Results of Algebraic and Analytic Methods

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DLMF Formula Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
1.2.E1 ( n k ) = n ! ( n - k ) ! ⁒ k ! binomial 𝑛 π‘˜ 𝑛 𝑛 π‘˜ π‘˜ {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{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 n ! ( n - k ) ! ⁒ k ! = ( n n - k ) 𝑛 𝑛 π‘˜ π‘˜ binomial 𝑛 𝑛 π‘˜ {\displaystyle{\displaystyle\frac{n!}{(n-k)!k!}=\genfrac{(}{)}{0.0pt}{}{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 ( z k ) = z ⁒ ( z - 1 ) ⁒ β‹― ⁒ ( z - k + 1 ) k ! binomial 𝑧 π‘˜ 𝑧 𝑧 1 β‹― 𝑧 π‘˜ 1 π‘˜ {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{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 ( z + 1 k ) = ( z k ) + ( z k - 1 ) binomial 𝑧 1 π‘˜ binomial 𝑧 π‘˜ binomial 𝑧 π‘˜ 1 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{z+1}{k}=\genfrac{(}{)}{0.0% pt}{}{z}{k}+\genfrac{(}{)}{0.0pt}{}{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 βˆ‘ k = 0 m ( z + k k ) = ( z + m + 1 m ) subscript superscript π‘š π‘˜ 0 binomial 𝑧 π‘˜ π‘˜ binomial 𝑧 π‘š 1 π‘š {\displaystyle{\displaystyle\sum^{m}_{k=0}\genfrac{(}{)}{0.0pt}{}{z+k}{k}=% \genfrac{(}{)}{0.0pt}{}{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 f ( 2 ) ⁒ ( x ) = d 2 f d x 2 superscript 𝑓 2 π‘₯ derivative 𝑓 π‘₯ 2 {\displaystyle{\displaystyle f^{(2)}(x)=\frac{{\mathrm{d}}^{2}f}{{\mathrm{d}x}% ^{2}}}} (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 d 2 f d x 2 = d d x ⁑ ( d f d x ) derivative 𝑓 π‘₯ 2 derivative π‘₯ derivative 𝑓 π‘₯ {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}f}{{\mathrm{d}x}^{2}}=\frac{% \mathrm{d}}{\mathrm{d}x}\left(\frac{\mathrm{d}f}{\mathrm{d}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 f ( n ) = f ( n ) ⁒ ( x ) superscript 𝑓 𝑛 superscript 𝑓 𝑛 π‘₯ {\displaystyle{\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 f ( n ) ⁒ ( x ) = d d x ⁑ f ( n - 1 ) ⁒ ( x ) superscript 𝑓 𝑛 π‘₯ derivative π‘₯ superscript 𝑓 𝑛 1 π‘₯ {\displaystyle{\displaystyle f^{(n)}(x)=\frac{\mathrm{d}}{\mathrm{d}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 ∫ f ⁒ g ⁒ d x = ( ∫ f ⁒ d x ) ⁒ g - ∫ ( ∫ f ⁒ d x ) ⁒ d g d x ⁒ d x 𝑓 𝑔 π‘₯ 𝑓 π‘₯ 𝑔 𝑓 π‘₯ derivative 𝑔 π‘₯ π‘₯ {\displaystyle{\displaystyle\int fg\mathrm{d}x=\left(\int f\mathrm{d}x\right)g% -\int\left(\int f\mathrm{d}x\right)\frac{\mathrm{d}g}{\mathrm{d}x}\mathrm{d}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 R n = 1 n ! ⁒ ∫ a x ( x - t ) n ⁒ f ( n + 1 ) ⁒ ( t ) ⁒ d t subscript 𝑅 𝑛 1 𝑛 subscript superscript π‘₯ π‘Ž superscript π‘₯ 𝑑 𝑛 superscript 𝑓 𝑛 1 𝑑 𝑑 {\displaystyle{\displaystyle R_{n}=\frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(% t)\mathrm{d}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 βˆ‚ ⁑ f βˆ‚ ⁑ y = D y ⁒ f partial-derivative 𝑓 𝑦 subscript 𝐷 𝑦 𝑓 {\displaystyle{\displaystyle\frac{\partial f}{\partial 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 D y ⁒ f = f y subscript 𝐷 𝑦 𝑓 subscript 𝑓 𝑦 {\displaystyle{\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 x = r ⁒ cos ⁑ Ο• π‘₯ π‘Ÿ italic-Ο• {\displaystyle{\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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex4 y = r ⁒ sin ⁑ Ο• 𝑦 π‘Ÿ italic-Ο• {\displaystyle{\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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5.E13 βˆ‚ 2 ⁑ f βˆ‚ ⁑ x 2 + βˆ‚ 2 ⁑ f βˆ‚ ⁑ y 2 = βˆ‚ 2 ⁑ f βˆ‚ ⁑ r 2 + 1 r ⁒ βˆ‚ ⁑ f βˆ‚ ⁑ r + 1 r 2 ⁒ βˆ‚ 2 ⁑ f βˆ‚ ⁑ Ο• 2 partial-derivative 𝑓 π‘₯ 2 partial-derivative 𝑓 𝑦 2 partial-derivative 𝑓 π‘Ÿ 2 1 π‘Ÿ partial-derivative 𝑓 π‘Ÿ 1 superscript π‘Ÿ 2 partial-derivative 𝑓 italic-Ο• 2 {\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}=\frac{{\partial}^{2}f}{{\partial r}^{2}}+% \frac{1}{r}\frac{\partial f}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}f}% {{\partial\phi}^{2}}}} 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 x = r ⁒ cos ⁑ Ο• π‘₯ π‘Ÿ italic-Ο• {\displaystyle{\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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex6 y = r ⁒ sin ⁑ Ο• 𝑦 π‘Ÿ italic-Ο• {\displaystyle{\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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, 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[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex8 x = ρ ⁒ sin ⁑ ΞΈ ⁒ cos ⁑ Ο• π‘₯ 𝜌 πœƒ italic-Ο• {\displaystyle{\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[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex9 y = ρ ⁒ sin ⁑ ΞΈ ⁒ sin ⁑ Ο• 𝑦 𝜌 πœƒ italic-Ο• {\displaystyle{\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[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Ο•, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex10 z = ρ ⁒ cos ⁑ ΞΈ 𝑧 𝜌 πœƒ {\displaystyle{\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 βˆ‚ 2 ⁑ f βˆ‚ ⁑ x 2 + βˆ‚ 2 ⁑ f βˆ‚ ⁑ y 2 + βˆ‚ 2 ⁑ f βˆ‚ ⁑ z 2 = 1 ρ 2 ⁒ βˆ‚ βˆ‚ ⁑ ρ ⁑ ( ρ 2 ⁒ βˆ‚ ⁑ f βˆ‚ ⁑ ρ ) + 1 ρ 2 ⁒ sin 2 ⁑ ΞΈ ⁒ βˆ‚ 2 ⁑ f βˆ‚ ⁑ Ο• 2 + 1 ρ 2 ⁒ sin ⁑ ΞΈ ⁒ βˆ‚ βˆ‚ ⁑ ΞΈ ⁑ ( sin ⁑ ΞΈ ⁒ βˆ‚ ⁑ f βˆ‚ ⁑ ΞΈ ) partial-derivative 𝑓 π‘₯ 2 partial-derivative 𝑓 𝑦 2 partial-derivative 𝑓 𝑧 2 1 superscript 𝜌 2 partial-derivative 𝜌 superscript 𝜌 2 partial-derivative 𝑓 𝜌 1 superscript 𝜌 2 2 πœƒ partial-derivative 𝑓 italic-Ο• 2 1 superscript 𝜌 2 πœƒ partial-derivative πœƒ πœƒ partial-derivative 𝑓 πœƒ {\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}+\frac{{\partial}^{2}f}{{\partial z}^{2}}={% \frac{1}{\rho^{2}}\frac{\partial}{\partial\rho}\left(\rho^{2}\frac{\partial f}% {\partial\rho}\right)+\frac{1}{\rho^{2}{\sin^{2}}\theta}\frac{{\partial}^{2}f}% {{\partial\phi}^{2}}}+\frac{1}{\rho^{2}\sin\theta}\frac{\partial}{\partial% \theta}\left(\sin\theta\frac{\partial f}{\partial\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 βˆ‚ ⁑ f βˆ‚ ⁑ x = βˆ‚ ⁑ f βˆ‚ ⁑ y partial-derivative 𝑓 π‘₯ partial-derivative 𝑓 𝑦 {\displaystyle{\displaystyle\frac{\partial f}{\partial x}=\frac{\partial f}{% \partial y}}} diff(f, x)= diff(f, y) D[f, x]= D[f, y] Successful Successful - -
1.5.E23 | ∫ c 1 d ( βˆ‚ ⁑ f / βˆ‚ ⁑ x ) ⁒ d y | < Ο΅ superscript subscript subscript 𝑐 1 𝑑 partial-derivative 𝑓 π‘₯ 𝑦 italic-Ο΅ {\displaystyle{\displaystyle\left|\int_{c_{1}}^{d}(\ifrac{\partial f}{\partial x% })\mathrm{d}y\right|<\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 ϡ 1 ⁣ 2 ⁣ 3 = ϡ 3 ⁣ 1 ⁣ 2 Levi-Civita 1 2 3 Levi-Civita 3 1 2 {\displaystyle{\displaystyle\epsilon_{123}=\epsilon_{312}}} 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 ϡ 3 ⁣ 1 ⁣ 2 = 1 Levi-Civita 3 1 2 1 {\displaystyle{\displaystyle\epsilon_{312}=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 ϡ 2 ⁣ 1 ⁣ 3 = ϡ 3 ⁣ 2 ⁣ 1 Levi-Civita 2 1 3 Levi-Civita 3 2 1 {\displaystyle{\displaystyle\epsilon_{213}=\epsilon_{321}}} 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 ϡ 3 ⁣ 2 ⁣ 1 = - 1 Levi-Civita 3 2 1 1 {\displaystyle{\displaystyle\epsilon_{321}=-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 ϡ 2 ⁣ 2 ⁣ 1 = 0 Levi-Civita 2 2 1 0 {\displaystyle{\displaystyle\epsilon_{221}=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 Ο΅ j ⁣ k ⁣ β„“ ⁒ Ο΅ β„“ ⁣ m ⁣ n = Ξ΄ j , m ⁒ Ξ΄ k , n - Ξ΄ j , n ⁒ Ξ΄ k , m Levi-Civita 𝑗 π‘˜ β„“ Levi-Civita β„“ π‘š 𝑛 Kronecker 𝑗 π‘š Kronecker π‘˜ 𝑛 Kronecker 𝑗 𝑛 Kronecker π‘˜ π‘š {\displaystyle{\displaystyle\epsilon_{jk\ell}\epsilon_{\ell mn}=\delta_{j,m}% \delta_{k,n}-\delta_{j,n}\delta_{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 𝐓 u = βˆ‚ ⁑ x βˆ‚ ⁑ u ⁒ ( u 0 , v 0 ) ⁒ 𝐒 + βˆ‚ ⁑ y βˆ‚ ⁑ u ⁒ ( u 0 , v 0 ) ⁒ 𝐣 + βˆ‚ ⁑ z βˆ‚ ⁑ u ⁒ ( u 0 , v 0 ) ⁒ 𝐀 subscript 𝐓 𝑒 partial-derivative π‘₯ 𝑒 subscript 𝑒 0 subscript 𝑣 0 𝐒 partial-derivative 𝑦 𝑒 subscript 𝑒 0 subscript 𝑣 0 𝐣 partial-derivative 𝑧 𝑒 subscript 𝑒 0 subscript 𝑣 0 𝐀 {\displaystyle{\displaystyle\mathbf{T}_{u}=\frac{\partial x}{\partial u}(u_{0}% ,v_{0})\mathbf{i}+\frac{\partial y}{\partial u}(u_{0},v_{0})\mathbf{j}+\frac{% \partial z}{\partial 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 𝐓 v = βˆ‚ ⁑ x βˆ‚ ⁑ v ⁒ ( u 0 , v 0 ) ⁒ 𝐒 + βˆ‚ ⁑ y βˆ‚ ⁑ v ⁒ ( u 0 , v 0 ) ⁒ 𝐣 + βˆ‚ ⁑ z βˆ‚ ⁑ v ⁒ ( u 0 , v 0 ) ⁒ 𝐀 subscript 𝐓 𝑣 partial-derivative π‘₯ 𝑣 subscript 𝑒 0 subscript 𝑣 0 𝐒 partial-derivative 𝑦 𝑣 subscript 𝑒 0 subscript 𝑣 0 𝐣 partial-derivative 𝑧 𝑣 subscript 𝑒 0 subscript 𝑣 0 𝐀 {\displaystyle{\displaystyle\mathbf{T}_{v}=\frac{\partial x}{\partial v}(u_{0}% ,v_{0})\mathbf{i}+\frac{\partial y}{\partial v}(u_{0},v_{0})\mathbf{j}+\frac{% \partial z}{\partial 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 βˆ‘ n = - ∞ ∞ e - ( n + x ) 2 ⁒ Ο‰ = Ο€ Ο‰ ⁒ ( 1 + 2 ⁒ βˆ‘ n = 1 ∞ e - n 2 ⁒ Ο€ 2 / Ο‰ ⁒ cos ⁑ ( 2 ⁒ n ⁒ Ο€ ⁒ x ) ) superscript subscript 𝑛 superscript 𝑒 superscript 𝑛 π‘₯ 2 πœ” πœ‹ πœ” 1 2 superscript subscript 𝑛 1 superscript 𝑒 superscript 𝑛 2 superscript πœ‹ 2 πœ” 2 𝑛 πœ‹ π‘₯ {\displaystyle{\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\left(2n\pi x\right)\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 β„œ ⁑ z = x 𝑧 π‘₯ {\displaystyle{\displaystyle\Re 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 β„‘ ⁑ z = y 𝑧 𝑦 {\displaystyle{\displaystyle\Im 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 x = r ⁒ cos ⁑ ΞΈ π‘₯ π‘Ÿ πœƒ {\displaystyle{\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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9#Ex4 y = r ⁒ sin ⁑ ΞΈ 𝑦 π‘Ÿ πœƒ {\displaystyle{\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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9.E6 Ο‰ = arctan ⁑ ( | y / x | ) ∈ [ 0 , 1 2 ⁒ Ο€ ] πœ” 𝑦 π‘₯ 0 1 2 πœ‹ {\displaystyle{\displaystyle\omega=\operatorname{arctan}\left(|y/x|\right)\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 ph ⁑ z = ΞΈ + 2 ⁒ n ⁒ Ο€ phase 𝑧 πœƒ 2 𝑛 πœ‹ {\displaystyle{\displaystyle\operatorname{ph}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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, 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[ΞΈ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9#Ex7 | β„œ ⁑ z | ≀ | z | 𝑧 𝑧 {\displaystyle{\displaystyle|\Re z|<=|z|}} abs(Re(z))< =abs(z) Abs[Re[z]]< =Abs[z] Failure Failure Successful Successful
1.9#Ex8 | β„‘ ⁑ z | ≀ | z | 𝑧 𝑧 {\displaystyle{\displaystyle|\Im z|<=|z|}} abs(Im(z))< =abs(z) Abs[Im[z]]< =Abs[z] Failure Failure Successful Successful
1.9.E10 e i ⁒ ΞΈ = cos ⁑ ΞΈ + i ⁒ sin ⁑ ΞΈ superscript 𝑒 𝑖 πœƒ πœƒ 𝑖 πœƒ {\displaystyle{\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 z Β― = x - i ⁒ y 𝑧 π‘₯ 𝑖 𝑦 {\displaystyle{\displaystyle\overline{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 | z Β― | = | z | 𝑧 𝑧 {\displaystyle{\displaystyle|\overline{z}|=|z|}} abs(conjugate(z))=abs(z) Abs[Conjugate[z]]=Abs[z] Successful Successful - -
1.9.E13 ph ⁑ z Β― = - ph ⁑ z phase 𝑧 phase 𝑧 {\displaystyle{\displaystyle\operatorname{ph}\overline{z}=-\operatorname{ph}z}} argument(conjugate(z))= - argument(z) Arg[Conjugate[z]]= - Arg[z] Failure Failure Successful Successful
1.9.E14 z 1 + z 2 = x 1 + x 2 + i ⁒ ( y 1 + y 2 ) subscript 𝑧 1 subscript 𝑧 2 subscript π‘₯ 1 subscript π‘₯ 2 imaginary-unit subscript 𝑦 1 subscript 𝑦 2 {\displaystyle{\displaystyle z_{1}+z_{2}=x_{1}+x_{2}+\mathrm{i}(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 z 1 - z 2 = x 1 - x 2 + i ⁒ ( y 1 - y 2 ) subscript 𝑧 1 subscript 𝑧 2 subscript π‘₯ 1 subscript π‘₯ 2 imaginary-unit subscript 𝑦 1 subscript 𝑦 2 {\displaystyle{\displaystyle z_{1}-z_{2}=x_{1}-x_{2}+\mathrm{i}(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 z 1 z 2 = z 1 ⁒ z Β― 2 | z 2 | 2 subscript 𝑧 1 subscript 𝑧 2 subscript 𝑧 1 subscript 𝑧 2 superscript subscript 𝑧 2 2 {\displaystyle{\displaystyle\frac{z_{1}}{z_{2}}=\frac{z_{1}\overline{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 z 1 ⁒ z Β― 2 | z 2 | 2 = x 1 ⁒ x 2 + y 1 ⁒ y 2 + i ⁒ ( x 2 ⁒ y 1 - x 1 ⁒ y 2 ) x 2 2 + y 2 2 subscript 𝑧 1 subscript 𝑧 2 superscript subscript 𝑧 2 2 subscript π‘₯ 1 subscript π‘₯ 2 subscript 𝑦 1 subscript 𝑦 2 𝑖 subscript π‘₯ 2 subscript 𝑦 1 subscript π‘₯ 1 subscript 𝑦 2 superscript subscript π‘₯ 2 2 superscript subscript 𝑦 2 2 {\displaystyle{\displaystyle\frac{z_{1}\overline{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 ph ⁑ ( z 1 ⁒ z 2 ) = ph ⁑ z 1 + ph ⁑ z 2 phase subscript 𝑧 1 subscript 𝑧 2 phase subscript 𝑧 1 phase subscript 𝑧 2 {\displaystyle{\displaystyle\operatorname{ph}\left(z_{1}z_{2}\right)=% \operatorname{ph}z_{1}+\operatorname{ph}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 | z 1 z 2 | = | z 1 | | z 2 | subscript 𝑧 1 subscript 𝑧 2 subscript 𝑧 1 subscript 𝑧 2 {\displaystyle{\displaystyle\left|\frac{z_{1}}{z_{2}}\right|=\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 ph ⁑ z 1 z 2 = ph ⁑ z 1 - ph ⁑ z 2 phase subscript 𝑧 1 subscript 𝑧 2 phase subscript 𝑧 1 phase subscript 𝑧 2 {\displaystyle{\displaystyle\operatorname{ph}\frac{z_{1}}{z_{2}}=\operatorname% {ph}z_{1}-\operatorname{ph}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 cos ⁑ n ⁒ ΞΈ + i ⁒ sin ⁑ n ⁒ ΞΈ = ( cos ⁑ ΞΈ + i ⁒ sin ⁑ ΞΈ ) n 𝑛 πœƒ 𝑖 𝑛 πœƒ superscript πœƒ 𝑖 πœƒ 𝑛 {\displaystyle{\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 | | z 1 | - | z 2 | | ≀ | z 1 + z 2 | subscript 𝑧 1 subscript 𝑧 2 subscript 𝑧 1 subscript 𝑧 2 {\displaystyle{\displaystyle\left|\left|z_{1}\right|-\left|z_{2}\right|\right|% <=\left|z_{1}+z_{2}\right|}} 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 | z 1 + z 2 | ≀ | z 1 | + | z 2 | subscript 𝑧 1 subscript 𝑧 2 subscript 𝑧 1 subscript 𝑧 2 {\displaystyle{\displaystyle\left|z_{1}+z_{2}\right|<=\left|z_{1}\right|+\left% |z_{2}\right|}} 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 βˆ‚ ⁑ u βˆ‚ ⁑ x = βˆ‚ ⁑ v βˆ‚ ⁑ y partial-derivative 𝑒 π‘₯ partial-derivative 𝑣 𝑦 {\displaystyle{\displaystyle\frac{\partial u}{\partial x}=\frac{\partial v}{% \partial y}}} diff(u, x)= diff(v, y) D[u, x]= D[v, y] Successful Successful - -
1.9#Ex10 βˆ‚ ⁑ u βˆ‚ ⁑ y = - βˆ‚ ⁑ v βˆ‚ ⁑ x partial-derivative 𝑒 𝑦 partial-derivative 𝑣 π‘₯ {\displaystyle{\displaystyle\frac{\partial u}{\partial y}=-\frac{\partial v}{% \partial x}}} diff(u, y)= - diff(v, x) D[u, y]= - D[v, x] Successful Successful - -
1.9.E26 βˆ‚ 2 ⁑ u βˆ‚ ⁑ x 2 + βˆ‚ 2 ⁑ u βˆ‚ ⁑ y 2 = βˆ‚ 2 ⁑ v βˆ‚ ⁑ x 2 + βˆ‚ 2 ⁑ v βˆ‚ ⁑ y 2 partial-derivative 𝑒 π‘₯ 2 partial-derivative 𝑒 𝑦 2 partial-derivative 𝑣 π‘₯ 2 partial-derivative 𝑣 𝑦 2 {\displaystyle{\displaystyle\frac{{\partial}^{2}u}{{\partial x}^{2}}+\frac{{% \partial}^{2}u}{{\partial y}^{2}}=\frac{{\partial}^{2}v}{{\partial x}^{2}}+% \frac{{\partial}^{2}v}{{\partial y}^{2}}}} 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 βˆ‚ 2 ⁑ v βˆ‚ ⁑ x 2 + βˆ‚ 2 ⁑ v βˆ‚ ⁑ y 2 = 0 partial-derivative 𝑣 π‘₯ 2 partial-derivative 𝑣 𝑦 2 0 {\displaystyle{\displaystyle\frac{{\partial}^{2}v}{{\partial x}^{2}}+\frac{{% \partial}^{2}v}{{\partial y}^{2}}=0}} diff(v, [x$(2)])+ diff(v, [y$(2)])= 0 D[v, {x, 2}]+ D[v, {y, 2}]= 0 Successful Successful - -
1.9.E27 βˆ‚ 2 ⁑ u βˆ‚ ⁑ r 2 + 1 r ⁒ βˆ‚ ⁑ u βˆ‚ ⁑ r + 1 r 2 ⁒ βˆ‚ 2 ⁑ u βˆ‚ ⁑ ΞΈ 2 = 0 partial-derivative 𝑒 π‘Ÿ 2 1 π‘Ÿ partial-derivative 𝑒 π‘Ÿ 1 superscript π‘Ÿ 2 partial-derivative 𝑒 πœƒ 2 0 {\displaystyle{\displaystyle\frac{{\partial}^{2}u}{{\partial r}^{2}}+\frac{1}{% r}\frac{\partial u}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}u}{{% \partial\theta}^{2}}=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 u ⁒ ( z ) = 1 2 ⁒ Ο€ ⁒ ∫ 0 2 ⁒ Ο€ u ⁒ ( z + r ⁒ e i ⁒ Ο• ) ⁒ d Ο• 𝑒 𝑧 1 2 πœ‹ subscript superscript 2 πœ‹ 0 𝑒 𝑧 π‘Ÿ superscript 𝑒 𝑖 italic-Ο• italic-Ο• {\displaystyle{\displaystyle u(z)=\frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})% \mathrm{d}\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 u ⁒ ( r ⁒ e i ⁒ ΞΈ ) = 1 2 ⁒ Ο€ ⁒ ∫ 0 2 ⁒ Ο€ ( R 2 - r 2 ) ⁒ h ⁒ ( R ⁒ e i ⁒ Ο• ) ⁒ d Ο• R 2 - 2 ⁒ R ⁒ r ⁒ cos ⁑ ( Ο• - ΞΈ ) + r 2 𝑒 π‘Ÿ superscript 𝑒 𝑖 πœƒ 1 2 πœ‹ subscript superscript 2 πœ‹ 0 superscript 𝑅 2 superscript π‘Ÿ 2 β„Ž 𝑅 superscript 𝑒 𝑖 italic-Ο• italic-Ο• superscript 𝑅 2 2 𝑅 π‘Ÿ italic-Ο• πœƒ superscript π‘Ÿ 2 {\displaystyle{\displaystyle u(re^{i\theta})=\frac{1}{2\pi}\int^{2\pi}_{0}% \frac{(R^{2}-r^{2})h(Re^{i\phi})\mathrm{d}\phi}{R^{2}-2Rr\cos\left(\phi-\theta% \right)+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 f ( m ) ⁒ ( z ) = βˆ‘ n = 0 ∞ ( n + 1 ) m ⁒ a n + m ⁒ ( z - z 0 ) n superscript 𝑓 π‘š 𝑧 superscript subscript 𝑛 0 Pochhammer 𝑛 1 π‘š subscript π‘Ž 𝑛 π‘š superscript 𝑧 subscript 𝑧 0 𝑛 {\displaystyle{\displaystyle f^{(m)}(z)=\sum_{n=0}^{\infty}{\left(n+1\right)_{% 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 ∫ a b βˆ‘ n = 0 ∞ f n ⁒ ( t ) ⁒ d t = βˆ‘ n = 0 ∞ ∫ a b f n ⁒ ( t ) ⁒ d t subscript superscript 𝑏 π‘Ž subscript superscript 𝑛 0 subscript 𝑓 𝑛 𝑑 𝑑 subscript superscript 𝑛 0 subscript superscript 𝑏 π‘Ž subscript 𝑓 𝑛 𝑑 𝑑 {\displaystyle{\displaystyle\int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\mathrm{d}t% =\sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\mathrm{d}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 | ln ⁑ ( 1 + a n ⁒ ( z ) ) | ≀ M n 1 subscript π‘Ž 𝑛 𝑧 subscript 𝑀 𝑛 {\displaystyle{\displaystyle|\ln\left(1+a_{n}(z)\right)|<=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 - 1 2 ⁒ Ο€ + Ξ΄ < ph ⁑ b n 1 2 πœ‹ 𝛿 phase subscript 𝑏 𝑛 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta<\operatorname{ph}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 ph ⁑ b n < 1 2 ⁒ Ο€ - Ξ΄ phase subscript 𝑏 𝑛 1 2 πœ‹ 𝛿 {\displaystyle{\displaystyle\operatorname{ph}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 - 1 2 ⁒ Ο€ + Ξ΄ < ph ⁑ C n 1 2 πœ‹ 𝛿 phase subscript 𝐢 𝑛 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta<\operatorname{ph}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 ph ⁑ C n < 1 2 ⁒ Ο€ - Ξ΄ phase subscript 𝐢 𝑛 1 2 πœ‹ 𝛿 {\displaystyle{\displaystyle\operatorname{ph}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 d 2 W d ΞΎ 2 + F ⁒ ( ΞΎ ) ⁒ d W d ΞΎ + G ⁒ ( ΞΎ ) ⁒ W = 0 derivative π‘Š πœ‰ 2 𝐹 πœ‰ derivative π‘Š πœ‰ 𝐺 πœ‰ π‘Š 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}\xi}^{2}}+F(% \xi)\frac{\mathrm{d}W}{\mathrm{d}\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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, 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[ΞΎ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.13.E14 d 2 W d z 2 - H ⁒ ( z ) ⁒ W = 0 derivative π‘Š 𝑧 2 𝐻 𝑧 π‘Š 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}z}^{2}}-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 d 2 U d z 2 + I ⁒ U = 0 derivative π‘ˆ 𝑧 2 𝐼 π‘ˆ 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}U}{{\mathrm{d}z}^{2}}+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 d 2 V d z 2 + J ⁒ V = 0 derivative 𝑉 𝑧 2 𝐽 𝑉 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}V}{{\mathrm{d}z}^{2}}+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 ( f * g ) ⁒ ( t ) = 1 2 ⁒ Ο€ ⁒ ∫ - ∞ ∞ F ⁒ ( x ) ⁒ G ⁒ ( x ) ⁒ e - i ⁒ t ⁒ x ⁒ d x 𝑓 𝑔 𝑑 1 2 πœ‹ subscript superscript 𝐹 π‘₯ 𝐺 π‘₯ superscript 𝑒 𝑖 𝑑 π‘₯ π‘₯ {\displaystyle{\displaystyle(f*g)(t)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}F(x)G(x)e^{-itx}\mathrm{d}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 1 2 ⁒ Ο€ ⁒ ∫ 0 2 ⁒ Ο€ P ⁒ ( r , ΞΈ ) ⁒ d ΞΈ = 1 1 2 πœ‹ subscript superscript 2 πœ‹ 0 𝑃 π‘Ÿ πœƒ πœƒ 1 {\displaystyle{\displaystyle\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\mathrm{d}% \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 1 2 ⁒ Ο€ ⁒ ∫ 0 2 ⁒ Ο€ K n ⁒ ( ΞΈ ) ⁒ d ΞΈ = 1 1 2 πœ‹ subscript superscript 2 πœ‹ 0 subscript 𝐾 𝑛 πœƒ πœƒ 1 {\displaystyle{\displaystyle\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\mathrm{% d}\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 1 2 ⁒ Ο€ ⁒ ∫ - ∞ ∞ P ⁒ ( x , y ) ⁒ d x = 1 1 2 πœ‹ subscript superscript 𝑃 π‘₯ 𝑦 π‘₯ 1 {\displaystyle{\displaystyle\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\mathrm% {d}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 h ⁒ ( x , y ) = 1 2 ⁒ Ο€ ⁒ ∫ - ∞ ∞ e - y ⁒ | t | ⁒ e - i ⁒ x ⁒ t ⁒ F ⁒ ( t ) ⁒ d t β„Ž π‘₯ 𝑦 1 2 πœ‹ subscript superscript superscript 𝑒 𝑦 𝑑 superscript 𝑒 𝑖 π‘₯ 𝑑 𝐹 𝑑 𝑑 {\displaystyle{\displaystyle h(x,y)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}e^{-y|t|}e^{-ixt}F(t)\mathrm{d}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 Ξ¦ ⁒ ( z ) = Ξ¦ ⁒ ( x + i ⁒ y ) Ξ¦ 𝑧 Ξ¦ π‘₯ 𝑖 𝑦 {\displaystyle{\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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, 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[Ξ¦, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.15.E42 ∫ - ∞ ∞ K R ⁒ ( s ) ⁒ d s = 1 subscript superscript subscript 𝐾 𝑅 𝑠 𝑠 1 {\displaystyle{\displaystyle\int^{\infty}_{-\infty}K_{R}(s)\mathrm{d}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 Οƒ R ⁒ ( ΞΈ ) = 1 2 ⁒ Ο€ ⁒ ∫ - R R ( 1 - | t | R ) ⁒ e - i ⁒ ΞΈ ⁒ t ⁒ F ⁒ ( t ) ⁒ d t subscript 𝜎 𝑅 πœƒ 1 2 πœ‹ subscript superscript 𝑅 𝑅 1 𝑑 𝑅 superscript 𝑒 𝑖 πœƒ 𝑑 𝐹 𝑑 𝑑 {\displaystyle{\displaystyle\sigma_{R}(\theta)=\frac{1}{\sqrt{2\pi}}\int^{R}_{% -R}\left(1-\frac{|t|}{R}\right)e^{-i\theta t}F(t)\mathrm{d}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 x + Ξ± = x Ξ± ⁒ H ⁑ ( x ) subscript superscript π‘₯ 𝛼 superscript π‘₯ 𝛼 Heaviside-H π‘₯ {\displaystyle{\displaystyle x^{\alpha}_{+}=x^{\alpha}H\left(x\right)}} (x[+])^(alpha)= (x)^(alpha)* Heaviside(x) (Subscript[x, +])^(\[Alpha])= (x)^(\[Alpha])* HeavisideTheta[x] Error Failure - Error
1.16#Ex1 F ⁒ ( 𝐱 ) = F 𝐹 𝐱 𝐹 {\displaystyle{\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 D 𝜢 = i - | 𝜢 | ⁒ D 𝜢 subscript 𝐷 𝜢 imaginary-unit 𝜢 superscript 𝐷 𝜢 {\displaystyle{\displaystyle D_{\boldsymbol{{\alpha}}}={\mathrm{i}^{-|% \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 P ⁒ ( 𝐃 ) = βˆ‘ 𝜢 c 𝜢 ⁒ 𝐃 Ξ± 𝑃 𝐃 subscript 𝜢 subscript 𝑐 𝜢 superscript 𝐃 𝛼 {\displaystyle{\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 ∫ - ∞ ∞ Ξ΄ ⁑ ( t ) ⁒ e i ⁒ x ⁒ t ⁒ d t = 1 subscript superscript Dirac-delta 𝑑 imaginary-unit π‘₯ 𝑑 𝑑 1 {\displaystyle{\displaystyle\int^{\infty}_{-\infty}\delta\left(t\right){% \mathrm{e}^{\mathrm{i}xt}}\mathrm{d}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 1 2 ⁒ Ο€ ⁒ ∫ - ∞ ∞ e i ⁒ x ⁒ t ⁒ d t = Ξ΄ ⁑ ( x ) 1 2 subscript superscript imaginary-unit π‘₯ 𝑑 𝑑 Dirac-delta π‘₯ {\displaystyle{\displaystyle\frac{1}{2\pi}\int^{\infty}_{-\infty}{\mathrm{e}^{% \mathrm{i}xt}}\mathrm{d}t=\delta\left(x\right)}} (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 sign ⁑ ( x ) = 2 ⁒ H ⁑ ( x ) - 1 sign π‘₯ 2 Heaviside-H π‘₯ 1 {\displaystyle{\displaystyle\operatorname{sign}\left(x\right)=2H\left(x\right)% -1}} signum(x)= 2*Heaviside(x)- 1 Sign[x]= 2*HeavisideTheta[x]- 1 Failure Failure Skip Successful
1.17.E1 Ξ΄ ⁑ ( x ) = 0 Dirac-delta π‘₯ 0 {\displaystyle{\displaystyle\delta\left(x\right)=0}} Dirac(x)= 0 DiracDelta[x]= 0 Error Failure - Successful
1.17.E2 ∫ - ∞ ∞ Ξ΄ ⁑ ( x - a ) ⁒ Ο• ⁒ ( x ) ⁒ d x = Ο• ⁒ ( a ) superscript subscript Dirac-delta π‘₯ π‘Ž italic-Ο• π‘₯ π‘₯ italic-Ο• π‘Ž {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\delta\left(x-a\right)\phi(% x)\mathrm{d}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 lim n β†’ ∞ ⁑ n Ο€ ⁒ ∫ - ∞ ∞ e - n ⁒ ( x - a ) 2 ⁒ Ο• ⁒ ( x ) ⁒ d x = Ο• ⁒ ( a ) subscript β†’ 𝑛 𝑛 πœ‹ superscript subscript superscript 𝑒 𝑛 superscript π‘₯ π‘Ž 2 italic-Ο• π‘₯ π‘₯ italic-Ο• π‘Ž {\displaystyle{\displaystyle\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty% }^{\infty}e^{-n(x-a)^{2}}\phi(x)\mathrm{d}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 lim n β†’ ∞ ⁑ n Ο€ ⁒ ∫ - ∞ ∞ e - n ⁒ ( x - a ) 2 ⁒ Ο• ⁒ ( x ) ⁒ d x = 1 2 ⁒ Ο• ⁒ ( a - ) + 1 2 ⁒ Ο• ⁒ ( a + ) subscript β†’ 𝑛 𝑛 πœ‹ superscript subscript superscript 𝑒 𝑛 superscript π‘₯ π‘Ž 2 italic-Ο• π‘₯ π‘₯ 1 2 italic-Ο• limit-from π‘Ž 1 2 italic-Ο• limit-from π‘Ž {\displaystyle{\displaystyle\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty% }^{\infty}e^{-n(x-a)^{2}}\phi(x)\mathrm{d}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 1 2 ⁒ Ο€ ⁒ ∫ - ∞ ∞ e - i ⁒ a ⁒ t ⁒ ( ∫ - ∞ ∞ Ο• ⁒ ( x ) ⁒ e i ⁒ t ⁒ x ⁒ d x ) ⁒ d t = Ο• ⁒ ( a ) 1 2 πœ‹ superscript subscript superscript 𝑒 𝑖 π‘Ž 𝑑 superscript subscript italic-Ο• π‘₯ superscript 𝑒 𝑖 𝑑 π‘₯ π‘₯ 𝑑 italic-Ο• π‘Ž {\displaystyle{\displaystyle\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left% (\int_{-\infty}^{\infty}\phi(x)e^{itx}\mathrm{d}x\right)\mathrm{d}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 ∫ - ∞ ∞ ( 1 2 ⁒ Ο€ ⁒ ∫ - ∞ ∞ e i ⁒ ( x - a ) ⁒ t ⁒ d t ) ⁒ Ο• ⁒ ( x ) ⁒ d x = Ο• ⁒ ( a ) superscript subscript 1 2 πœ‹ superscript subscript superscript 𝑒 𝑖 π‘₯ π‘Ž 𝑑 𝑑 italic-Ο• π‘₯ π‘₯ italic-Ο• π‘Ž {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-% \infty}^{\infty}e^{i(x-a)t}\mathrm{d}t\right)\phi(x)\mathrm{d}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 1 2 ⁒ Ο€ ⁒ ∫ - ∞ ∞ e - t 2 / ( 4 ⁒ n ) ⁒ e i ⁒ ( x - a ) ⁒ t ⁒ d t = n Ο€ ⁒ e - n ⁒ ( x - a ) 2 1 2 πœ‹ superscript subscript superscript 𝑒 superscript 𝑑 2 4 𝑛 superscript 𝑒 𝑖 π‘₯ π‘Ž 𝑑 𝑑 𝑛 πœ‹ superscript 𝑒 𝑛 superscript π‘₯ π‘Ž 2 {\displaystyle{\displaystyle\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n% )}e^{i(x-a)t}\mathrm{d}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 Ξ΄ ⁑ ( x - a ) = 1 2 ⁒ Ο€ ⁒ ∫ - ∞ ∞ e i ⁒ ( x - a ) ⁒ t ⁒ d t Dirac-delta π‘₯ π‘Ž 1 2 πœ‹ superscript subscript superscript 𝑒 𝑖 π‘₯ π‘Ž 𝑑 𝑑 {\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{1}{2\pi}\int_{-\infty% }^{\infty}e^{i(x-a)t}\mathrm{d}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 Ξ΄ ⁑ ( x - a ) = x ⁒ ∫ 0 ∞ t ⁒ J Ξ½ ⁑ ( x ⁒ t ) ⁒ J Ξ½ ⁑ ( a ⁒ t ) ⁒ d t Dirac-delta π‘₯ π‘Ž π‘₯ superscript subscript 0 𝑑 Bessel-J 𝜈 π‘₯ 𝑑 Bessel-J 𝜈 π‘Ž 𝑑 𝑑 {\displaystyle{\displaystyle\delta\left(x-a\right)=x\int_{0}^{\infty}tJ_{\nu}% \left(xt\right)J_{\nu}\left(at\right)\mathrm{d}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 Ξ΄ ⁑ ( x - a ) = 2 ⁒ x ⁒ a Ο€ ⁒ ∫ 0 ∞ t 2 ⁒ 𝗃 β„“ ⁑ ( x ⁒ t ) ⁒ 𝗃 β„“ ⁑ ( a ⁒ t ) ⁒ d t Dirac-delta π‘₯ π‘Ž 2 π‘₯ π‘Ž πœ‹ superscript subscript 0 superscript 𝑑 2 spherical-Bessel-J β„“ π‘₯ 𝑑 spherical-Bessel-J β„“ π‘Ž 𝑑 𝑑 {\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{2xa}{\pi}\int_{0}^{% \infty}t^{2}\mathsf{j}_{\ell}\left(xt\right)\mathsf{j}_{\ell}\left(at\right)% \mathrm{d}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 1 2 ⁒ Ο€ ⁒ βˆ‘ k = - ∞ ∞ e - i ⁒ k ⁒ a ⁒ ( ∫ - Ο€ Ο€ Ο• ⁒ ( x ) ⁒ e i ⁒ k ⁒ x ⁒ d x ) = Ο• ⁒ ( a ) 1 2 πœ‹ superscript subscript π‘˜ superscript 𝑒 𝑖 π‘˜ π‘Ž superscript subscript πœ‹ πœ‹ italic-Ο• π‘₯ superscript 𝑒 𝑖 π‘˜ π‘₯ π‘₯ italic-Ο• π‘Ž {\displaystyle{\displaystyle\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}% \left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\mathrm{d}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 ∫ - Ο€ Ο€ Ο• ⁒ ( x ) ⁒ ( 1 2 ⁒ Ο€ ⁒ βˆ‘ k = - ∞ ∞ e i ⁒ k ⁒ ( x - a ) ) ⁒ d x = Ο• ⁒ ( a ) superscript subscript πœ‹ πœ‹ italic-Ο• π‘₯ 1 2 πœ‹ superscript subscript π‘˜ superscript 𝑒 𝑖 π‘˜ π‘₯ π‘Ž π‘₯ italic-Ο• π‘Ž {\displaystyle{\displaystyle\int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{% k=-\infty}^{\infty}e^{ik(x-a)}\right)\mathrm{d}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 Ξ΄ ⁑ ( x - a ) = 1 2 ⁒ Ο€ ⁒ βˆ‘ k = - ∞ ∞ e i ⁒ k ⁒ ( x - a ) Dirac-delta π‘₯ π‘Ž 1 2 πœ‹ superscript subscript π‘˜ superscript 𝑒 𝑖 π‘˜ π‘₯ π‘Ž {\displaystyle{\displaystyle\delta\left(x-a\right)=\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 Ξ΄ ⁑ ( x - a ) = βˆ‘ k = 0 ∞ ( k + 1 2 ) ⁒ P k ⁑ ( x ) ⁒ P k ⁑ ( a ) Dirac-delta π‘₯ π‘Ž superscript subscript π‘˜ 0 π‘˜ 1 2 Legendre-spherical-polynomial π‘˜ π‘₯ Legendre-spherical-polynomial π‘˜ π‘Ž {\displaystyle{\displaystyle\delta\left(x-a\right)=\sum_{k=0}^{\infty}(k+% \tfrac{1}{2})P_{k}\left(x\right)P_{k}\left(a\right)}} 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 Ξ΄ ⁑ ( x - a ) = e - ( x + a ) / 2 ⁒ βˆ‘ k = 0 ∞ L k ⁑ ( x ) ⁒ L k ⁑ ( a ) Dirac-delta π‘₯ π‘Ž superscript 𝑒 π‘₯ π‘Ž 2 superscript subscript π‘˜ 0 shorthand-Laguerre-polynomial-L π‘˜ π‘₯ shorthand-Laguerre-polynomial-L π‘˜ π‘Ž {\displaystyle{\displaystyle\delta\left(x-a\right)=e^{-(x+a)/2}\sum_{k=0}^{% \infty}L_{k}\left(x\right)L_{k}\left(a\right)}} Dirac(x - a)= exp(-(x + a)/ 2)*sum(LaguerreL(k, x)*LaguerreL(k, a), k = 0..infinity) Error Failure Error - -
1.17.E24 Ξ΄ ⁑ ( x - a ) = e - ( x 2 + a 2 ) / 2 Ο€ ⁒ βˆ‘ k = 0 ∞ H k ⁑ ( x ) ⁒ H k ⁑ ( a ) 2 k ⁒ k ! Dirac-delta π‘₯ π‘Ž superscript 𝑒 superscript π‘₯ 2 superscript π‘Ž 2 2 πœ‹ superscript subscript π‘˜ 0 Hermite-polynomial-H π‘˜ π‘₯ Hermite-polynomial-H π‘˜ π‘Ž superscript 2 π‘˜ π‘˜ {\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{e^{-(x^{2}+a^{2})/2}}% {\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{H_{k}\left(x\right)H_{k}\left(a\right)}{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