871192857, 4.242640687119286] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[-1.4142135623730951, 2.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}Complex[-1.4142135623730951, 6.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[-1.4142135623730951, 10.585786437626904] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[-5.656854249492381, 1.6568542494923806] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}Complex[-11.313708498984761, 7.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[-16.970562748477143, 12.970562748477143] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}Complex[1.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[3.2426406871192857, -4.242640687119286] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[-1.4142135623730951, -2.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}Complex[-1.4142135623730951, -6.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[-1.4142135623730951, -10.585786437626904] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[-5.656854249492381, -1.6568542494923806] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}Complex[-11.313708498984761, -7.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[-16.970562748477143, -12.970562748477143] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}Complex[-3.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[-5.242640687119286, -4.242640687119286] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[1.4142135623730951, 5.414213562373095] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}Complex[1.4142135623730951, 9.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[1.4142135623730951, 13.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[5.656854249492381, -9.65685424949238] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}Complex[11.313708498984761, -15.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[16.970562748477143, -20.970562748477143] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}Complex[-3.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}Complex[-5.242640687119286, 4.242640687119286] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}Complex[1.4142135623730951, -5.414213562373095] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}Complex[1.4142135623730951, -9.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}Complex[1.4142135623730951, -13.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}Complex[5.656854249492381, 9.65685424949238] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}Complex[11.313708498984761, 15.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}Complex[16.970562748477143, 20.970562748477143] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]} |
| 1.4.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}} | int(f*g, x)=(int(f, x))* g - int((int(f, x))* diff(g, x), x) |
Integrate[f*g, x]=(Integrate[f, x])* g - Integrate[(Integrate[f, x])* D[g, x], x] |
Successful | Successful | - | - |
| 1.4.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t}} | R[n]=(1)/(factorial(n))*int((x - t)^(n)* (f)^(n + 1)*(t), t = a..x) |
Subscript[R, n]=Divide[1,(n)!]*Integrate[(x - t)^(n)* (f)^(n + 1)*(t), {t, a, x}] |
Failure | Failure | Skip | Skip |
| 1.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{y} = D_{y}f} | diff(f, y)= D[y]*f |
D[f, y]= Subscript[D, y]*f |
Failure | Failure | Fail -0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}-3.999999998-0.*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}-0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}3.999999998-0.*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}-3.999999998-0.*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}3.999999998-0.*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}-0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}-0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}3.999999998-0.*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}-3.999999998-0.*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}3.999999998-0.*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}-0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}-3.999999998-0.*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{y}f = f_{y}} | D[y]*f = f[y] |
Subscript[D, y]*f = Subscript[f, y] |
Failure | Failure | Fail -1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-1.414213562+5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}1.414213562+5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}2.585786436-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}2.585786436+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}5.414213560+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}5.414213560-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-1.414213562-5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-1.414213562-2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}1.414213562-2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-5.414213560-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-5.414213560+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}-2.585786436+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}-2.585786436-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}2.585786436-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}2.585786436+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}5.414213560+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}5.414213560-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-1.414213562-5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-5.414213560-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-5.414213560+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}-2.585786436+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}-2.585786436-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-1.414213562+2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-1.414213562+5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}1.414213562+5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}1.414213562+2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-1.414213562-5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-1.414213562-2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}1.414213562-2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-5.414213560-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-5.414213560+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}-2.585786436+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}-2.585786436-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-1.414213562+2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}1.414213562+2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}2.585786436-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}2.585786436+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}5.414213560+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}5.414213560-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-5.414213560-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-5.414213560+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}-2.585786436+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}-2.585786436-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-1.414213562+2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-1.414213562+5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}1.414213562+5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}1.414213562+2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}2.585786436-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}2.585786436+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}5.414213560+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}5.414213560-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}-1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}-1.414213562-2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}1.414213562-2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)} |
Successful |
| 1.5#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\phi}} | x = r*cos(phi) |
x = r*Cos[\[Phi]] |
Failure | Failure | Fail -2.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}-1.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}-.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}3.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}4.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}5.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}4.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}5.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}6.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}-1.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}-.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}.777253510-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}3.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}4.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}5.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}-2.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}-1.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}-.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}-1.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}-.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}.777253510+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}4.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}5.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}6.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}-2.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}-1.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}-.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}3.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}4.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}5.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}4.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}5.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}6.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}-1.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}-.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}.777253510-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}3.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}4.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}5.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}-2.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}-1.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}-.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}-1.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}-.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}.777253510+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}4.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}5.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}6.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.5#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\phi}} | y = r*sin(phi) |
y = r*Sin[\[Phi]] |
Failure | Failure | Fail -1.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}-.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}.384024424-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}-2.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}-1.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}-.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}3.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}4.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}5.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}4.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}5.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}6.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}-2.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}-1.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}-.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}-1.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}-.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}.384024424+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}4.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}5.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}6.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}3.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}4.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}5.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}3.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}4.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}5.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}4.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}5.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}6.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}-1.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}-.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}.384024424-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}-2.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}-1.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}-.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}4.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}5.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}6.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}3.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}4.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}5.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}-2.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}-1.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}-.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}-1.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}-.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}.384024424+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3} |
Fail
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.5.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}} | diff(f, [x$(2)])+ diff(f, [y$(2)])= diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)]) |
D[f, {x, 2}]+ D[f, {y, 2}]= D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}] |
Successful | Successful | - | - |
| 1.5#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\phi}} | x = r*cos(phi) |
x = r*Cos[\[Phi]] |
Failure | Failure | Fail -2.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}-1.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}-.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}3.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}4.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}5.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}4.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}5.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}6.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}-1.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}-.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}.777253510-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}3.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}4.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}5.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}-2.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}-1.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}-.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}-1.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}-.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}.777253510+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}4.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}5.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}6.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}-2.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}-1.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}-.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}3.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}4.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}5.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}4.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}5.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}6.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}-1.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}-.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}.777253510-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}3.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}4.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}5.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}-2.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}-1.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}-.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}-1.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}-.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}.777253510+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}4.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}5.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}6.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.5#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\phi}} | y = r*sin(phi) |
y = r*Sin[\[Phi]] |
Failure | Failure | Fail -1.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}-.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}.384024424-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}-2.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}-1.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}-.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}3.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}4.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}5.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}4.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}5.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}6.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}-2.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}-1.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}-.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}-1.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}-.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}.384024424+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}4.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}5.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}6.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}3.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}4.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}5.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}3.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}4.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}5.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}4.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}5.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}6.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}-1.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}-.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}.384024424-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}-2.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}-1.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}-.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}4.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}5.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}6.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}3.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}4.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}5.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}-2.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}-1.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}-.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}-1.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}-.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}.384024424+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3} |
Fail
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.5#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \rho\sin@@{\theta}\cos@@{\phi}} | x = rho*sin(theta)*cos(phi) |
x = \[Rho]*Sin[\[Theta]]*Cos[\[Phi]] |
Failure | Failure | Fail -6.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-5.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-4.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-5.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-4.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-3.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}8.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}9.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}10.52013032-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}7.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}8.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}9.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}4.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}5.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}6.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}6.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}7.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}8.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-2.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-1.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-4.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-3.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-2.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}8.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}9.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}10.52013032-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}7.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}8.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}9.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-6.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-5.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-4.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-5.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-4.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-3.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}-2.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-1.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-4.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-3.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-2.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}4.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}5.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}6.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}6.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}7.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}8.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}6.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}7.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}8.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}4.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}5.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}6.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-4.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-3.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-2.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-2.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-1.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}-5.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-4.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-3.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-6.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-5.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-4.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}7.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}8.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}9.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}8.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}9.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}10.52013032+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}-4.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-3.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-2.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-2.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-1.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}6.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}7.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}8.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}4.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}5.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}6.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}7.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}8.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}9.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}8.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}9.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}10.52013032+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-5.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-4.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-3.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-6.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-5.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-4.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}-6.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-5.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-4.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-5.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-4.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-3.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}8.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}9.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}10.52013032-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}7.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}8.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}9.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}4.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}5.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}6.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}6.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}7.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}8.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-2.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-1.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-4.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-3.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-2.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}8.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}9.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}10.52013032-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}7.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}8.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}9.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-6.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-5.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-4.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-5.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-4.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-3.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}-2.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-1.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-4.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-3.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-2.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}4.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}5.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}6.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}6.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}7.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}8.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}6.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}7.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}8.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}4.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}5.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}6.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-4.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-3.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-2.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-2.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-1.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}-5.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-4.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-3.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-6.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-5.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-4.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}7.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}8.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}9.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}8.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}9.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}10.52013032+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}-4.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-3.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-2.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-2.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-1.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}6.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}7.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}8.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}4.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}5.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}6.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}7.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}8.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}9.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}8.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}9.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}10.52013032+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-5.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-4.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-3.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-6.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-5.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-4.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.5#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \rho\sin@@{\theta}\sin@@{\phi}} | y = rho*sin(theta)*sin(phi) |
y = \[Rho]*Sin[\[Theta]]*Sin[\[Phi]] |
Failure | Failure | Fail -3.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-2.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-1.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-5.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-4.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-3.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}5.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}6.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}7.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}7.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}8.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}9.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}-7.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-6.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-5.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-5.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-4.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-3.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}9.254122865-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}10.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}11.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}7.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}5.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}6.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}7.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}7.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}8.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}9.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-3.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-2.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-1.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-5.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-4.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-3.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}9.254122865-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}10.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}11.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}7.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-7.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-6.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-5.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-5.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-4.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-3.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}-5.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-4.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-3.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-7.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-6.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-5.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}7.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}8.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}9.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}9.254122865+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}10.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}11.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}-5.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-4.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-3.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-3.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-2.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-1.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}7.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}5.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}6.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}7.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}7.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}8.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}9.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}9.254122865+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}10.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}11.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-5.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-4.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-3.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-7.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-6.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-5.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}7.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}5.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}6.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}7.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-5.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-4.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-3.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-3.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-2.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-1.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}5.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}6.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}7.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}7.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}8.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}9.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-3.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-2.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-1.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-5.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-4.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-3.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}9.254122865-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}10.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}11.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}7.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-7.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-6.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-5.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-5.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-4.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-3.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}-3.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-2.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-1.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-5.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-4.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-3.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}5.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}6.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}7.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}7.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}8.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}9.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}-7.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-6.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-5.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-5.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-4.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-3.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}9.254122865-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}10.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}11.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}7.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}7.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}8.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}9.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}9.254122865+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}10.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}11.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-5.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-4.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-3.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-7.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-6.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-5.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}7.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}5.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}6.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}7.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-5.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-4.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-3.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-3.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-2.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-1.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}-5.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-4.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-3.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-7.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-6.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-5.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}7.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}8.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}9.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}9.254122865+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}10.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}11.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}-5.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-4.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-3.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-3.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-2.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-1.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}7.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}8.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}9.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}5.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}6.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}7.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3} |
Fail
Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.5#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \rho\cos@@{\theta}} | z = rho*cos(theta) |
z = \[Rho]*Cos[\[Theta]] |
Failure | Failure | Fail -1.769276062+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-1.769276062+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-4.597703186+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-4.597703186+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}3.636960052-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}3.636960052-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}.808532928-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.808532928-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-1.769276062+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-1.769276062+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-4.597703186+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-4.597703186+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}3.636960052-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}3.636960052-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}.808532928-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.808532928-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}3.636960052+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}3.636960052+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}.808532928+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.808532928+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-1.769276062-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-1.769276062-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-4.597703186-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-4.597703186-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}3.636960052+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}3.636960052+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}.808532928+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.808532928+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-1.769276062-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-1.769276062-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-4.597703186-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-4.597703186-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}4.597703186-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}4.597703186-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.769276062-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.769276062-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-.808532928+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.808532928+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-3.636960052+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-3.636960052+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}4.597703186-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}4.597703186-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.769276062-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.769276062-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-.808532928+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.808532928+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-3.636960052+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-3.636960052+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-.808532928-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.808532928-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-3.636960052-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-3.636960052-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}4.597703186+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}4.597703186+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.769276062+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.769276062+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-.808532928-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.808532928-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-3.636960052-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-3.636960052-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}4.597703186+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}4.597703186+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.769276062+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.769276062+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.5.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)} | diff(f, [x$(2)])+ diff(f, [y$(2)])+ diff(f, [z$(2)])=(1)/((rho)^(2))*diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))*diff(f, [phi$(2)]), rho)+(1)/((rho)^(2)* sin(theta))*diff(sin(theta)*diff(f, theta), theta) |
D[f, {x, 2}]+ D[f, {y, 2}]+ D[f, {z, 2}]=Divide[1,(\[Rho])^(2)]*D[((\[Rho])^(2)* D[f, \[Rho]])+Divide[1,(\[Rho])^(2)* (Sin[\[Theta]])^(2)]*D[f, {\[Phi], 2}], \[Rho]]+Divide[1,(\[Rho])^(2)* Sin[\[Theta]]]*D[Sin[\[Theta]]*D[f, \[Theta]], \[Theta]] |
Successful | Successful | - | - |
| 1.5.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{x} = \pderiv{f}{y}} | diff(f, x)= diff(f, y) |
D[f, x]= D[f, y] |
Successful | Successful | - | - |
| 1.5.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon} | abs(int(diff(f, x), y = c[1]..d))< epsilon |
Abs[Integrate[D[f, x], {y, Subscript[c, 1], d}]]< \[Epsilon] |
Failure | Failure | Skip | Successful |
| 1.6#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2}} | LeviCivita[1, 2, 3]= LeviCivita[3, 1, 2] |
Part[LeviCivitaTensor[3,List], 1, 2, 3]= Part[LeviCivitaTensor[3,List], 3, 1, 2] |
Failure | Successful | Fail 2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}2.828427124+2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}2.828427124 <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}-2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}2.828427124 <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}2.828427124-2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}-2.828427124-2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}-2.828427124 <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}-2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}-2.828427124 <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}-2.828427124+2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)} |
- |
| 1.6#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{3}{1}{2} = 1} | LeviCivita[3, 1, 2]= 1 |
Part[LeviCivitaTensor[3,List], 3, 1, 2]= 1 |
Failure | Successful | Fail .414213562+1.414213562*I <- {LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}.414213562-1.414213562*I <- {LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}-2.414213562-1.414213562*I <- {LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}-2.414213562+1.414213562*I <- {LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)} |
- |
| 1.6#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1}} | LeviCivita[2, 1, 3]= LeviCivita[3, 2, 1] |
Part[LeviCivitaTensor[3,List], 2, 1, 3]= Part[LeviCivitaTensor[3,List], 3, 2, 1] |
Failure | Successful | Fail 2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}2.828427124+2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}2.828427124 <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}-2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}2.828427124 <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}2.828427124-2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}-2.828427124-2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}-2.828427124 <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}-2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}-2.828427124 <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}-2.828427124+2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)} |
- |
| 1.6#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{3}{2}{1} = -1} | LeviCivita[3, 2, 1]= - 1 |
Part[LeviCivitaTensor[3,List], 3, 2, 1]= - 1 |
Failure | Successful | Fail 2.414213562+1.414213562*I <- {LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}2.414213562-1.414213562*I <- {LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}-.414213562-1.414213562*I <- {LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}-.414213562+1.414213562*I <- {LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)} |
- |
| 1.6#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{2}{2}{1} = 0} | LeviCivita[2, 2, 1]= 0 |
Part[LeviCivitaTensor[3,List], 2, 2, 1]= 0 |
Failure | Successful | Fail 1.414213562+1.414213562*I <- {LeviCivita[2,2,1] = 2^(1/2)+I*2^(1/2)}1.414213562-1.414213562*I <- {LeviCivita[2,2,1] = 2^(1/2)-I*2^(1/2)}-1.414213562-1.414213562*I <- {LeviCivita[2,2,1] = -2^(1/2)-I*2^(1/2)}-1.414213562+1.414213562*I <- {LeviCivita[2,2,1] = -2^(1/2)+I*2^(1/2)} |
- |
| 1.6.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m}} | LeviCivita[j, k, ell]*LeviCivita[ell, m, n]= KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m] |
Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Part[LeviCivitaTensor[3,List], \[ScriptL], m, n]= KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m] |
Failure | Failure | Skip | Successful |
| 1.6.E46 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{T}_{u} = \pderiv{x}{u}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{u}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{u}(u_{0},v_{0})\mathbf{k}} | T[u]= diff(x, u)*(u[0], v[0])* I + diff(y, u)*(u[0], v[0])* j + diff(z, u)*(u[0], v[0])* k |
Subscript[T, u]= D[x, u]*(Subscript[u, 0], Subscript[v, 0])* I + D[y, u]*(Subscript[u, 0], Subscript[v, 0])* j + D[z, u]*(Subscript[u, 0], Subscript[v, 0])* k |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {T[u] = 2^(1/2)+I*2^(1/2)}1.414213562-1.414213562*I <- {T[u] = 2^(1/2)-I*2^(1/2)}-1.414213562-1.414213562*I <- {T[u] = -2^(1/2)-I*2^(1/2)}-1.414213562+1.414213562*I <- {T[u] = -2^(1/2)+I*2^(1/2)} |
Error |
| 1.6.E47 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{T}_{v} = \pderiv{x}{v}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{v}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{v}(u_{0},v_{0})\mathbf{k}} | T[v]= diff(x, v)*(u[0], v[0])* I + diff(y, v)*(u[0], v[0])* j + diff(z, v)*(u[0], v[0])* k |
Subscript[T, v]= D[x, v]*(Subscript[u, 0], Subscript[v, 0])* I + D[y, v]*(Subscript[u, 0], Subscript[v, 0])* j + D[z, v]*(Subscript[u, 0], Subscript[v, 0])* k |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {T[v] = 2^(1/2)+I*2^(1/2)}1.414213562-1.414213562*I <- {T[v] = 2^(1/2)-I*2^(1/2)}-1.414213562-1.414213562*I <- {T[v] = -2^(1/2)-I*2^(1/2)}-1.414213562+1.414213562*I <- {T[v] = -2^(1/2)+I*2^(1/2)} |
Error |
| 1.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}} | sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity)=sqrt((Pi)/(omega))*(1 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/ omega)*cos(2*n*Pi*x), n = 1..infinity)) |
Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}]=Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/ \[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}]) |
Failure | Successful | Skip | - |
| 1.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{z} = x} | Re(z)= x |
Re[z]= x |
Failure | Failure | Fail .414213562 <- {z = 2^(1/2)+I*2^(1/2), x = 1}-.585786438 <- {z = 2^(1/2)+I*2^(1/2), x = 2}-1.585786438 <- {z = 2^(1/2)+I*2^(1/2), x = 3}.414213562 <- {z = 2^(1/2)-I*2^(1/2), x = 1}-.585786438 <- {z = 2^(1/2)-I*2^(1/2), x = 2}-1.585786438 <- {z = 2^(1/2)-I*2^(1/2), x = 3}-2.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 1}-3.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 2}-4.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 3}-2.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 1}-3.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 2}-4.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
0.41421356237309515 <- {Rule[x, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-0.5857864376269049 <- {Rule[x, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-1.5857864376269049 <- {Rule[x, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}0.41421356237309515 <- {Rule[x, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-0.5857864376269049 <- {Rule[x, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-1.5857864376269049 <- {Rule[x, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-2.414213562373095 <- {Rule[x, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-3.414213562373095 <- {Rule[x, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-4.414213562373095 <- {Rule[x, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-2.414213562373095 <- {Rule[x, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-3.414213562373095 <- {Rule[x, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-4.414213562373095 <- {Rule[x, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@{z} = y} | Im(z)= y |
Im[z]= y |
Failure | Failure | Fail .414213562 <- {z = 2^(1/2)+I*2^(1/2), y = 1}-.585786438 <- {z = 2^(1/2)+I*2^(1/2), y = 2}-1.585786438 <- {z = 2^(1/2)+I*2^(1/2), y = 3}-2.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 1}-3.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 2}-4.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 3}-2.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 1}-3.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 2}-4.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 3}.414213562 <- {z = -2^(1/2)+I*2^(1/2), y = 1}-.585786438 <- {z = -2^(1/2)+I*2^(1/2), y = 2}-1.585786438 <- {z = -2^(1/2)+I*2^(1/2), y = 3} |
Fail
0.41421356237309515 <- {Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-0.5857864376269049 <- {Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-1.5857864376269049 <- {Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-2.414213562373095 <- {Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-3.414213562373095 <- {Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-4.414213562373095 <- {Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-2.414213562373095 <- {Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-3.414213562373095 <- {Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-4.414213562373095 <- {Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}0.41421356237309515 <- {Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-0.5857864376269049 <- {Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-1.5857864376269049 <- {Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.9#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\theta}} | x = r*cos(theta) |
x = r*Cos[\[Theta]] |
Failure | Failure | Fail -2.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-1.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}-.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}3.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}4.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}5.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-2.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-1.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}-.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}3.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}4.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}5.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}3.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}4.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}5.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-2.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-1.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}-.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}3.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}4.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}5.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-2.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-1.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}-.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}4.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}5.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}6.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}-1.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}-.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}.777253510+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}4.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}5.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}6.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}-1.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}-.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}.777253510+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}-1.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}-.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}.777253510-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}4.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}5.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}6.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}-1.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}-.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}.777253510-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}4.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}5.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}6.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.9#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\theta}} | y = r*sin(theta) |
y = r*Sin[\[Theta]] |
Failure | Failure | Fail -1.615975576-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-.615975576-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}.384024424-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-2.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-1.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}-.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}3.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}4.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}5.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}4.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}5.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}6.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}-2.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}-1.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}-.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}-1.615975576+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}-.615975576+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}.384024424+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}4.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}5.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}6.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}3.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}4.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}5.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}3.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}4.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}5.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}4.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}5.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}6.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-1.615975576-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-.615975576-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}.384024424-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-2.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-1.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}-.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}4.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}5.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}6.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}3.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}4.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}5.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}-2.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}-1.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}-.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}-1.615975576+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}-.615975576+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}.384024424+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3} |
Fail
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \omega = \atan@{|y/x|}\in\left[0,\tfrac{1}{2}\pi\right]} | omega = arctan(abs(y/ x))in[0 ,(1)/(2)*Pi] |
\[Omega]= ArcTan[Abs[y/ x]]\[Element][0 ,Divide[1,2]*Pi] |
Failure | Failure | Error | Error |
| 1.9#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{z} = \theta+2n\pi} | argument(z)= theta + 2*n*Pi |
Arg[z]= \[Theta]+ 2*n*Pi |
Failure | Failure | Fail -6.912000706-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-13.19518602-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-19.47837132-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}-8.482797034-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}-14.76598234-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}-21.04916764-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}-10.05359336-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}-16.33677867-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}-22.61996397-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}-5.341204380-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}-11.62438969-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}-17.90757499-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}-6.912000706+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-13.19518602+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-19.47837132+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}-8.482797034+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}-14.76598234+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}-21.04916764+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}-10.05359336+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}-16.33677867+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}-22.61996397+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}-5.341204380+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}-11.62438969+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}-17.90757499+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}-4.083573582+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-10.36675890+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-16.64994420+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}-5.654369910+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}-11.93755522+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}-18.22074052+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}-7.225166236+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}-13.50835155+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}-19.79153685+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}-2.512777256+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}-8.795962568+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}-15.07914787+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}-4.083573582-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-10.36675890-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-16.64994420-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}-5.654369910-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}-11.93755522-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}-18.22074052-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}-7.225166236-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}-13.50835155-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}-19.79153685-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}-2.512777256-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}-8.795962568-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}-15.07914787-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3} |
Fail
Complex[-6.912000706155233, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-13.195186013334819, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-19.478371320514405, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.912000706155233, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-13.195186013334819, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-19.478371320514405, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.083573581409043, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-10.366758888588627, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-16.649944195768214, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.083573581409043, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-10.366758888588627, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-16.649944195768214, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.48279703295013, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-14.765982340129717, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-21.049167647309304, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.48279703295013, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-14.765982340129717, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-21.049167647309304, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.65436990820394, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-11.937555215383526, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-18.220740522563112, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.65436990820394, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-11.937555215383526, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-18.220740522563112, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-10.053593359745026, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-16.336778666924612, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-22.6199639741042, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-10.053593359745026, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-16.336778666924612, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-22.6199639741042, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.225166234998835, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-13.50835154217842, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-19.791536849358007, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.225166234998835, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-13.50835154217842, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-19.791536849358007, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.341204379360336, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-11.624389686539924, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-17.90757499371951, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.341204379360336, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-11.624389686539924, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-17.90757499371951, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.5127772546141465, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-8.795962561793733, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-15.079147868973319, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.5127772546141465, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-8.795962561793733, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-15.079147868973319, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.9#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\realpart@@{z}| <= |z|} | abs(Re(z))< =abs(z) |
Abs[Re[z]]< =Abs[z] |
Failure | Failure | Successful | Successful |
| 1.9#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\imagpart@@{z}| <= |z|} | abs(Im(z))< =abs(z) |
Abs[Im[z]]< =Abs[z] |
Failure | Failure | Successful | Successful |
| 1.9.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{i\theta} = \cos@@{\theta}+i\sin@@{\theta}} | exp(I*theta)= cos(theta)+ I*sin(theta) |
Exp[I*\[Theta]]= Cos[\[Theta]]+ I*Sin[\[Theta]] |
Successful | Successful | - | - |
| 1.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \conj{z} = x-iy} | conjugate(z)= x - I*y |
Conjugate[z]= x - I*y |
Failure | Failure | Fail .414213562-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.414213562+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}.414213562+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-.585786438-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}-.585786438+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}-.585786438+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}-1.585786438-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}-1.585786438+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}-1.585786438+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}.414213562+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}.414213562+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}.414213562+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}-.585786438+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}-.585786438+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}-.585786438+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}-1.585786438+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}-1.585786438+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}-1.585786438+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}-2.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}-2.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}-2.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}-3.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}-3.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}-3.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}-4.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}-4.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}-4.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}-2.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}-2.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}-2.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}-3.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}-3.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}-3.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}-4.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}-4.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}-4.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 3} |
Fail
Complex[0.41421356237309515, -0.41421356237309515] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.41421356237309515, 0.5857864376269049] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.41421356237309515, 1.5857864376269049] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5857864376269049, -0.41421356237309515] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5857864376269049, 0.5857864376269049] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5857864376269049, 1.5857864376269049] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5857864376269049, -0.41421356237309515] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5857864376269049, 0.5857864376269049] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.5857864376269049, 1.5857864376269049] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.41421356237309515, 2.414213562373095] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.41421356237309515, 3.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.41421356237309515, 4.414213562373095] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.5857864376269049, 2.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.5857864376269049, 3.414213562373095] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.5857864376269049, 4.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5857864376269049, 2.414213562373095] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5857864376269049, 3.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5857864376269049, 4.414213562373095] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, 2.414213562373095] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, 3.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, 4.414213562373095] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.414213562373095, 2.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.414213562373095, 3.414213562373095] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.414213562373095, 4.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.414213562373095, 2.414213562373095] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.414213562373095, 3.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.414213562373095, 4.414213562373095] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, -0.41421356237309515] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, 0.5857864376269049] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, 1.5857864376269049] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.414213562373095, -0.41421356237309515] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.414213562373095, 0.5857864376269049] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-3.414213562373095, 1.5857864376269049] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.414213562373095, -0.41421356237309515] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.414213562373095, 0.5857864376269049] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.414213562373095, 1.5857864376269049] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\conj{z}| = |z|} | abs(conjugate(z))=abs(z) |
Abs[Conjugate[z]]=Abs[z] |
Successful | Successful | - | - |
| 1.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{\conj{z}} = -\phase@@{z}} | argument(conjugate(z))= - argument(z) |
Arg[Conjugate[z]]= - Arg[z] |
Failure | Failure | Successful | Successful |
| 1.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}+ z_{2} = x_{1}+ x_{2}+\iunit(y_{1}+ y_{2})} | z[1]+ z[2]= x[1]+ x[2]+ I*(y[1]+ y[2]) |
Subscript[z, 1]+ Subscript[z, 2]= Subscript[x, 1]+ Subscript[x, 2]+ I*(Subscript[y, 1]+ Subscript[y, 2]) |
Failure | Failure | Skip | Skip |
| 1.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}- z_{2} = x_{1}- x_{2}+\iunit(y_{1}- y_{2})} | z[1]- z[2]= x[1]- x[2]+ I*(y[1]- y[2]) |
Subscript[z, 1]- Subscript[z, 2]= Subscript[x, 1]- Subscript[x, 2]+ I*(Subscript[y, 1]- Subscript[y, 2]) |
Failure | Failure | Skip | Skip |
| 1.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}} | (z[1])/(z[2])=(z[1]*conjugate(z)[2])/((abs(z[2]))^(2)) |
Divide[Subscript[z, 1],Subscript[z, 2]]=Divide[Subscript[z, 1]*Subscript[Conjugate[z], 2],(Abs[Subscript[z, 2]])^(2)] |
Failure | Failure | Error | Fail
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}} | (x[1]*x[2]+ y[1]*y[2]+ I*(x[2]*y[1]- x[1]*y[2]))/(x(x[2])^(2)+ y(y[2])^(2)) |
Divide[Subscript[x, 1]*Subscript[x, 2]+ Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 2]*Subscript[y, 1]- Subscript[x, 1]*Subscript[y, 2]),x(Subscript[x, 2])^(2)+ y(Subscript[y, 2])^(2)] |
Failure | Failure | Skip | Skip |
| 1.9.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@{z_{1}z_{2}} = \phase@@{z_{1}}+\phase@@{z_{2}}} | argument(z[1]*z[2])= argument(z[1])+ argument(z[2]) |
Arg[Subscript[z, 1]*Subscript[z, 2]]= Arg[Subscript[z, 1]]+ Arg[Subscript[z, 2]] |
Failure | Failure | Fail 6.283185308 <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}6.283185308 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)-I*2^(1/2)}6.283185307 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}-6.283185307 <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)} |
Fail
6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.9.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\frac{z_{1}}{z_{2}}} = \frac{|z_{1}|}{|z_{2}|}} | abs((z[1])/(z[2]))=(abs(z[1]))/(abs(z[2])) |
Abs[Divide[Subscript[z, 1],Subscript[z, 2]]]=Divide[Abs[Subscript[z, 1]],Abs[Subscript[z, 2]]] |
Successful | Successful | - | - |
| 1.9.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{\frac{z_{1}}{z_{2}}} = \phase@@{z_{1}}-\phase@@{z_{2}}} | argument((z[1])/(z[2]))= argument(z[1])- argument(z[2]) |
Arg[Divide[Subscript[z, 1],Subscript[z, 2]]]= Arg[Subscript[z, 1]]- Arg[Subscript[z, 2]] |
Failure | Failure | Fail 6.283185308 <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}6.283185308 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2)}6.283185307 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}-6.283185307 <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)} |
Fail
6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} |
| 1.9.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{n\theta}+i\sin@@{n\theta} = (\cos@@{\theta}+i\sin@@{\theta})^{n}} | cos(n*theta)+ I*sin(n*theta)=(cos(theta)+ I*sin(theta))^(n) |
Cos[n*\[Theta]]+ I*Sin[n*\[Theta]]=(Cos[\[Theta]]+ I*Sin[\[Theta]])^(n) |
Successful | Failure | - | Skip |
| 1.9.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\abs{z_{1}}-\abs{z_{2}}} <= \abs{z_{1}+z_{2}}} | abs(abs(z[1])- abs(z[2]))< = abs(z[1]+ z[2]) |
Abs[Abs[Subscript[z, 1]]- Abs[Subscript[z, 2]]]< = Abs[Subscript[z, 1]+ Subscript[z, 2]] |
Failure | Failure | Successful | Successful |
| 1.9.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{z_{1}+z_{2}} <= \abs{z_{1}}+\abs{z_{2}}} | abs(z[1]+ z[2])< = abs(z[1])+ abs(z[2]) |
Abs[Subscript[z, 1]+ Subscript[z, 2]]< = Abs[Subscript[z, 1]]+ Abs[Subscript[z, 2]] |
Failure | Failure | Successful | Successful |
| 1.9#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{u}{x} = \pderiv{v}{y}} | diff(u, x)= diff(v, y) |
D[u, x]= D[v, y] |
Successful | Successful | - | - |
| 1.9#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{u}{y} = -\pderiv{v}{x}} | diff(u, y)= - diff(v, x) |
D[u, y]= - D[v, x] |
Successful | Successful | - | - |
| 1.9.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{u}{x}+\pderiv[2]{u}{y} = \pderiv[2]{v}{x}+\pderiv[2]{v}{y}} | diff(u, [x$(2)])+ diff(u, [y$(2)])= diff(v, [x$(2)])+ diff(v, [y$(2)]) |
D[u, {x, 2}]+ D[u, {y, 2}]= D[v, {x, 2}]+ D[v, {y, 2}] |
Successful | Successful | - | - |
| 1.9.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{v}{x}+\pderiv[2]{v}{y} = 0} | diff(v, [x$(2)])+ diff(v, [y$(2)])= 0 |
D[v, {x, 2}]+ D[v, {y, 2}]= 0 |
Successful | Successful | - | - |
| 1.9.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{u}{r}+\frac{1}{r}\pderiv{u}{r}+\frac{1}{r^{2}}\pderiv[2]{u}{\theta} = 0} | diff(u, [r$(2)])+(1)/(r)*diff(u, r)+(1)/((r)^(2))*diff(u, [theta$(2)])= 0 |
D[u, {r, 2}]+Divide[1,r]*D[u, r]+Divide[1,(r)^(2)]*D[u, {\[Theta], 2}]= 0 |
Successful | Successful | - | - |
| 1.9.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(z) = \frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})\diff{\phi}} | u*(z)=(1)/(2*Pi)*int(u*(z + r*exp(I*phi)), phi = 0..2*Pi) |
u*(z)=Divide[1,2*Pi]*Integrate[u*(z + r*Exp[I*\[Phi]]), {\[Phi], 0, 2*Pi}] |
Successful | Successful | - | - |
| 1.9.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(re^{i\theta}) = \frac{1}{2\pi}\int^{2\pi}_{0}\frac{(R^{2}-r^{2})h(Re^{i\phi})\diff{\phi}}{R^{2}-2Rr\cos@{\phi-\theta}+r^{2}}} | u*(r*exp(I*theta))=(1)/(2*Pi)*int((((R)^(2)- (r)^(2))* h*(R*exp(I*phi)))/((R)^(2)- 2*R*r*cos(phi - theta)+ (r)^(2)), phi = 0..2*Pi) |
u*(r*Exp[I*\[Theta]])=Divide[1,2*Pi]*Integrate[Divide[((R)^(2)- (r)^(2))* h*(R*Exp[I*\[Phi]]),(R)^(2)- 2*R*r*Cos[\[Phi]- \[Theta]]+ (r)^(2)], {\[Phi], 0, 2*Pi}] |
Error | Failure | - | Skip |
| 1.9.E63 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}} | (f)^(m)*(z)= sum(pochhammer(n + 1, m)*a[n + m]*(z - z[0])^(n), n = 0..infinity) |
(f)^(m)*(z)= Sum[Pochhammer[n + 1, m]*Subscript[a, n + m]*(z - Subscript[z, 0])^(n), {n, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 1.9.E71 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\diff{t} = \sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\diff{t}} | int(sum(f[n]*(t), n = 0..infinity), t = a..b)= sum(int(f[n]*(t), t = a..b), n = 0..infinity) |
Integrate[Sum[Subscript[f, n]*(t), {n, 0, Infinity}], {t, a, b}]= Sum[Integrate[Subscript[f, n]*(t), {t, a, b}], {n, 0, Infinity}] |
Successful | Failure | - | Error |
| 1.10.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\ln@{1+a_{n}(z)}| <= M_{n}} | abs(ln(1 + a[n]*(z)))< = M[n] |
Abs[Log[1 + Subscript[a, n]*(z)]]< = Subscript[M, n] |
Failure | Failure | Skip | Successful |
| 1.12.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}} | -(1)/(2)*Pi + delta < argument(b[n]) |
-Divide[1,2]*Pi + \[Delta]< Arg[Subscript[b, n]] |
Failure | Failure | Successful | Successful |
| 1.12.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta} | argument(b[n])<(1)/(2)*Pi - delta |
Arg[Subscript[b, n]]<Divide[1,2]*Pi - \[Delta] |
Failure | Failure | Successful | Successful |
| 1.12.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}} | -(1)/(2)*Pi + delta < argument(C[n]) |
-Divide[1,2]*Pi + \[Delta]< Arg[Subscript[C, n]] |
Failure | Failure | Successful | Successful |
| 1.12.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta} | argument(C[n])<(1)/(2)*Pi - delta |
Arg[Subscript[C, n]]<Divide[1,2]*Pi - \[Delta] |
Failure | Failure | Successful | Successful |
| 1.13.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{W}{\xi}+F(\xi)\deriv{W}{\xi}+G(\xi)W = 0} | diff(W, [xi$(2)])+ F*(xi)* diff(W, xi)+ G*(xi)* W = 0 |
D[W, {\[Xi], 2}]+ F*(\[Xi])* D[W, \[Xi]]+ G*(\[Xi])* W = 0 |
Failure | Failure | Fail -5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.13.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{W}{z}-H(z)W = 0} | diff(W, [z$(2)])- H*(z)* W = 0 |
D[W, {z, 2}]- H*(z)* W = 0 |
Failure | Failure | Fail 5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.13#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{U}{z}+IU = 0} | diff(U, [z$(2)])+ I*U = 0 |
D[U, {z, 2}]+ I*U = 0 |
Failure | Failure | Fail -1.414213562+1.414213562*I <- {U = 2^(1/2)+I*2^(1/2)}1.414213562+1.414213562*I <- {U = 2^(1/2)-I*2^(1/2)}1.414213562-1.414213562*I <- {U = -2^(1/2)-I*2^(1/2)}-1.414213562-1.414213562*I <- {U = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[U, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[U, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.13#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{V}{z}+JV = 0} | diff(V, [z$(2)])+ J*V = 0 |
D[V, {z, 2}]+ J*V = 0 |
Failure | Failure | Fail 0.+3.999999998*I <- {J = 2^(1/2)+I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}3.999999998+0.*I <- {J = 2^(1/2)+I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}0.-3.999999998*I <- {J = 2^(1/2)+I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}-3.999999998+0.*I <- {J = 2^(1/2)+I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}3.999999998+0.*I <- {J = 2^(1/2)-I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}0.-3.999999998*I <- {J = 2^(1/2)-I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}-3.999999998+0.*I <- {J = 2^(1/2)-I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}0.+3.999999998*I <- {J = 2^(1/2)-I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}0.-3.999999998*I <- {J = -2^(1/2)-I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}-3.999999998+0.*I <- {J = -2^(1/2)-I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}0.+3.999999998*I <- {J = -2^(1/2)-I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}3.999999998+0.*I <- {J = -2^(1/2)-I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}-3.999999998+0.*I <- {J = -2^(1/2)+I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}0.+3.999999998*I <- {J = -2^(1/2)+I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}3.999999998+0.*I <- {J = -2^(1/2)+I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}0.-3.999999998*I <- {J = -2^(1/2)+I*2^(1/2), V = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.0, 4.0] <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -4.0] <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -4.0] <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.0] <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -4.0] <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.0] <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.0] <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -4.0] <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (f*g)(t) = \frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}F(x)G(x)e^{-itx}\diff{x}} | (f * g)*(t)=(1)/(sqrt(2*Pi))*int(F*(x)* G*(x)* exp(- I*t*x), x = - infinity..infinity) |
(f * g)*(t)=Divide[1,Sqrt[2*Pi]]*Integrate[F*(x)* G*(x)* Exp[- I*t*x], {x, - Infinity, Infinity}] |
Failure | Failure | Skip | Skip |
| 1.15.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1} | (1)/(2*Pi)*int(P*(r , theta), theta = 0..2*Pi)= 1 |
Divide[1,2*Pi]*Integrate[P*(r , \[Theta]), {\[Theta], 0, 2*Pi}]= 1 |
Error | Failure | - | Error |
| 1.15.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1} | (1)/(2*Pi)*int(K[n]*(theta), theta = 0..2*Pi)= 1 |
Divide[1,2*Pi]*Integrate[Subscript[K, n]*(\[Theta]), {\[Theta], 0, 2*Pi}]= 1 |
Failure | Failure | Skip | Fail
Complex[3.442882938158366, 4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.442882938158366, -4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.442882938158366, -4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.442882938158366, 4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.15.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1} | (1)/(2*Pi)*int(P*(x , y), x = - infinity..infinity)= 1 |
Divide[1,2*Pi]*Integrate[P*(x , y), {x, - Infinity, Infinity}]= 1 |
Error | Failure | - | Error |
| 1.15.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h(x,y) = \frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}e^{-y|t|}e^{-ixt}F(t)\diff{t}} | h*(x , y)=(1)/(sqrt(2*Pi))*int(exp(- y*abs(t))*exp(- I*x*t)*F*(t), t = - infinity..infinity) |
h*(x , y)=Divide[1,Sqrt[2*Pi]]*Integrate[Exp[- y*Abs[t]]*Exp[- I*x*t]*F*(t), {t, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 1.15.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Phi(z) = \Phi(x+iy)} | Phi*(z)= Phi*(x + I*y) |
\[CapitalPhi]*(z)= \[CapitalPhi]*(x + I*y) |
Failure | Failure | Fail 0.+1.171572874*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}1.414213562-.242640688*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}2.828427124-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-1.414213562-.242640688*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}0.-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}1.414213562-3.071067812*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}-2.828427124-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}-1.414213562-3.071067812*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}0.-4.485281374*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}3.999999998-2.828427124*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}5.414213560-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}6.828427122-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}2.585786436-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}3.999999998-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}5.414213560-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}1.171572874-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}2.585786436-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}3.999999998-8.485281372*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}0.-6.828427122*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}1.414213562-8.242640684*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}2.828427124-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}-1.414213562-8.242640684*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}0.-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}1.414213562-11.07106781*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}-2.828427124-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}-1.414213562-11.07106781*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}0.-12.48528137*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}-3.999999998-2.828427124*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}-2.585786436-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}-1.171572874-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}-5.414213560-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}-3.999999998-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}-2.585786436-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}-6.828427122-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}-5.414213560-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}-3.999999998-8.485281372*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}1.171572874+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-.242640688-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}-1.656854250-2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}-.242640688+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}-1.656854250+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}-3.071067812-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}-1.656854250+2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}-3.071067812+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}-4.485281374+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}-2.828427124-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}-4.242640686-5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}-5.656854248-6.828427122*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}-4.242640686-2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}-5.656854248-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}-7.071067810-5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}-5.656854248-1.171572874*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}-7.071067810-2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}-8.485281372-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}-6.828427122+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}-8.242640684-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}-9.656854246-2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}-8.242640684+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}-9.656854246+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}-11.07106781-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}-9.656854246+2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}-11.07106781+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}-12.48528137+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}-2.828427124+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}-4.242640686+2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}-5.656854248+1.171572874*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}-4.242640686+5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}-5.656854248+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}-7.071067810+2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}-5.656854248+6.828427122*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}-7.071067810+5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}-8.485281372+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}0.-1.171572874*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}-1.414213562+.242640688*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}-2.828427124+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}1.414213562+.242640688*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}0.+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}-1.414213562+3.071067812*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}2.828427124+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}1.414213562+3.071067812*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}0.+4.485281374*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}-3.999999998+2.828427124*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}-5.414213560+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}-6.828427122+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}-2.585786436+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}-3.999999998+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}-5.414213560+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}-1.171572874+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}-2.585786436+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}-3.999999998+8.485281372*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}0.+6.828427122*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}-1.414213562+8.242640684*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}-2.828427124+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}1.414213562+8.242640684*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}0.+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}-1.414213562+11.07106781*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}2.828427124+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}1.414213562+11.07106781*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}0.+12.48528137*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}3.999999998+2.828427124*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}2.585786436+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}1.171572874+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}5.414213560+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}3.999999998+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}2.585786436+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}6.828427122+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}5.414213560+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}3.999999998+8.485281372*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}-1.171572874+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}.242640688+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}1.656854250+2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}.242640688-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}1.656854250+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}3.071067812+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}1.656854250-2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}3.071067812-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}4.485281374+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}2.828427124+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}4.242640686+5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}5.656854248+6.828427122*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}4.242640686+2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}5.656854248+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}7.071067810+5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}5.656854248+1.171572874*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}7.071067810+2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}8.485281372+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}6.828427122+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}8.242640684+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}9.656854246+2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}8.242640684-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}9.656854246+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}11.07106781+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}9.656854246-2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}11.07106781-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}12.48528137+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}2.828427124-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}4.242640686-2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}5.656854248-1.171572874*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}4.242640686-5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}5.656854248-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}7.071067810-2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}5.656854248-6.828427122*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}7.071067810-5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}8.485281372-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3} |
Fail
Complex[0.0, 1.1715728752538097] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -0.24264068711928566] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, -1.6568542494923806] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -0.24264068711928566] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -1.6568542494923806] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -3.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -1.6568542494923806] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -3.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -4.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}1.1715728752538097 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.24264068711928566, -1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6568542494923806, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.24264068711928566, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-1.6568542494923806 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.0710678118654755, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6568542494923806, 2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.0710678118654755, 1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-4.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -1.1715728752538097] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 0.24264068711928566] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, 1.6568542494923806] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 0.24264068711928566] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 1.6568542494923806] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 3.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, 1.6568542494923806] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 3.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-1.1715728752538097 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.24264068711928566, 1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6568542494923806, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.24264068711928566, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}1.6568542494923806 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.0710678118654755, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6568542494923806, -2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.0710678118654755, -1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}4.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.0, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.414213562373095, -4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.82842712474619, -5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.585786437626905, -4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.0, -5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.414213562373095, -7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1715728752538097, -5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.585786437626905, -7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[4.0, -8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.242640687119286, -5.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -6.82842712474619] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.242640687119286, -2.585786437626905] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.0710678118654755, -5.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, -1.1715728752538097] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.0710678118654755, -2.585786437626905] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-8.485281374238571, -4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.0, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.414213562373095, 4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.82842712474619, 5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.585786437626905, 4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.0, 5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.414213562373095, 7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1715728752538097, 5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.585786437626905, 7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.0, 8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, 4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.242640687119286, 5.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 6.82842712474619] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.242640687119286, 2.585786437626905] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.0710678118654755, 5.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, 1.1715728752538097] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.0710678118654755, 2.585786437626905] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.485281374238571, 4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -6.82842712474619] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -8.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, -9.65685424949238] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -8.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -9.65685424949238] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -11.071067811865476] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -9.65685424949238] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -11.071067811865476] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -12.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-6.82842712474619 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-8.242640687119286, -1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-9.65685424949238, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-8.242640687119286, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-9.65685424949238 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-11.071067811865476, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-9.65685424949238, 2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-11.071067811865476, 1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}-12.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 6.82842712474619] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 8.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, 9.65685424949238] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 8.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 9.65685424949238] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 11.071067811865476] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, 9.65685424949238] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, 11.071067811865476] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 12.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}6.82842712474619 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.242640687119286, 1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.65685424949238, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.242640687119286, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}9.65685424949238 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[11.071067811865476, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[9.65685424949238, -2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[11.071067811865476, -1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}12.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.0, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.585786437626905, -4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1715728752538097, -5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.414213562373095, -4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.0, -5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.585786437626905, -7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.82842712474619, -5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-5.414213562373095, -7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-4.0, -8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, 4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.242640687119286, 2.585786437626905] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 1.1715728752538097] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.242640687119286, 5.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.0710678118654755, 2.585786437626905] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.656854249492381, 6.82842712474619] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-7.0710678118654755, 5.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-8.485281374238571, 4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[4.0, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.585786437626905, 4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.1715728752538097, 5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.414213562373095, 4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.0, 5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.585786437626905, 7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.82842712474619, 5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.414213562373095, 7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[4.0, 8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, -4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.242640687119286, -2.585786437626905] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -1.1715728752538097] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[4.242640687119286, -5.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.0710678118654755, -2.585786437626905] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[5.656854249492381, -6.82842712474619] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[7.0710678118654755, -5.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[8.485281374238571, -4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.15.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{\infty}_{-\infty}K_{R}(s)\diff{s} = 1} | int(K[R]*(s), s = - infinity..infinity)= 1 |
Integrate[Subscript[K, R]*(s), {s, - Infinity, Infinity}]= 1 |
Failure | Failure | Skip | Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.15.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma_{R}(\theta) = \frac{1}{\sqrt{2\pi}}\int^{R}_{-R}\left(1-\frac{|t|}{R}\right)e^{-i\theta t}F(t)\diff{t}} | sigma[R]*(theta)=(1)/(sqrt(2*Pi))*int((1 -(abs(t))/(R))* exp(- I*theta*t)*F*(t), t = - R..R) |
Subscript[\[Sigma], R]*(\[Theta])=Divide[1,Sqrt[2*Pi]]*Integrate[(1 -Divide[Abs[t],R])* Exp[- I*\[Theta]*t]*F*(t), {t, - R, R}] |
Failure | Failure | Skip | Successful |
| 1.16.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{\alpha}_{+} = x^{\alpha}\HeavisideH@{x}} | (x[+])^(alpha)= (x)^(alpha)* Heaviside(x) |
(Subscript[x, +])^(\[Alpha])= (x)^(\[Alpha])* HeavisideTheta[x] |
Error | Failure | - | Error |
| 1.16#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle F(\mathbf{x}) = F} | F*(x)= F |
F*(x)= F |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {F = 2^(1/2)+I*2^(1/2), x = 2}2.828427124+2.828427124*I <- {F = 2^(1/2)+I*2^(1/2), x = 3}1.414213562-1.414213562*I <- {F = 2^(1/2)-I*2^(1/2), x = 2}2.828427124-2.828427124*I <- {F = 2^(1/2)-I*2^(1/2), x = 3}-1.414213562-1.414213562*I <- {F = -2^(1/2)-I*2^(1/2), x = 2}-2.828427124-2.828427124*I <- {F = -2^(1/2)-I*2^(1/2), x = 3}-1.414213562+1.414213562*I <- {F = -2^(1/2)+I*2^(1/2), x = 2}-2.828427124+2.828427124*I <- {F = -2^(1/2)+I*2^(1/2), x = 3} |
Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[F, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[F, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[F, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[F, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[F, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[F, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} |
| 1.16#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{\boldsymbol{{\alpha}}} = \iunit^{-|\boldsymbol{{\alpha}}|}D^{\boldsymbol{{\alpha}}}} | D[alpha]= (I)^(-abs(alpha))* (D)^(alpha) |
Subscript[D, \[Alpha]]= (I)^(-Abs[\[Alpha]])* (D)^(\[Alpha]) |
Failure | Failure | Fail .9779681321+2.175809568*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}.9779681321-.6526175556*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.850458992-.6526175556*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.850458992+2.175809568*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}9.438272386+2.467033025*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}9.438272386-.361394099*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}6.609845262-.361394099*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}6.609845262+2.467033025*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}.8479100469+.4255625275*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}.8479100469-2.402864596*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.980517077-2.402864596*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.980517077+.4255625275*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}1.536729595+1.398138497*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}1.536729595-1.430288627*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.291697529-1.430288627*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.291697529+1.398138497*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}9.438272386+.361394099*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}9.438272386-2.467033025*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}6.609845262-2.467033025*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}6.609845262+.361394099*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}.9779681321+.6526175556*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}.9779681321-2.175809568*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.850458992-2.175809568*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.850458992+.6526175556*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}1.536729595+1.430288627*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}1.536729595-1.398138497*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.291697529-1.398138497*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.291697529+1.430288627*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}.8479100469+2.402864596*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}.8479100469-.4255625275*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.980517077-.4255625275*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.980517077+2.402864596*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}-51.12384670-51.57661382*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}-51.12384670-54.40504094*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-53.95227382-54.40504094*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-53.95227382-51.57661382*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}1.377148458+1.501888445*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}1.377148458-1.326538679*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.451278666-1.326538679*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.451278666+1.501888445*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}1.404778314+1.423730122*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}1.404778314-1.404697002*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.423648810-1.404697002*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.423648810+1.423730122*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}-2.676538322-8.262170665*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}-2.676538322-11.09059779*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-5.504965446-11.09059779*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-5.504965446-8.262170665*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}1.377148458+1.326538679*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}1.377148458-1.501888445*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.451278666-1.501888445*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.451278666+1.326538679*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}-51.12384670+54.40504094*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}-51.12384670+51.57661382*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-53.95227382+51.57661382*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-53.95227382+54.40504094*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}-2.676538322+11.09059779*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}-2.676538322+8.262170665*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-5.504965446+8.262170665*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-5.504965446+11.09059779*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}1.404778314+1.404697002*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}1.404778314-1.423730122*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}-1.423648810-1.423730122*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}-1.423648810+1.404697002*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)} |
Successful |
| 1.16.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(\mathbf{D}) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{D}^{\alpha}} | P*(D)= sum(c[alpha]*(D)^(alpha), alpha = - infinity..infinity) |
P*(D)= Sum[Subscript[c, \[Alpha]]*(D)^(\[Alpha]), {\[Alpha], - Infinity, Infinity}] |
Failure | Failure | Skip | Skip |
| 1.16.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{\infty}_{-\infty}\Diracdelta@{t}\expe^{\iunit xt}\diff{t} = 1} | int(Dirac(t)*exp(I*x*t), t = - infinity..infinity)= 1 |
Integrate[DiracDelta[t]*Exp[I*x*t], {t, - Infinity, Infinity}]= 1 |
Successful | Successful | - | - |
| 1.16.E43 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\cpi}\int^{\infty}_{-\infty}\expe^{\iunit xt}\diff{t} = \Diracdelta@{x}} | (1)/(2*Pi)*int(exp(I*x*t), t = - infinity..infinity)= Dirac(x) |
Divide[1,2*Pi]*Integrate[Exp[I*x*t], {t, - Infinity, Infinity}]= DiracDelta[x] |
Successful | Failure | - | Fail
Complex[-1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.16.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sign@{x} = 2\HeavisideH@{x}-1} | signum(x)= 2*Heaviside(x)- 1 |
Sign[x]= 2*HeavisideTheta[x]- 1 |
Failure | Failure | Skip | Successful |
| 1.17.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x} = 0} | Dirac(x)= 0 |
DiracDelta[x]= 0 |
Error | Failure | - | Successful |
| 1.17.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\Diracdelta@{x-a}\phi(x)\diff{x} = \phi(a)} | int(Dirac(x - a)*phi*(x), x = - infinity..infinity)= phi*(a) |
Integrate[DiracDelta[x - a]*\[Phi]*(x), {x, - Infinity, Infinity}]= \[Phi]*(a) |
Successful | Failure | - | Successful |
| 1.17.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \phi(a)} | limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi*(x), x = - infinity..infinity), n = infinity)= phi*(a) |
Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi]*(x), {x, - Infinity, Infinity}], n -> Infinity]= \[Phi]*(a) |
Successful | Failure | - | Error |
| 1.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \tfrac{1}{2}\phi(a-)+\tfrac{1}{2}\phi(a+)} | limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi*(x), x = - infinity..infinity), n = infinity)=(1)/(2)*phi*(a -)+(1)/(2)*phi*(a +) |
Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi]*(x), {x, - Infinity, Infinity}], n -> Infinity]=Divide[1,2]*\[Phi]*(a -)+Divide[1,2]*\[Phi]*(a +) |
Error | Failure | - | Error |
| 1.17.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left(\int_{-\infty}^{\infty}\phi(x)e^{itx}\diff{x}\right)\diff{t} = \phi(a)} | (1)/(2*Pi)*int(exp(- I*a*t)*(int(phi*(x)* exp(I*t*x), x = - infinity..infinity)), t = - infinity..infinity)= phi*(a) |
Divide[1,2*Pi]*Integrate[Exp[- I*a*t]*(Integrate[\[Phi]*(x)* Exp[I*t*x], {x, - Infinity, Infinity}]), {t, - Infinity, Infinity}]= \[Phi]*(a) |
Failure | Failure | Skip | Skip |
| 1.17.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}\right)\phi(x)\diff{x} = \phi(a)} | int(((1)/(2*Pi)*int(exp(I*(x - a)* t), t = - infinity..infinity))* phi*(x), x = - infinity..infinity)= phi*(a) |
Integrate[(Divide[1,2*Pi]*Integrate[Exp[I*(x - a)* t], {t, - Infinity, Infinity}])* \[Phi]*(x), {x, - Infinity, Infinity}]= \[Phi]*(a) |
Failure | Failure | Skip | Skip |
| 1.17.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\diff{t} = \sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}} | (1)/(2*Pi)*int(exp(- (t)^(2)/(4*n))*exp(I*(x - a)* t), t = - infinity..infinity)=sqrt((n)/(Pi))*exp(- n*(x - a)^(2)) |
Divide[1,2*Pi]*Integrate[Exp[- (t)^(2)/(4*n)]*Exp[I*(x - a)* t], {t, - Infinity, Infinity}]=Sqrt[Divide[n,Pi]]*Exp[- n*(x - a)^(2)] |
Failure | Failure | Skip | Skip |
| 1.17.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}} | Dirac(x - a)=(1)/(2*Pi)*int(exp(I*(x - a)* t), t = - infinity..infinity) |
DiracDelta[x - a]=Divide[1,2*Pi]*Integrate[Exp[I*(x - a)* t], {t, - Infinity, Infinity}] |
Failure | Failure | Skip | Fail
Complex[1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, Plus[Times[-1, a], x]]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.17.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = x\int_{0}^{\infty}t\BesselJ{\nu}@{xt}\BesselJ{\nu}@{at}\diff{t}} | Dirac(x - a)= x*int(t*BesselJ(nu, x*t)*BesselJ(nu, a*t), t = 0..infinity) |
DiracDelta[x - a]= x*Integrate[t*BesselJ[\[Nu], x*t]*BesselJ[\[Nu], a*t], {t, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 1.17.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{2xa}{\pi}\int_{0}^{\infty}t^{2}\sphBesselJ{\ell}@{xt}\sphBesselJ{\ell}@{at}\diff{t}} | Error |
DiracDelta[x - a]=Divide[2*x*a,Pi]*Integrate[(t)^(2)* SphericalBesselJ[\[ScriptL], x*t]*SphericalBesselJ[\[ScriptL], a*t], {t, 0, Infinity}] |
Error | Failure | - | Successful |
| 1.17.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}\left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\diff{x}\right) = \phi(a)} | (1)/(2*Pi)*sum(exp(- I*k*a)*(int(phi*(x)* exp(I*k*x), x = - Pi..Pi)), k = - infinity..infinity)= phi*(a) |
Divide[1,2*Pi]*Sum[Exp[- I*k*a]*(Integrate[\[Phi]*(x)* Exp[I*k*x], {x, - Pi, Pi}]), {k, - Infinity, Infinity}]= \[Phi]*(a) |
Error | Failure | - | Successful |
| 1.17.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}\right)\diff{x} = \phi(a)} | int(phi*(x)*((1)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity)), x = - Pi..Pi)= phi*(a) |
Integrate[\[Phi]*(x)*(Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}]), {x, - Pi, Pi}]= \[Phi]*(a) |
Failure | Failure | Skip | Error |
| 1.17.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}} | Dirac(x - a)=(1)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity) |
DiracDelta[x - a]=Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}] |
Failure | Failure | Skip | Fail
Complex[1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Power[E, Times[Complex[0, 1], k, Plus[Times[-1, a], x]]], {k, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 1.17.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \sum_{k=0}^{\infty}(k+\tfrac{1}{2})\LegendrepolyP{k}@{x}\LegendrepolyP{k}@{a}} | Dirac(x - a)= sum((k +(1)/(2))* LegendreP(k, x)*LegendreP(k, a), k = 0..infinity) |
DiracDelta[x - a]= Sum[(k +Divide[1,2])* LegendreP[k, x]*LegendreP[k, a], {k, 0, Infinity}] |
Failure | Failure | Skip | Fail
Complex[0.0, 2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}2.8284271247461903 <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}2.8284271247461903 <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-2.8284271247461903 <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}-2.8284271247461903 <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 2.8284271247461903] <- {Rule[DiracDelta[Plus[Times[-1, a], x]], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Sum[Times[Plus[Rational[1, 2], k], LegendreP[k, a], LegendreP[k, x]], {k, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} |
| 1.17.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = e^{-(x+a)/2}\sum_{k=0}^{\infty}\LaguerrepolyL[]{k}@{x}\LaguerrepolyL[]{k}@{a}} | Dirac(x - a)= exp(-(x + a)/ 2)*sum(LaguerreL(k, x)*LaguerreL(k, a), k = 0..infinity) |
Error |
Failure | Error | - | - |
| 1.17.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{e^{-(x^{2}+a^{2})/2}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{\HermitepolyH{k}@{x}\HermitepolyH{k}@{a}}{2^{k}k!}} | Dirac(x - a)=(exp(-((x)^(2)+ (a)^(2))/ 2))/(sqrt(Pi))*sum((HermiteH(k, x)*HermiteH(k, a))/((2)^(k)* factorial(k)), k = 0..infinity) |
DiracDelta[x - a]=Divide[Exp[-((x)^(2)+ (a)^(2))/ 2],Sqrt[Pi]]*Sum[Divide[HermiteH[k, x]*HermiteH[k, a],(2)^(k)* (k)!], {k, 0, Infinity}] |
Error | Failure | - | Skip |