Results of Algebraic and Analytic Methods

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
1.2.E1	${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}=\frac{n!}{(n-k)!k!}}}$	`binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k))`	`Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!]`	Successful	Successful	-	-
1.2.E1	${\displaystyle{\displaystyle\frac{n!}{(n-k)!k!}=\genfrac{(}{)}{0.0pt}{}{n}{n-k% }}}$	`(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	${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{z}{k}=\frac{z(z-1)\cdots(z% -k+1)}{k!}}}$	`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	${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{z+1}{k}=\genfrac{(}{)}{0.0% pt}{}{z}{k}+\genfrac{(}{)}{0.0pt}{}{z}{k-1}}}$	`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	${\displaystyle{\displaystyle\sum^{m}_{k=0}\genfrac{(}{)}{0.0pt}{}{z+k}{k}=% \genfrac{(}{)}{0.0pt}{}{z+m+1}{m}}}$	`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	${\displaystyle{\displaystyle f^{(2)}(x)=\frac{{\mathrm{d}}^{2}f}{{\mathrm{d}x}% ^{2}}}}$	`(f)^(2)*(x)= diff(f, [x$(2)])`	`(f)^(2)*(x)= D[f, {x, 2}]`	Failure	Failure	Fail `0.+3.999999998I <- {f = 2^(1/2)+I2^(1/2), x = 1}` `0.+7.999999996I <- {f = 2^(1/2)+I2^(1/2), x = 2}` `0.+11.99999999I <- {f = 2^(1/2)+I2^(1/2), x = 3}` `0.-3.999999998I <- {f = 2^(1/2)-I2^(1/2), x = 1}` `0.-7.999999996I <- {f = 2^(1/2)-I2^(1/2), x = 2}` `0.-11.99999999I <- {f = 2^(1/2)-I2^(1/2), x = 3}` `0.+3.999999998I <- {f = -2^(1/2)-I2^(1/2), x = 1}` `0.+7.999999996I <- {f = -2^(1/2)-I2^(1/2), x = 2}` `0.+11.99999999I <- {f = -2^(1/2)-I2^(1/2), x = 3}` `0.-3.999999998I <- {f = -2^(1/2)+I2^(1/2), x = 1}` `0.-7.999999996I <- {f = -2^(1/2)+I2^(1/2), x = 2}` `0.-11.99999999I <- {f = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}f}{{\mathrm{d}x}^{2}}=\frac{% \mathrm{d}}{\mathrm{d}x}\left(\frac{\mathrm{d}f}{\mathrm{d}x}\right)}}$	`diff(f, [x$(2)])= diff(diff(f, x), x)`	`D[f, {x, 2}]= D[D[f, x], x]`	Successful	Successful	-	-
1.4.E9	${\displaystyle{\displaystyle f^{(n)}=f^{(n)}(x)}}$	`(f)^(n)= (f)^(n)*(x)`	`(f)^(n)= (f)^(n)*(x)`	Failure	Failure	Fail `-1.414213562-1.414213562I <- {f = 2^(1/2)+I2^(1/2), n = 1, x = 2}` `-2.828427124-2.828427124I <- {f = 2^(1/2)+I2^(1/2), n = 1, x = 3}` `-0.-3.999999998I <- {f = 2^(1/2)+I2^(1/2), n = 2, x = 2}` `-0.-7.999999996I <- {f = 2^(1/2)+I2^(1/2), n = 2, x = 3}` `5.656854245-5.656854245I <- {f = 2^(1/2)+I2^(1/2), n = 3, x = 2}` `11.31370849-11.31370849I <- {f = 2^(1/2)+I2^(1/2), n = 3, x = 3}` `-1.414213562+1.414213562I <- {f = 2^(1/2)-I2^(1/2), n = 1, x = 2}` `-2.828427124+2.828427124I <- {f = 2^(1/2)-I2^(1/2), n = 1, x = 3}` `-0.+3.999999998I <- {f = 2^(1/2)-I2^(1/2), n = 2, x = 2}` `-0.+7.999999996I <- {f = 2^(1/2)-I2^(1/2), n = 2, x = 3}` `5.656854245+5.656854245I <- {f = 2^(1/2)-I2^(1/2), n = 3, x = 2}` `11.31370849+11.31370849I <- {f = 2^(1/2)-I2^(1/2), n = 3, x = 3}` `1.414213562+1.414213562I <- {f = -2^(1/2)-I2^(1/2), n = 1, x = 2}` `2.828427124+2.828427124I <- {f = -2^(1/2)-I2^(1/2), n = 1, x = 3}` `-0.-3.999999998I <- {f = -2^(1/2)-I2^(1/2), n = 2, x = 2}` `-0.-7.999999996I <- {f = -2^(1/2)-I2^(1/2), n = 2, x = 3}` `-5.656854245+5.656854245I <- {f = -2^(1/2)-I2^(1/2), n = 3, x = 2}` `-11.31370849+11.31370849I <- {f = -2^(1/2)-I2^(1/2), n = 3, x = 3}` `1.414213562-1.414213562I <- {f = -2^(1/2)+I2^(1/2), n = 1, x = 2}` `2.828427124-2.828427124I <- {f = -2^(1/2)+I2^(1/2), n = 1, x = 3}` `-0.+3.999999998I <- {f = -2^(1/2)+I2^(1/2), n = 2, x = 2}` `-0.+7.999999996I <- {f = -2^(1/2)+I2^(1/2), n = 2, x = 3}` `-5.656854245-5.656854245I <- {f = -2^(1/2)+I2^(1/2), n = 3, x = 2}` `-11.31370849-11.31370849I <- {f = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle f^{(n)}(x)=\frac{\mathrm{d}}{\mathrm{d}x}f^{(n-1)% }(x)}}$	`(f)^(n)(x)= diff((f)^(n - 1)(x), x)`	`(f)^(n)(x)= D[(f)^(n - 1)(x), x]`	Failure	Failure	Fail `.414213562+1.414213562I <- {f = 2^(1/2)+I2^(1/2), n = 1, x = 1}` `1.828427124+2.828427124I <- {f = 2^(1/2)+I2^(1/2), n = 1, x = 2}` `3.242640686+4.242640686I <- {f = 2^(1/2)+I2^(1/2), n = 1, x = 3}` `-1.414213562+2.585786436I <- {f = 2^(1/2)+I2^(1/2), n = 2, x = 1}` `-1.414213562+6.585786434I <- {f = 2^(1/2)+I2^(1/2), n = 2, x = 2}` `-1.414213562+10.58578643I <- {f = 2^(1/2)+I2^(1/2), n = 2, x = 3}` `-5.656854245+1.656854247I <- {f = 2^(1/2)+I2^(1/2), n = 3, x = 1}` `-11.31370849+7.313708492I <- {f = 2^(1/2)+I2^(1/2), n = 3, x = 2}` `-16.97056274+12.97056274I <- {f = 2^(1/2)+I2^(1/2), n = 3, x = 3}` `.414213562-1.414213562I <- {f = 2^(1/2)-I2^(1/2), n = 1, x = 1}` `1.828427124-2.828427124I <- {f = 2^(1/2)-I2^(1/2), n = 1, x = 2}` `3.242640686-4.242640686I <- {f = 2^(1/2)-I2^(1/2), n = 1, x = 3}` `-1.414213562-2.585786436I <- {f = 2^(1/2)-I2^(1/2), n = 2, x = 1}` `-1.414213562-6.585786434I <- {f = 2^(1/2)-I2^(1/2), n = 2, x = 2}` `-1.414213562-10.58578643I <- {f = 2^(1/2)-I2^(1/2), n = 2, x = 3}` `-5.656854245-1.656854247I <- {f = 2^(1/2)-I2^(1/2), n = 3, x = 1}` `-11.31370849-7.313708492I <- {f = 2^(1/2)-I2^(1/2), n = 3, x = 2}` `-16.97056274-12.97056274I <- {f = 2^(1/2)-I2^(1/2), n = 3, x = 3}` `-2.414213562-1.414213562I <- {f = -2^(1/2)-I2^(1/2), n = 1, x = 1}` `-3.828427124-2.828427124I <- {f = -2^(1/2)-I2^(1/2), n = 1, x = 2}` `-5.242640686-4.242640686I <- {f = -2^(1/2)-I2^(1/2), n = 1, x = 3}` `1.414213562+5.414213560I <- {f = -2^(1/2)-I2^(1/2), n = 2, x = 1}` `1.414213562+9.414213558I <- {f = -2^(1/2)-I2^(1/2), n = 2, x = 2}` `1.414213562+13.41421355I <- {f = -2^(1/2)-I2^(1/2), n = 2, x = 3}` `5.656854245-9.656854243I <- {f = -2^(1/2)-I2^(1/2), n = 3, x = 1}` `11.31370849-15.31370849I <- {f = -2^(1/2)-I2^(1/2), n = 3, x = 2}` `16.97056274-20.97056274I <- {f = -2^(1/2)-I2^(1/2), n = 3, x = 3}` `-2.414213562+1.414213562I <- {f = -2^(1/2)+I2^(1/2), n = 1, x = 1}` `-3.828427124+2.828427124I <- {f = -2^(1/2)+I2^(1/2), n = 1, x = 2}` `-5.242640686+4.242640686I <- {f = -2^(1/2)+I2^(1/2), n = 1, x = 3}` `1.414213562-5.414213560I <- {f = -2^(1/2)+I2^(1/2), n = 2, x = 1}` `1.414213562-9.414213558I <- {f = -2^(1/2)+I2^(1/2), n = 2, x = 2}` `1.414213562-13.41421355I <- {f = -2^(1/2)+I2^(1/2), n = 2, x = 3}` `5.656854245+9.656854243I <- {f = -2^(1/2)+I2^(1/2), n = 3, x = 1}` `11.31370849+15.31370849I <- {f = -2^(1/2)+I2^(1/2), n = 3, x = 2}` `16.97056274+20.97056274I <- {f = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle\int fg\mathrm{d}x=\left(\int f\mathrm{d}x\right)g% -\int\left(\int f\mathrm{d}x\right)\frac{\mathrm{d}g}{\mathrm{d}x}\mathrm{d}x}}$	`int(fg, x)=(int(f, x)) g - int((int(f, x))* diff(g, x), x)`	`Integrate[fg, x]=(Integrate[f, x]) g - Integrate[(Integrate[f, x])* D[g, x], x]`	Successful	Successful	-	-
1.4.E37	${\displaystyle{\displaystyle R_{n}=\frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(% t)\mathrm{d}t}}$	`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	${\displaystyle{\displaystyle\frac{\partial f}{\partial y}=D_{y}f}}$	`diff(f, y)= D[y]*f`	`D[f, y]= Subscript[D, y]*f`	Failure	Failure	Fail `-0.-3.999999998I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2)}` `-3.999999998-0.I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2)}` `-0.+3.999999998I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2)}` `3.999999998-0.I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2)}` `-3.999999998-0.I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2)}` `-0.+3.999999998I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2)}` `3.999999998-0.I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2)}` `-0.-3.999999998I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2)}` `-0.+3.999999998I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2)}` `3.999999998-0.I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2)}` `-0.-3.999999998I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2)}` `-3.999999998-0.I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2)}` `3.999999998-0.I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2)}` `-0.-3.999999998I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2)}` `-3.999999998-0.I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2)}` `-0.+3.999999998I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle D_{y}f=f_{y}}}$	`D[y]*f = f[y]`	`Subscript[D, y]*f = Subscript[f, y]`	Failure	Failure	Fail `-1.414213562+2.585786436I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-1.414213562+5.414213560I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `1.414213562+5.414213560I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `1.414213562+2.585786436I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `2.585786436-1.414213562I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `2.585786436+1.414213562I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `5.414213560+1.414213562I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `5.414213560-1.414213562I <- {f = 2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-1.414213562-5.414213560I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-1.414213562-2.585786436I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `1.414213562-2.585786436I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `1.414213562-5.414213560I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-5.414213560-1.414213562I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-5.414213560+1.414213562I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `-2.585786436+1.414213562I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `-2.585786436-1.414213562I <- {f = 2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `2.585786436-1.414213562I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `2.585786436+1.414213562I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `5.414213560+1.414213562I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `5.414213560-1.414213562I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-1.414213562-5.414213560I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-1.414213562-2.585786436I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `1.414213562-2.585786436I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `1.414213562-5.414213560I <- {f = 2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-5.414213560-1.414213562I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-5.414213560+1.414213562I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `-2.585786436+1.414213562I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `-2.585786436-1.414213562I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-1.414213562+2.585786436I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-1.414213562+5.414213560I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `1.414213562+5.414213560I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `1.414213562+2.585786436I <- {f = 2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-1.414213562-5.414213560I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-1.414213562-2.585786436I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `1.414213562-2.585786436I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `1.414213562-5.414213560I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-5.414213560-1.414213562I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-5.414213560+1.414213562I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `-2.585786436+1.414213562I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `-2.585786436-1.414213562I <- {f = -2^(1/2)-I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-1.414213562+2.585786436I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-1.414213562+5.414213560I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `1.414213562+5.414213560I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `1.414213562+2.585786436I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `2.585786436-1.414213562I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `2.585786436+1.414213562I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `5.414213560+1.414213562I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `5.414213560-1.414213562I <- {f = -2^(1/2)-I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-5.414213560-1.414213562I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-5.414213560+1.414213562I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `-2.585786436+1.414213562I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `-2.585786436-1.414213562I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)+I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-1.414213562+2.585786436I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-1.414213562+5.414213560I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `1.414213562+5.414213560I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `1.414213562+2.585786436I <- {f = -2^(1/2)+I2^(1/2), D[y] = 2^(1/2)-I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `2.585786436-1.414213562I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `2.585786436+1.414213562I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `5.414213560+1.414213562I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `5.414213560-1.414213562I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)-I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}` `-1.414213562-5.414213560I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = 2^(1/2)+I2^(1/2)}` `-1.414213562-2.585786436I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = 2^(1/2)-I2^(1/2)}` `1.414213562-2.585786436I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = -2^(1/2)-I2^(1/2)}` `1.414213562-5.414213560I <- {f = -2^(1/2)+I2^(1/2), D[y] = -2^(1/2)+I2^(1/2), f[y] = -2^(1/2)+I2^(1/2)}`	Successful
1.5#Ex3	${\displaystyle{\displaystyle x=r\cos\phi}}$	`x = r*cos(phi)`	`x = r*Cos[\[Phi]]`	Failure	Failure	Fail `-2.183489624+2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 1}` `-1.183489624+2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 2}` `-.183489624+2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 3}` `3.222746490+3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 1}` `4.222746490+3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 2}` `5.222746490+3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 3}` `4.183489624-2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 1}` `5.183489624-2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 2}` `6.183489624-2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 3}` `-1.222746490-3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 1}` `-.222746490-3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 2}` `.777253510-3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 3}` `3.222746490-3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 1}` `4.222746490-3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 2}` `5.222746490-3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 3}` `-2.183489624-2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 1}` `-1.183489624-2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 2}` `-.183489624-2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 3}` `-1.222746490+3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 1}` `-.222746490+3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 2}` `.777253510+3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 3}` `4.183489624+2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 1}` `5.183489624+2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 2}` `6.183489624+2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 3}` `-2.183489624+2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 1}` `-1.183489624+2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 2}` `-.183489624+2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 3}` `3.222746490+3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 1}` `4.222746490+3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 2}` `5.222746490+3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 3}` `4.183489624-2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 1}` `5.183489624-2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 2}` `6.183489624-2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 3}` `-1.222746490-3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 1}` `-.222746490-3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 2}` `.777253510-3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 3}` `3.222746490-3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 1}` `4.222746490-3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 2}` `5.222746490-3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 3}` `-2.183489624-2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 1}` `-1.183489624-2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 2}` `-.183489624-2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 3}` `-1.222746490+3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 1}` `-.222746490+3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 2}` `.777253510+3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 3}` `4.183489624+2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 1}` `5.183489624+2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 2}` `6.183489624+2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 3}`	Fail `Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.5#Ex4	${\displaystyle{\displaystyle y=r\sin\phi}}$	`y = r*sin(phi)`	`y = r*Sin[\[Phi]]`	Failure	Failure	Fail `-1.615975576-3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 1}` `-.615975576-3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 2}` `.384024424-3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 3}` `-2.469485904+2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 1}` `-1.469485904+2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 2}` `-.469485904+2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 3}` `3.615975576+3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 1}` `4.615975576+3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 2}` `5.615975576+3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 3}` `4.469485904-2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 1}` `5.469485904-2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 2}` `6.469485904-2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 3}` `-2.469485904-2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 1}` `-1.469485904-2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 2}` `-.469485904-2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 3}` `-1.615975576+3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 1}` `-.615975576+3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 2}` `.384024424+3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 3}` `4.469485904+2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 1}` `5.469485904+2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 2}` `6.469485904+2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 3}` `3.615975576-3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 1}` `4.615975576-3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 2}` `5.615975576-3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 3}` `3.615975576+3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 1}` `4.615975576+3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 2}` `5.615975576+3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 3}` `4.469485904-2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 1}` `5.469485904-2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 2}` `6.469485904-2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 3}` `-1.615975576-3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 1}` `-.615975576-3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 2}` `.384024424-3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 3}` `-2.469485904+2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 1}` `-1.469485904+2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 2}` `-.469485904+2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 3}` `4.469485904+2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 1}` `5.469485904+2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 2}` `6.469485904+2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 3}` `3.615975576-3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 1}` `4.615975576-3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 2}` `5.615975576-3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 3}` `-2.469485904-2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 1}` `-1.469485904-2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 2}` `-.469485904-2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 3}` `-1.615975576+3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 1}` `-.615975576+3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 2}` `.384024424+3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 3}`	Fail `Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.5.E13	${\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}=\frac{{\partial}^{2}f}{{\partial r}^{2}}+% \frac{1}{r}\frac{\partial f}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}f}% {{\partial\phi}^{2}}}}$	`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	${\displaystyle{\displaystyle x=r\cos\phi}}$	`x = r*cos(phi)`	`x = r*Cos[\[Phi]]`	Failure	Failure	Fail `-2.183489624+2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 1}` `-1.183489624+2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 2}` `-.183489624+2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 3}` `3.222746490+3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 1}` `4.222746490+3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 2}` `5.222746490+3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 3}` `4.183489624-2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 1}` `5.183489624-2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 2}` `6.183489624-2.222746490I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 3}` `-1.222746490-3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 1}` `-.222746490-3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 2}` `.777253510-3.183489624I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 3}` `3.222746490-3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 1}` `4.222746490-3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 2}` `5.222746490-3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 3}` `-2.183489624-2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 1}` `-1.183489624-2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 2}` `-.183489624-2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 3}` `-1.222746490+3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 1}` `-.222746490+3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 2}` `.777253510+3.183489624I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 3}` `4.183489624+2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 1}` `5.183489624+2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 2}` `6.183489624+2.222746490I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 3}` `-2.183489624+2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 1}` `-1.183489624+2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 2}` `-.183489624+2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 3}` `3.222746490+3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 1}` `4.222746490+3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 2}` `5.222746490+3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 3}` `4.183489624-2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 1}` `5.183489624-2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 2}` `6.183489624-2.222746490I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 3}` `-1.222746490-3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 1}` `-.222746490-3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 2}` `.777253510-3.183489624I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 3}` `3.222746490-3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 1}` `4.222746490-3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 2}` `5.222746490-3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), x = 3}` `-2.183489624-2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 1}` `-1.183489624-2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 2}` `-.183489624-2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), x = 3}` `-1.222746490+3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 1}` `-.222746490+3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 2}` `.777253510+3.183489624I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), x = 3}` `4.183489624+2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 1}` `5.183489624+2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 2}` `6.183489624+2.222746490I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), x = 3}`	Fail `Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.5#Ex6	${\displaystyle{\displaystyle y=r\sin\phi}}$	`y = r*sin(phi)`	`y = r*Sin[\[Phi]]`	Failure	Failure	Fail `-1.615975576-3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 1}` `-.615975576-3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 2}` `.384024424-3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 3}` `-2.469485904+2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 1}` `-1.469485904+2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 2}` `-.469485904+2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 3}` `3.615975576+3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 1}` `4.615975576+3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 2}` `5.615975576+3.469485904I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 3}` `4.469485904-2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 1}` `5.469485904-2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 2}` `6.469485904-2.615975576I <- {phi = 2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 3}` `-2.469485904-2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 1}` `-1.469485904-2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 2}` `-.469485904-2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 3}` `-1.615975576+3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 1}` `-.615975576+3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 2}` `.384024424+3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 3}` `4.469485904+2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 1}` `5.469485904+2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 2}` `6.469485904+2.615975576I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 3}` `3.615975576-3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 1}` `4.615975576-3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 2}` `5.615975576-3.469485904I <- {phi = 2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 3}` `3.615975576+3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 1}` `4.615975576+3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 2}` `5.615975576+3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 3}` `4.469485904-2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 1}` `5.469485904-2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 2}` `6.469485904-2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 3}` `-1.615975576-3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 1}` `-.615975576-3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 2}` `.384024424-3.469485904I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 3}` `-2.469485904+2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 1}` `-1.469485904+2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 2}` `-.469485904+2.615975576I <- {phi = -2^(1/2)-I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 3}` `4.469485904+2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 1}` `5.469485904+2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 2}` `6.469485904+2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)+I2^(1/2), y = 3}` `3.615975576-3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 1}` `4.615975576-3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 2}` `5.615975576-3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = 2^(1/2)-I2^(1/2), y = 3}` `-2.469485904-2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 1}` `-1.469485904-2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 2}` `-.469485904-2.615975576I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)-I2^(1/2), y = 3}` `-1.615975576+3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 1}` `-.615975576+3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 2}` `.384024424+3.469485904I <- {phi = -2^(1/2)+I2^(1/2), r = -2^(1/2)+I2^(1/2), y = 3}`	Fail `Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.5#Ex8	${\displaystyle{\displaystyle x=\rho\sin\theta\cos\phi}}$	`x = rhosin(theta)cos(phi)`	`x = \[Rho]Sin[\[Theta]]Cos[\[Phi]]`	Failure	Failure	Fail `-6.520130316+3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-5.520130316+3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-4.520130316+3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-5.178651817+5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-4.178651817+5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-3.178651817+5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `8.520130316-3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `9.520130316-3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `10.52013032-3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `7.178651817-5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `8.178651817-5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `9.178651817-5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `4.821663559+7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `5.821663559+7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `6.821663559+7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `6.742972580+6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `7.742972580+6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `8.742972580+6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-2.821663559-7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-1.821663559-7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-.821663559-7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-4.742972580-6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-3.742972580-6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-2.742972580-6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `8.520130316-3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `9.520130316-3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `10.52013032-3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `7.178651817-5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `8.178651817-5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `9.178651817-5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-6.520130316+3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-5.520130316+3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-4.520130316+3.821663559I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-5.178651817+5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-4.178651817+5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-3.178651817+5.742972580I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `-2.821663559-7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-1.821663559-7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-.821663559-7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-4.742972580-6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-3.742972580-6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-2.742972580-6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `4.821663559+7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `5.821663559+7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `6.821663559+7.520130316I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `6.742972580+6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `7.742972580+6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `8.742972580+6.178651817I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `6.742972580-6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `7.742972580-6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `8.742972580-6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `4.821663559-7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `5.821663559-7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `6.821663559-7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-4.742972580+6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-3.742972580+6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-2.742972580+6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-2.821663559+7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-1.821663559+7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-.821663559+7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `-5.178651817-5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-4.178651817-5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-3.178651817-5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-6.520130316-3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-5.520130316-3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-4.520130316-3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `7.178651817+5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `8.178651817+5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `9.178651817+5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `8.520130316+3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `9.520130316+3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `10.52013032+3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `-4.742972580+6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-3.742972580+6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-2.742972580+6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-2.821663559+7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-1.821663559+7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-.821663559+7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `6.742972580-6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `7.742972580-6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `8.742972580-6.178651817I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `4.821663559-7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `5.821663559-7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `6.821663559-7.520130316I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `7.178651817+5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `8.178651817+5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `9.178651817+5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `8.520130316+3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `9.520130316+3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `10.52013032+3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-5.178651817-5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-4.178651817-5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-3.178651817-5.742972580I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-6.520130316-3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-5.520130316-3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-4.520130316-3.821663559I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `-6.520130316+3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-5.520130316+3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-4.520130316+3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-5.178651817+5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-4.178651817+5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-3.178651817+5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `8.520130316-3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `9.520130316-3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `10.52013032-3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `7.178651817-5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `8.178651817-5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `9.178651817-5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `4.821663559+7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `5.821663559+7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `6.821663559+7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `6.742972580+6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `7.742972580+6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `8.742972580+6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-2.821663559-7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-1.821663559-7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-.821663559-7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-4.742972580-6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-3.742972580-6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-2.742972580-6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `8.520130316-3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `9.520130316-3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `10.52013032-3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `7.178651817-5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `8.178651817-5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `9.178651817-5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-6.520130316+3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-5.520130316+3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-4.520130316+3.821663559I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-5.178651817+5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-4.178651817+5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-3.178651817+5.742972580I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `-2.821663559-7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-1.821663559-7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-.821663559-7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-4.742972580-6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-3.742972580-6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-2.742972580-6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `4.821663559+7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `5.821663559+7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `6.821663559+7.520130316I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `6.742972580+6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `7.742972580+6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `8.742972580+6.178651817I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `6.742972580-6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `7.742972580-6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `8.742972580-6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `4.821663559-7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `5.821663559-7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `6.821663559-7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-4.742972580+6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-3.742972580+6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-2.742972580+6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-2.821663559+7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-1.821663559+7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-.821663559+7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `-5.178651817-5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-4.178651817-5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-3.178651817-5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-6.520130316-3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-5.520130316-3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-4.520130316-3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `7.178651817+5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `8.178651817+5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `9.178651817+5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `8.520130316+3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `9.520130316+3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `10.52013032+3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `-4.742972580+6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-3.742972580+6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-2.742972580+6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-2.821663559+7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-1.821663559+7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-.821663559+7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `6.742972580-6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `7.742972580-6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `8.742972580-6.178651817I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `4.821663559-7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `5.821663559-7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `6.821663559-7.520130316I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `7.178651817+5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `8.178651817+5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `9.178651817+5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `8.520130316+3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `9.520130316+3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `10.52013032+3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-5.178651817-5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-4.178651817-5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-3.178651817-5.742972580I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-6.520130316-3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-5.520130316-3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-4.520130316-3.821663559I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}`	Fail `Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.5#Ex9	${\displaystyle{\displaystyle y=\rho\sin\theta\sin\phi}}$	`y = rhosin(theta)sin(phi)`	`y = \[Rho]Sin[\[Theta]]Sin[\[Phi]]`	Failure	Failure	Fail `-3.581407255-8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-2.581407255-8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-1.581407255-8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-5.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-4.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-3.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `5.581407255+8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `6.581407255+8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `7.581407255+8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `7.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `8.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `9.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `-7.254122865+4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-6.254122865+4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-5.254122865+4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-5.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-4.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-3.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `9.254122865-4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `10.25412286-4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `11.25412286-4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `7.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `8.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `9.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `5.581407255+8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `6.581407255+8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `7.581407255+8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `7.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `8.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `9.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-3.581407255-8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-2.581407255-8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-1.581407255-8.254122865I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-5.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-4.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-3.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `9.254122865-4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `10.25412286-4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `11.25412286-4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `7.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `8.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `9.675321591-6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-7.254122865+4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-6.254122865+4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-5.254122865+4.581407255I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-5.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-4.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-3.675321591+6.675321591I <- {phi = 2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `-5.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-4.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-3.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-7.254122865-4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-6.254122865-4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-5.254122865-4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `7.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `8.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `9.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `9.254122865+4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `10.25412286+4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `11.25412286+4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `-5.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-4.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-3.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-3.581407255+8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-2.581407255+8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-1.581407255+8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `7.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `8.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `9.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `5.581407255-8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `6.581407255-8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `7.581407255-8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `7.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `8.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `9.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `9.254122865+4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `10.25412286+4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `11.25412286+4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-5.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-4.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-3.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-7.254122865-4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-6.254122865-4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-5.254122865-4.581407255I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `7.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `8.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `9.675321591-6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `5.581407255-8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `6.581407255-8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `7.581407255-8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-5.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-4.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-3.675321591+6.675321591I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-3.581407255+8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-2.581407255+8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-1.581407255+8.254122865I <- {phi = 2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `5.581407255+8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `6.581407255+8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `7.581407255+8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `7.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `8.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `9.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-3.581407255-8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-2.581407255-8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-1.581407255-8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-5.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-4.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-3.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `9.254122865-4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `10.25412286-4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `11.25412286-4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `7.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `8.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `9.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-7.254122865+4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-6.254122865+4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-5.254122865+4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-5.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-4.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-3.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `-3.581407255-8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-2.581407255-8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-1.581407255-8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-5.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-4.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-3.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `5.581407255+8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `6.581407255+8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `7.581407255+8.254122865I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `7.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `8.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `9.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `-7.254122865+4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-6.254122865+4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-5.254122865+4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-5.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-4.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-3.675321591+6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `9.254122865-4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `10.25412286-4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `11.25412286-4.581407255I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `7.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `8.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `9.675321591-6.675321591I <- {phi = -2^(1/2)-I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `7.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `8.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `9.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `9.254122865+4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `10.25412286+4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `11.25412286+4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-5.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-4.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-3.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-7.254122865-4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-6.254122865-4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-5.254122865-4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `7.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `8.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `9.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `5.581407255-8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `6.581407255-8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `7.581407255-8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-5.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-4.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-3.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-3.581407255+8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-2.581407255+8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-1.581407255+8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `-5.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-4.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-3.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-7.254122865-4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-6.254122865-4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-5.254122865-4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `7.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `8.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `9.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `9.254122865+4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `10.25412286+4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `11.25412286+4.581407255I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `-5.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-4.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-3.675321591+6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-3.581407255+8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-2.581407255+8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-1.581407255+8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `7.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `8.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `9.675321591-6.675321591I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `5.581407255-8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `6.581407255-8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `7.581407255-8.254122865I <- {phi = -2^(1/2)+I2^(1/2), rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}`	Fail `Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.5#Ex10	${\displaystyle{\displaystyle z=\rho\cos\theta}}$	`z = rho*cos(theta)`	`z = \[Rho]*Cos[\[Theta]]`	Failure	Failure	Fail `-1.769276062+3.636960052I <- {rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-1.769276062+.808532928I <- {rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-4.597703186+.808532928I <- {rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-4.597703186+3.636960052I <- {rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `3.636960052-1.769276062I <- {rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `3.636960052-4.597703186I <- {rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `.808532928-4.597703186I <- {rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `.808532928-1.769276062I <- {rho = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-1.769276062+3.636960052I <- {rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-1.769276062+.808532928I <- {rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-4.597703186+.808532928I <- {rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-4.597703186+3.636960052I <- {rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `3.636960052-1.769276062I <- {rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `3.636960052-4.597703186I <- {rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `.808532928-4.597703186I <- {rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `.808532928-1.769276062I <- {rho = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `3.636960052+4.597703186I <- {rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `3.636960052+1.769276062I <- {rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `.808532928+1.769276062I <- {rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `.808532928+4.597703186I <- {rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-1.769276062-.808532928I <- {rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-1.769276062-3.636960052I <- {rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-4.597703186-3.636960052I <- {rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-4.597703186-.808532928I <- {rho = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `3.636960052+4.597703186I <- {rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `3.636960052+1.769276062I <- {rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `.808532928+1.769276062I <- {rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `.808532928+4.597703186I <- {rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-1.769276062-.808532928I <- {rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-1.769276062-3.636960052I <- {rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-4.597703186-3.636960052I <- {rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-4.597703186-.808532928I <- {rho = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `4.597703186-.808532928I <- {rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `4.597703186-3.636960052I <- {rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `1.769276062-3.636960052I <- {rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `1.769276062-.808532928I <- {rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-.808532928+4.597703186I <- {rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-.808532928+1.769276062I <- {rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-3.636960052+1.769276062I <- {rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-3.636960052+4.597703186I <- {rho = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `4.597703186-.808532928I <- {rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `4.597703186-3.636960052I <- {rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `1.769276062-3.636960052I <- {rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `1.769276062-.808532928I <- {rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-.808532928+4.597703186I <- {rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-.808532928+1.769276062I <- {rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-3.636960052+1.769276062I <- {rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-3.636960052+4.597703186I <- {rho = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-.808532928-1.769276062I <- {rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-.808532928-4.597703186I <- {rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-3.636960052-4.597703186I <- {rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-3.636960052-1.769276062I <- {rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `4.597703186+3.636960052I <- {rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `4.597703186+.808532928I <- {rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `1.769276062+.808532928I <- {rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `1.769276062+3.636960052I <- {rho = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-.808532928-1.769276062I <- {rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-.808532928-4.597703186I <- {rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-3.636960052-4.597703186I <- {rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-3.636960052-1.769276062I <- {rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `4.597703186+3.636960052I <- {rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `4.597703186+.808532928I <- {rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `1.769276062+.808532928I <- {rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `1.769276062+3.636960052I <- {rho = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}+\frac{{\partial}^{2}f}{{\partial z}^{2}}={% \frac{1}{\rho^{2}}\frac{\partial}{\partial\rho}\left(\rho^{2}\frac{\partial f}% {\partial\rho}\right)+\frac{1}{\rho^{2}{\sin^{2}}\theta}\frac{{\partial}^{2}f}% {{\partial\phi}^{2}}}+\frac{1}{\rho^{2}\sin\theta}\frac{\partial}{\partial% \theta}\left(\sin\theta\frac{\partial f}{\partial\theta}\right)}}$	`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	${\displaystyle{\displaystyle\frac{\partial f}{\partial x}=\frac{\partial f}{% \partial y}}}$	`diff(f, x)= diff(f, y)`	`D[f, x]= D[f, y]`	Successful	Successful	-	-
1.5.E23	${\displaystyle{\displaystyle\left\|\int_{c_{1}}^{d}(\ifrac{\partial f}{\partial x% })\mathrm{d}y\right\|<\epsilon}}$	`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	${\displaystyle{\displaystyle\epsilon_{123}=\epsilon_{312}}}$	`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 `2.828427124I <- {LeviCivita[1,2,3] = 2^(1/2)+I2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I2^(1/2)}` `2.828427124+2.828427124I <- {LeviCivita[1,2,3] = 2^(1/2)+I2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I2^(1/2)}` `2.828427124 <- {LeviCivita[1,2,3] = 2^(1/2)+I2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I2^(1/2)}` `-2.828427124I <- {LeviCivita[1,2,3] = 2^(1/2)-I2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I2^(1/2)}` `2.828427124 <- {LeviCivita[1,2,3] = 2^(1/2)-I2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I2^(1/2)}` `2.828427124-2.828427124I <- {LeviCivita[1,2,3] = 2^(1/2)-I2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I2^(1/2)}` `-2.828427124-2.828427124I <- {LeviCivita[1,2,3] = -2^(1/2)-I2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I2^(1/2)}` `-2.828427124 <- {LeviCivita[1,2,3] = -2^(1/2)-I2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I2^(1/2)}` `-2.828427124I <- {LeviCivita[1,2,3] = -2^(1/2)-I2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I2^(1/2)}` `-2.828427124 <- {LeviCivita[1,2,3] = -2^(1/2)+I2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I2^(1/2)}` `-2.828427124+2.828427124I <- {LeviCivita[1,2,3] = -2^(1/2)+I2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I2^(1/2)}` `2.828427124I <- {LeviCivita[1,2,3] = -2^(1/2)+I2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I2^(1/2)}`	-
1.6#Ex15	${\displaystyle{\displaystyle\epsilon_{312}=1}}$	`LeviCivita[3, 1, 2]= 1`	`Part[LeviCivitaTensor[3,List], 3, 1, 2]= 1`	Failure	Successful	Fail `.414213562+1.414213562I <- {LeviCivita[3,1,2] = 2^(1/2)+I2^(1/2)}` `.414213562-1.414213562I <- {LeviCivita[3,1,2] = 2^(1/2)-I2^(1/2)}` `-2.414213562-1.414213562I <- {LeviCivita[3,1,2] = -2^(1/2)-I2^(1/2)}` `-2.414213562+1.414213562I <- {LeviCivita[3,1,2] = -2^(1/2)+I2^(1/2)}`	-
1.6#Ex16	${\displaystyle{\displaystyle\epsilon_{213}=\epsilon_{321}}}$	`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 `2.828427124I <- {LeviCivita[2,1,3] = 2^(1/2)+I2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I2^(1/2)}` `2.828427124+2.828427124I <- {LeviCivita[2,1,3] = 2^(1/2)+I2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I2^(1/2)}` `2.828427124 <- {LeviCivita[2,1,3] = 2^(1/2)+I2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I2^(1/2)}` `-2.828427124I <- {LeviCivita[2,1,3] = 2^(1/2)-I2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I2^(1/2)}` `2.828427124 <- {LeviCivita[2,1,3] = 2^(1/2)-I2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I2^(1/2)}` `2.828427124-2.828427124I <- {LeviCivita[2,1,3] = 2^(1/2)-I2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I2^(1/2)}` `-2.828427124-2.828427124I <- {LeviCivita[2,1,3] = -2^(1/2)-I2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I2^(1/2)}` `-2.828427124 <- {LeviCivita[2,1,3] = -2^(1/2)-I2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I2^(1/2)}` `-2.828427124I <- {LeviCivita[2,1,3] = -2^(1/2)-I2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I2^(1/2)}` `-2.828427124 <- {LeviCivita[2,1,3] = -2^(1/2)+I2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I2^(1/2)}` `-2.828427124+2.828427124I <- {LeviCivita[2,1,3] = -2^(1/2)+I2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I2^(1/2)}` `2.828427124I <- {LeviCivita[2,1,3] = -2^(1/2)+I2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I2^(1/2)}`	-
1.6#Ex16	${\displaystyle{\displaystyle\epsilon_{321}=-1}}$	`LeviCivita[3, 2, 1]= - 1`	`Part[LeviCivitaTensor[3,List], 3, 2, 1]= - 1`	Failure	Successful	Fail `2.414213562+1.414213562I <- {LeviCivita[3,2,1] = 2^(1/2)+I2^(1/2)}` `2.414213562-1.414213562I <- {LeviCivita[3,2,1] = 2^(1/2)-I2^(1/2)}` `-.414213562-1.414213562I <- {LeviCivita[3,2,1] = -2^(1/2)-I2^(1/2)}` `-.414213562+1.414213562I <- {LeviCivita[3,2,1] = -2^(1/2)+I2^(1/2)}`	-
1.6#Ex17	${\displaystyle{\displaystyle\epsilon_{221}=0}}$	`LeviCivita[2, 2, 1]= 0`	`Part[LeviCivitaTensor[3,List], 2, 2, 1]= 0`	Failure	Successful	Fail `1.414213562+1.414213562I <- {LeviCivita[2,2,1] = 2^(1/2)+I2^(1/2)}` `1.414213562-1.414213562I <- {LeviCivita[2,2,1] = 2^(1/2)-I2^(1/2)}` `-1.414213562-1.414213562I <- {LeviCivita[2,2,1] = -2^(1/2)-I2^(1/2)}` `-1.414213562+1.414213562I <- {LeviCivita[2,2,1] = -2^(1/2)+I2^(1/2)}`	-
1.6.E16	${\displaystyle{\displaystyle\epsilon_{jk\ell}\epsilon_{\ell mn}=\delta_{j,m}% \delta_{k,n}-\delta_{j,n}\delta_{k,m}}}$	`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	${\displaystyle{\displaystyle\mathbf{T}_{u}=\frac{\partial x}{\partial u}(u_{0}% ,v_{0})\mathbf{i}+\frac{\partial y}{\partial u}(u_{0},v_{0})\mathbf{j}+\frac{% \partial z}{\partial u}(u_{0},v_{0})\mathbf{k}}}$	`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+1.414213562I <- {T[u] = 2^(1/2)+I2^(1/2)}` `1.414213562-1.414213562I <- {T[u] = 2^(1/2)-I2^(1/2)}` `-1.414213562-1.414213562I <- {T[u] = -2^(1/2)-I2^(1/2)}` `-1.414213562+1.414213562I <- {T[u] = -2^(1/2)+I2^(1/2)}`	Error
1.6.E47	${\displaystyle{\displaystyle\mathbf{T}_{v}=\frac{\partial x}{\partial v}(u_{0}% ,v_{0})\mathbf{i}+\frac{\partial y}{\partial v}(u_{0},v_{0})\mathbf{j}+\frac{% \partial z}{\partial v}(u_{0},v_{0})\mathbf{k}}}$	`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+1.414213562I <- {T[v] = 2^(1/2)+I2^(1/2)}` `1.414213562-1.414213562I <- {T[v] = 2^(1/2)-I2^(1/2)}` `-1.414213562-1.414213562I <- {T[v] = -2^(1/2)-I2^(1/2)}` `-1.414213562+1.414213562I <- {T[v] = -2^(1/2)+I2^(1/2)}`	Error
1.8.E16	${\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega}={% \sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega% }\cos\left(2n\pi x\right)\right)}}}$	`sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity)=sqrt((Pi)/(omega))(1 + 2sum(exp(- (n)^(2)* (Pi)^(2)/ omega)cos(2nPix), n = 1..infinity))`	`Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}]=Sqrt[Divide[Pi,\[Omega]]](1 + 2Sum[Exp[- (n)^(2)* (Pi)^(2)/ \[Omega]]Cos[2nPix], {n, 1, Infinity}])`	Failure	Successful	Skip	-
1.9#Ex1	${\displaystyle{\displaystyle\Re z=x}}$	`Re(z)= x`	`Re[z]= x`	Failure	Failure	Fail `.414213562 <- {z = 2^(1/2)+I2^(1/2), x = 1}` `-.585786438 <- {z = 2^(1/2)+I2^(1/2), x = 2}` `-1.585786438 <- {z = 2^(1/2)+I2^(1/2), x = 3}` `.414213562 <- {z = 2^(1/2)-I2^(1/2), x = 1}` `-.585786438 <- {z = 2^(1/2)-I2^(1/2), x = 2}` `-1.585786438 <- {z = 2^(1/2)-I2^(1/2), x = 3}` `-2.414213562 <- {z = -2^(1/2)-I2^(1/2), x = 1}` `-3.414213562 <- {z = -2^(1/2)-I2^(1/2), x = 2}` `-4.414213562 <- {z = -2^(1/2)-I2^(1/2), x = 3}` `-2.414213562 <- {z = -2^(1/2)+I2^(1/2), x = 1}` `-3.414213562 <- {z = -2^(1/2)+I2^(1/2), x = 2}` `-4.414213562 <- {z = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle\Im z=y}}$	`Im(z)= y`	`Im[z]= y`	Failure	Failure	Fail `.414213562 <- {z = 2^(1/2)+I2^(1/2), y = 1}` `-.585786438 <- {z = 2^(1/2)+I2^(1/2), y = 2}` `-1.585786438 <- {z = 2^(1/2)+I2^(1/2), y = 3}` `-2.414213562 <- {z = 2^(1/2)-I2^(1/2), y = 1}` `-3.414213562 <- {z = 2^(1/2)-I2^(1/2), y = 2}` `-4.414213562 <- {z = 2^(1/2)-I2^(1/2), y = 3}` `-2.414213562 <- {z = -2^(1/2)-I2^(1/2), y = 1}` `-3.414213562 <- {z = -2^(1/2)-I2^(1/2), y = 2}` `-4.414213562 <- {z = -2^(1/2)-I2^(1/2), y = 3}` `.414213562 <- {z = -2^(1/2)+I2^(1/2), y = 1}` `-.585786438 <- {z = -2^(1/2)+I2^(1/2), y = 2}` `-1.585786438 <- {z = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle x=r\cos\theta}}$	`x = r*cos(theta)`	`x = r*Cos[\[Theta]]`	Failure	Failure	Fail `-2.183489624+2.222746490I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-1.183489624+2.222746490I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `-.183489624+2.222746490I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `3.222746490-3.183489624I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `4.222746490-3.183489624I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `5.222746490-3.183489624I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-2.183489624+2.222746490I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-1.183489624+2.222746490I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `-.183489624+2.222746490I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `3.222746490-3.183489624I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `4.222746490-3.183489624I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `5.222746490-3.183489624I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `3.222746490+3.183489624I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `4.222746490+3.183489624I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `5.222746490+3.183489624I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-2.183489624-2.222746490I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-1.183489624-2.222746490I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `-.183489624-2.222746490I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `3.222746490+3.183489624I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `4.222746490+3.183489624I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `5.222746490+3.183489624I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-2.183489624-2.222746490I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-1.183489624-2.222746490I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `-.183489624-2.222746490I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `4.183489624-2.222746490I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `5.183489624-2.222746490I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `6.183489624-2.222746490I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `-1.222746490+3.183489624I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `-.222746490+3.183489624I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `.777253510+3.183489624I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `4.183489624-2.222746490I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `5.183489624-2.222746490I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `6.183489624-2.222746490I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `-1.222746490+3.183489624I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `-.222746490+3.183489624I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `.777253510+3.183489624I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}` `-1.222746490-3.183489624I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 1}` `-.222746490-3.183489624I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 2}` `.777253510-3.183489624I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), x = 3}` `4.183489624+2.222746490I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 1}` `5.183489624+2.222746490I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 2}` `6.183489624+2.222746490I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), x = 3}` `-1.222746490-3.183489624I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 1}` `-.222746490-3.183489624I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 2}` `.777253510-3.183489624I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), x = 3}` `4.183489624+2.222746490I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 1}` `5.183489624+2.222746490I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 2}` `6.183489624+2.222746490I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), x = 3}`	Fail `Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.9#Ex4	${\displaystyle{\displaystyle y=r\sin\theta}}$	`y = r*sin(theta)`	`y = r*Sin[\[Theta]]`	Failure	Failure	Fail `-1.615975576-3.469485904I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-.615975576-3.469485904I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `.384024424-3.469485904I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-2.469485904-2.615975576I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-1.469485904-2.615975576I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `-.469485904-2.615975576I <- {r = 2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `3.615975576+3.469485904I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `4.615975576+3.469485904I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `5.615975576+3.469485904I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `4.469485904+2.615975576I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `5.469485904+2.615975576I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `6.469485904+2.615975576I <- {r = 2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `-2.469485904+2.615975576I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `-1.469485904+2.615975576I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `-.469485904+2.615975576I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `-1.615975576+3.469485904I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `-.615975576+3.469485904I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `.384024424+3.469485904I <- {r = 2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `4.469485904-2.615975576I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `5.469485904-2.615975576I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `6.469485904-2.615975576I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `3.615975576-3.469485904I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `4.615975576-3.469485904I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `5.615975576-3.469485904I <- {r = 2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `3.615975576+3.469485904I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `4.615975576+3.469485904I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `5.615975576+3.469485904I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `4.469485904+2.615975576I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `5.469485904+2.615975576I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `6.469485904+2.615975576I <- {r = -2^(1/2)-I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-1.615975576-3.469485904I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-.615975576-3.469485904I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `.384024424-3.469485904I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-2.469485904-2.615975576I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-1.469485904-2.615975576I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `-.469485904-2.615975576I <- {r = -2^(1/2)-I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}` `4.469485904-2.615975576I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 1}` `5.469485904-2.615975576I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 2}` `6.469485904-2.615975576I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)+I2^(1/2), y = 3}` `3.615975576-3.469485904I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 1}` `4.615975576-3.469485904I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 2}` `5.615975576-3.469485904I <- {r = -2^(1/2)+I2^(1/2), theta = 2^(1/2)-I2^(1/2), y = 3}` `-2.469485904+2.615975576I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 1}` `-1.469485904+2.615975576I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 2}` `-.469485904+2.615975576I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)-I2^(1/2), y = 3}` `-1.615975576+3.469485904I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 1}` `-.615975576+3.469485904I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 2}` `.384024424+3.469485904I <- {r = -2^(1/2)+I2^(1/2), theta = -2^(1/2)+I2^(1/2), y = 3}`	Fail `Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.9.E6	${\displaystyle{\displaystyle\omega=\operatorname{arctan}\left(\|y/x\|\right)\in% \left[0,\tfrac{1}{2}\pi\right]}}$	`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	${\displaystyle{\displaystyle\operatorname{ph}z=\theta+2n\pi}}$	`argument(z)= theta + 2nPi`	`Arg[z]= \[Theta]+ 2nPi`	Failure	Failure	Fail `-6.912000706-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `-13.19518602-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `-19.47837132-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `-8.482797034-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` `-14.76598234-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 2}` `-21.04916764-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 3}` `-10.05359336-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 1}` `-16.33677867-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 2}` `-22.61996397-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 3}` `-5.341204380-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 1}` `-11.62438969-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 2}` `-17.90757499-1.414213562I <- {theta = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 3}` `-6.912000706+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `-13.19518602+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `-19.47837132+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `-8.482797034+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` `-14.76598234+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 2}` `-21.04916764+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 3}` `-10.05359336+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 1}` `-16.33677867+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 2}` `-22.61996397+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 3}` `-5.341204380+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 1}` `-11.62438969+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 2}` `-17.90757499+1.414213562I <- {theta = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 3}` `-4.083573582+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `-10.36675890+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `-16.64994420+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `-5.654369910+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` `-11.93755522+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 2}` `-18.22074052+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 3}` `-7.225166236+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 1}` `-13.50835155+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 2}` `-19.79153685+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 3}` `-2.512777256+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 1}` `-8.795962568+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 2}` `-15.07914787+1.414213562I <- {theta = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 3}` `-4.083573582-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `-10.36675890-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `-16.64994420-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `-5.654369910-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` `-11.93755522-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 2}` `-18.22074052-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 3}` `-7.225166236-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 1}` `-13.50835155-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 2}` `-19.79153685-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), n = 3}` `-2.512777256-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 1}` `-8.795962568-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 2}` `-15.07914787-1.414213562I <- {theta = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), n = 3}`	Fail `Complex[-6.912000706155233, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-13.195186013334819, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-19.478371320514405, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.912000706155233, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-13.195186013334819, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-19.478371320514405, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.083573581409043, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-10.366758888588627, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-16.649944195768214, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.083573581409043, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-10.366758888588627, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-16.649944195768214, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-8.48279703295013, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-14.765982340129717, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-21.049167647309304, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-8.48279703295013, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-14.765982340129717, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-21.049167647309304, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.65436990820394, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-11.937555215383526, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-18.220740522563112, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.65436990820394, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-11.937555215383526, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-18.220740522563112, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-10.053593359745026, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-16.336778666924612, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-22.6199639741042, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-10.053593359745026, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-16.336778666924612, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-22.6199639741042, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.225166234998835, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-13.50835154217842, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-19.791536849358007, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.225166234998835, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-13.50835154217842, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-19.791536849358007, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.341204379360336, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-11.624389686539924, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-17.90757499371951, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.341204379360336, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-11.624389686539924, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-17.90757499371951, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5127772546141465, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-8.795962561793733, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-15.079147868973319, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.5127772546141465, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-8.795962561793733, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-15.079147868973319, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.9#Ex7	${\displaystyle{\displaystyle\|\Re z\|<=\|z\|}}$	`abs(Re(z))< =abs(z)`	`Abs[Re[z]]< =Abs[z]`	Failure	Failure	Successful	Successful
1.9#Ex8	${\displaystyle{\displaystyle\|\Im z\|<=\|z\|}}$	`abs(Im(z))< =abs(z)`	`Abs[Im[z]]< =Abs[z]`	Failure	Failure	Successful	Successful
1.9.E10	${\displaystyle{\displaystyle e^{i\theta}=\cos\theta+i\sin\theta}}$	`exp(Itheta)= cos(theta)+ Isin(theta)`	`Exp[I\[Theta]]= Cos[\[Theta]]+ ISin[\[Theta]]`	Successful	Successful	-	-
1.9.E11	${\displaystyle{\displaystyle\overline{z}=x-iy}}$	`conjugate(z)= x - I*y`	`Conjugate[z]= x - I*y`	Failure	Failure	Fail `.414213562-.414213562I <- {z = 2^(1/2)+I2^(1/2), x = 1, y = 1}` `.414213562+.585786438I <- {z = 2^(1/2)+I2^(1/2), x = 1, y = 2}` `.414213562+1.585786438I <- {z = 2^(1/2)+I2^(1/2), x = 1, y = 3}` `-.585786438-.414213562I <- {z = 2^(1/2)+I2^(1/2), x = 2, y = 1}` `-.585786438+.585786438I <- {z = 2^(1/2)+I2^(1/2), x = 2, y = 2}` `-.585786438+1.585786438I <- {z = 2^(1/2)+I2^(1/2), x = 2, y = 3}` `-1.585786438-.414213562I <- {z = 2^(1/2)+I2^(1/2), x = 3, y = 1}` `-1.585786438+.585786438I <- {z = 2^(1/2)+I2^(1/2), x = 3, y = 2}` `-1.585786438+1.585786438I <- {z = 2^(1/2)+I2^(1/2), x = 3, y = 3}` `.414213562+2.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 1, y = 1}` `.414213562+3.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 1, y = 2}` `.414213562+4.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 1, y = 3}` `-.585786438+2.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 2, y = 1}` `-.585786438+3.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 2, y = 2}` `-.585786438+4.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 2, y = 3}` `-1.585786438+2.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 3, y = 1}` `-1.585786438+3.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 3, y = 2}` `-1.585786438+4.414213562I <- {z = 2^(1/2)-I2^(1/2), x = 3, y = 3}` `-2.414213562+2.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 1, y = 1}` `-2.414213562+3.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 1, y = 2}` `-2.414213562+4.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 1, y = 3}` `-3.414213562+2.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 2, y = 1}` `-3.414213562+3.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 2, y = 2}` `-3.414213562+4.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 2, y = 3}` `-4.414213562+2.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 3, y = 1}` `-4.414213562+3.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 3, y = 2}` `-4.414213562+4.414213562I <- {z = -2^(1/2)-I2^(1/2), x = 3, y = 3}` `-2.414213562-.414213562I <- {z = -2^(1/2)+I2^(1/2), x = 1, y = 1}` `-2.414213562+.585786438I <- {z = -2^(1/2)+I2^(1/2), x = 1, y = 2}` `-2.414213562+1.585786438I <- {z = -2^(1/2)+I2^(1/2), x = 1, y = 3}` `-3.414213562-.414213562I <- {z = -2^(1/2)+I2^(1/2), x = 2, y = 1}` `-3.414213562+.585786438I <- {z = -2^(1/2)+I2^(1/2), x = 2, y = 2}` `-3.414213562+1.585786438I <- {z = -2^(1/2)+I2^(1/2), x = 2, y = 3}` `-4.414213562-.414213562I <- {z = -2^(1/2)+I2^(1/2), x = 3, y = 1}` `-4.414213562+.585786438I <- {z = -2^(1/2)+I2^(1/2), x = 3, y = 2}` `-4.414213562+1.585786438I <- {z = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle\|\overline{z}\|=\|z\|}}$	`abs(conjugate(z))=abs(z)`	`Abs[Conjugate[z]]=Abs[z]`	Successful	Successful	-	-
1.9.E13	${\displaystyle{\displaystyle\operatorname{ph}\overline{z}=-\operatorname{ph}z}}$	`argument(conjugate(z))= - argument(z)`	`Arg[Conjugate[z]]= - Arg[z]`	Failure	Failure	Successful	Successful
1.9.E14	${\displaystyle{\displaystyle z_{1}+z_{2}=x_{1}+x_{2}+\mathrm{i}(y_{1}+y_{2})}}$	`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	${\displaystyle{\displaystyle z_{1}-z_{2}=x_{1}-x_{2}+\mathrm{i}(y_{1}-y_{2})}}$	`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	${\displaystyle{\displaystyle\frac{z_{1}}{z_{2}}=\frac{z_{1}\overline{z}_{2}}{\|% z_{2}\|^{2}}}}$	`(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	${\displaystyle{\displaystyle\frac{z_{1}\overline{z}_{2}}{\|z_{2}\|^{2}}=\frac{x_% {1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}}}$	`(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	${\displaystyle{\displaystyle\operatorname{ph}\left(z_{1}z_{2}\right)=% \operatorname{ph}z_{1}+\operatorname{ph}z_{2}}}$	`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)-I2^(1/2), z[2] = -2^(1/2)-I2^(1/2)}` `6.283185308 <- {z[1] = -2^(1/2)-I2^(1/2), z[2] = 2^(1/2)-I2^(1/2)}` `6.283185307 <- {z[1] = -2^(1/2)-I2^(1/2), z[2] = -2^(1/2)-I2^(1/2)}` `-6.283185307 <- {z[1] = -2^(1/2)+I2^(1/2), z[2] = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle\left\|\frac{z_{1}}{z_{2}}\right\|=\frac{\|z_{1}\|}{\|z% _{2}\|}}}$	`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	${\displaystyle{\displaystyle\operatorname{ph}\frac{z_{1}}{z_{2}}=\operatorname% {ph}z_{1}-\operatorname{ph}z_{2}}}$	`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)-I2^(1/2), z[2] = -2^(1/2)+I2^(1/2)}` `6.283185308 <- {z[1] = -2^(1/2)-I2^(1/2), z[2] = 2^(1/2)+I2^(1/2)}` `6.283185307 <- {z[1] = -2^(1/2)-I2^(1/2), z[2] = -2^(1/2)+I2^(1/2)}` `-6.283185307 <- {z[1] = -2^(1/2)+I2^(1/2), z[2] = -2^(1/2)-I2^(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	${\displaystyle{\displaystyle\cos n\theta+i\sin n\theta=(\cos\theta+i\sin\theta% )^{n}}}$	`cos(ntheta)+ Isin(ntheta)=(cos(theta)+ Isin(theta))^(n)`	`Cos[n\[Theta]]+ ISin[n\[Theta]]=(Cos[\[Theta]]+ ISin[\[Theta]])^(n)`	Successful	Failure	-	Skip
1.9.E23	${\displaystyle{\displaystyle\left\|\left\|z_{1}\right\|-\left\|z_{2}\right\|\right\|% <=\left\|z_{1}+z_{2}\right\|}}$	`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	${\displaystyle{\displaystyle\left\|z_{1}+z_{2}\right\|<=\left\|z_{1}\right\|+\left% \|z_{2}\right\|}}$	`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	${\displaystyle{\displaystyle\frac{\partial u}{\partial x}=\frac{\partial v}{% \partial y}}}$	`diff(u, x)= diff(v, y)`	`D[u, x]= D[v, y]`	Successful	Successful	-	-
1.9#Ex10	${\displaystyle{\displaystyle\frac{\partial u}{\partial y}=-\frac{\partial v}{% \partial x}}}$	`diff(u, y)= - diff(v, x)`	`D[u, y]= - D[v, x]`	Successful	Successful	-	-
1.9.E26	${\displaystyle{\displaystyle\frac{{\partial}^{2}u}{{\partial x}^{2}}+\frac{{% \partial}^{2}u}{{\partial y}^{2}}=\frac{{\partial}^{2}v}{{\partial x}^{2}}+% \frac{{\partial}^{2}v}{{\partial y}^{2}}}}$	`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	${\displaystyle{\displaystyle\frac{{\partial}^{2}v}{{\partial x}^{2}}+\frac{{% \partial}^{2}v}{{\partial y}^{2}}=0}}$	`diff(v, [x$(2)])+ diff(v, [y$(2)])= 0`	`D[v, {x, 2}]+ D[v, {y, 2}]= 0`	Successful	Successful	-	-
1.9.E27	${\displaystyle{\displaystyle\frac{{\partial}^{2}u}{{\partial r}^{2}}+\frac{1}{% r}\frac{\partial u}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}u}{{% \partial\theta}^{2}}=0}}$	`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	${\displaystyle{\displaystyle u(z)=\frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})% \mathrm{d}\phi}}$	`u(z)=(1)/(2Pi)int(u(z + rexp(Iphi)), phi = 0..2*Pi)`	`u(z)=Divide[1,2Pi]Integrate[u(z + rExp[I\[Phi]]), {\[Phi], 0, 2*Pi}]`	Successful	Successful	-	-
1.9.E34	${\displaystyle{\displaystyle u(re^{i\theta})=\frac{1}{2\pi}\int^{2\pi}_{0}% \frac{(R^{2}-r^{2})h(Re^{i\phi})\mathrm{d}\phi}{R^{2}-2Rr\cos\left(\phi-\theta% \right)+r^{2}}}}$	`u(rexp(Itheta))=(1)/(2Pi)int((((R)^(2)- (r)^(2)) h(Rexp(Iphi)))/((R)^(2)- 2Rrcos(phi - theta)+ (r)^(2)), phi = 0..2*Pi)`	`u(rExp[I\[Theta]])=Divide[1,2Pi]Integrate[Divide[((R)^(2)- (r)^(2)) h(RExp[I\[Phi]]),(R)^(2)- 2RrCos[\[Phi]- \[Theta]]+ (r)^(2)], {\[Phi], 0, 2*Pi}]`	Error	Failure	-	Skip
1.9.E63	${\displaystyle{\displaystyle f^{(m)}(z)=\sum_{n=0}^{\infty}{\left(n+1\right)_{% m}}a_{n+m}(z-z_{0})^{n}}}$	`(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	${\displaystyle{\displaystyle\int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\mathrm{d}t% =\sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\mathrm{d}t}}$	`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	${\displaystyle{\displaystyle\|\ln\left(1+a_{n}(z)\right)\|<=M_{n}}}$	`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	${\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta<\operatorname{ph}b_{n}}}$	`-(1)/(2)*Pi + delta < argument(b[n])`	`-Divide[1,2]*Pi + \[Delta]< Arg[Subscript[b, n]]`	Failure	Failure	Successful	Successful
1.12.E26	${\displaystyle{\displaystyle\operatorname{ph}b_{n}<\tfrac{1}{2}\pi-\delta}}$	`argument(b[n])<(1)/(2)*Pi - delta`	`Arg[Subscript[b, n]]<Divide[1,2]*Pi - \[Delta]`	Failure	Failure	Successful	Successful
1.12.E27	${\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta<\operatorname{ph}C_{n}}}$	`-(1)/(2)*Pi + delta < argument(C[n])`	`-Divide[1,2]*Pi + \[Delta]< Arg[Subscript[C, n]]`	Failure	Failure	Successful	Successful
1.12.E27	${\displaystyle{\displaystyle\operatorname{ph}C_{n}<\tfrac{1}{2}\pi-\delta}}$	`argument(C[n])<(1)/(2)*Pi - delta`	`Arg[Subscript[C, n]]<Divide[1,2]*Pi - \[Delta]`	Failure	Failure	Successful	Successful
1.13.E11	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}\xi}^{2}}+F(% \xi)\frac{\mathrm{d}W}{\mathrm{d}\xi}+G(\xi)W=0}}$	`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+5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {G = 2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {G = 2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {G = -2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), xi = -2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = 2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = 2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = -2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {G = -2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), xi = -2^(1/2)+I2^(1/2)}`	Fail `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.13.E14	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}z}^{2}}-H(z)W=% 0}}$	`diff(W, [z$(2)])- H(z) W = 0`	`D[W, {z, 2}]- H(z) W = 0`	Failure	Failure	Fail `5.656854245-5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {H = 2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {H = 2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {H = -2^(1/2)-I2^(1/2), W = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `5.656854245-5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-5.656854245+5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-5.656854245-5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `5.656854245+5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-5.656854245+5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.656854245+5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `5.656854245-5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-5.656854245-5.656854245I <- {H = -2^(1/2)+I2^(1/2), W = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}U}{{\mathrm{d}z}^{2}}+IU=0}}$	`diff(U, [z$(2)])+ I*U = 0`	`D[U, {z, 2}]+ I*U = 0`	Failure	Failure	Fail `-1.414213562+1.414213562I <- {U = 2^(1/2)+I2^(1/2)}` `1.414213562+1.414213562I <- {U = 2^(1/2)-I2^(1/2)}` `1.414213562-1.414213562I <- {U = -2^(1/2)-I2^(1/2)}` `-1.414213562-1.414213562I <- {U = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}V}{{\mathrm{d}z}^{2}}+JV=0}}$	`diff(V, [z$(2)])+ J*V = 0`	`D[V, {z, 2}]+ J*V = 0`	Failure	Failure	Fail `0.+3.999999998I <- {J = 2^(1/2)+I2^(1/2), V = 2^(1/2)+I2^(1/2)}` `3.999999998+0.I <- {J = 2^(1/2)+I2^(1/2), V = 2^(1/2)-I2^(1/2)}` `0.-3.999999998I <- {J = 2^(1/2)+I2^(1/2), V = -2^(1/2)-I2^(1/2)}` `-3.999999998+0.I <- {J = 2^(1/2)+I2^(1/2), V = -2^(1/2)+I2^(1/2)}` `3.999999998+0.I <- {J = 2^(1/2)-I2^(1/2), V = 2^(1/2)+I2^(1/2)}` `0.-3.999999998I <- {J = 2^(1/2)-I2^(1/2), V = 2^(1/2)-I2^(1/2)}` `-3.999999998+0.I <- {J = 2^(1/2)-I2^(1/2), V = -2^(1/2)-I2^(1/2)}` `0.+3.999999998I <- {J = 2^(1/2)-I2^(1/2), V = -2^(1/2)+I2^(1/2)}` `0.-3.999999998I <- {J = -2^(1/2)-I2^(1/2), V = 2^(1/2)+I2^(1/2)}` `-3.999999998+0.I <- {J = -2^(1/2)-I2^(1/2), V = 2^(1/2)-I2^(1/2)}` `0.+3.999999998I <- {J = -2^(1/2)-I2^(1/2), V = -2^(1/2)-I2^(1/2)}` `3.999999998+0.I <- {J = -2^(1/2)-I2^(1/2), V = -2^(1/2)+I2^(1/2)}` `-3.999999998+0.I <- {J = -2^(1/2)+I2^(1/2), V = 2^(1/2)+I2^(1/2)}` `0.+3.999999998I <- {J = -2^(1/2)+I2^(1/2), V = 2^(1/2)-I2^(1/2)}` `3.999999998+0.I <- {J = -2^(1/2)+I2^(1/2), V = -2^(1/2)-I2^(1/2)}` `0.-3.999999998I <- {J = -2^(1/2)+I2^(1/2), V = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle(f*g)(t)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}F(x)G(x)e^{-itx}\mathrm{d}x}}$	`(f * g)(t)=(1)/(sqrt(2Pi))int(F(x)* G(x) exp(- Itx), x = - infinity..infinity)`	`(f * g)(t)=Divide[1,Sqrt[2Pi]]Integrate[F(x)* G(x) Exp[- Itx], {x, - Infinity, Infinity}]`	Failure	Failure	Skip	Skip
1.15.E13	${\displaystyle{\displaystyle\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\mathrm{d}% \theta=1}}$	`(1)/(2Pi)int(P(r , theta), theta = 0..2Pi)= 1`	`Divide[1,2Pi]Integrate[P(r , \[Theta]), {\[Theta], 0, 2Pi}]= 1`	Error	Failure	-	Error
1.15.E16	${\displaystyle{\displaystyle\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\mathrm{% d}\theta=1}}$	`(1)/(2Pi)int(K[n](theta), theta = 0..2Pi)= 1`	`Divide[1,2Pi]Integrate[Subscript[K, n](\[Theta]), {\[Theta], 0, 2Pi}]= 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	${\displaystyle{\displaystyle\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\mathrm% {d}x=1}}$	`(1)/(2Pi)int(P*(x , y), x = - infinity..infinity)= 1`	`Divide[1,2Pi]Integrate[P*(x , y), {x, - Infinity, Infinity}]= 1`	Error	Failure	-	Error
1.15.E36	${\displaystyle{\displaystyle h(x,y)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}e^{-y\|t\|}e^{-ixt}F(t)\mathrm{d}t}}$	`h(x , y)=(1)/(sqrt(2Pi))int(exp(- yabs(t))exp(- Ixt)F*(t), t = - infinity..infinity)`	`h(x , y)=Divide[1,Sqrt[2Pi]]Integrate[Exp[- yAbs[t]]Exp[- Ixt]F*(t), {t, - Infinity, Infinity}]`	Failure	Failure	Skip	Error
1.15.E39	${\displaystyle{\displaystyle\Phi(z)=\Phi(x+iy)}}$	`Phi(z)= Phi(x + I*y)`	`\[CapitalPhi](z)= \[CapitalPhi](x + I*y)`	Failure	Failure	Fail `0.+1.171572874I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 1}` `1.414213562-.242640688I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 2}` `2.828427124-1.656854250I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 3}` `-1.414213562-.242640688I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 1}` `0.-1.656854250I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 2}` `1.414213562-3.071067812I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 3}` `-2.828427124-1.656854250I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 1}` `-1.414213562-3.071067812I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 2}` `0.-4.485281374I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 3}` `3.999999998-2.828427124I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 1}` `5.414213560-4.242640686I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 2}` `6.828427122-5.656854248I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 3}` `2.585786436-4.242640686I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 1}` `3.999999998-5.656854248I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 2}` `5.414213560-7.071067810I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 3}` `1.171572874-5.656854248I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 1}` `2.585786436-7.071067810I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 2}` `3.999999998-8.485281372I <- {Phi = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 3}` `0.-6.828427122I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 1}` `1.414213562-8.242640684I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 2}` `2.828427124-9.656854246I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 3}` `-1.414213562-8.242640684I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 1}` `0.-9.656854246I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 2}` `1.414213562-11.07106781I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 3}` `-2.828427124-9.656854246I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 1}` `-1.414213562-11.07106781I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 2}` `0.-12.48528137I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 3}` `-3.999999998-2.828427124I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 1}` `-2.585786436-4.242640686I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 2}` `-1.171572874-5.656854248I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 3}` `-5.414213560-4.242640686I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 1}` `-3.999999998-5.656854248I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 2}` `-2.585786436-7.071067810I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 3}` `-6.828427122-5.656854248I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 1}` `-5.414213560-7.071067810I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 2}` `-3.999999998-8.485281372I <- {Phi = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 3}` `1.171572874+0.I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 1}` `-.242640688-1.414213562I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 2}` `-1.656854250-2.828427124I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 3}` `-.242640688+1.414213562I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 1}` `-1.656854250+0.I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 2}` `-3.071067812-1.414213562I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 3}` `-1.656854250+2.828427124I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 1}` `-3.071067812+1.414213562I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 2}` `-4.485281374+0.I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 3}` `-2.828427124-3.999999998I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 1}` `-4.242640686-5.414213560I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 2}` `-5.656854248-6.828427122I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 3}` `-4.242640686-2.585786436I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 1}` `-5.656854248-3.999999998I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 2}` `-7.071067810-5.414213560I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 3}` `-5.656854248-1.171572874I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 1}` `-7.071067810-2.585786436I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 2}` `-8.485281372-3.999999998I <- {Phi = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 3}` `-6.828427122+0.I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 1}` `-8.242640684-1.414213562I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 2}` `-9.656854246-2.828427124I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 3}` `-8.242640684+1.414213562I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 1}` `-9.656854246+0.I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 2}` `-11.07106781-1.414213562I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 3}` `-9.656854246+2.828427124I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 1}` `-11.07106781+1.414213562I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 2}` `-12.48528137+0.I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 3}` `-2.828427124+3.999999998I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 1}` `-4.242640686+2.585786436I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 2}` `-5.656854248+1.171572874I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 3}` `-4.242640686+5.414213560I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 1}` `-5.656854248+3.999999998I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 2}` `-7.071067810+2.585786436I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 3}` `-5.656854248+6.828427122I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 1}` `-7.071067810+5.414213560I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 2}` `-8.485281372+3.999999998I <- {Phi = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 3}` `0.-1.171572874I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 1}` `-1.414213562+.242640688I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 2}` `-2.828427124+1.656854250I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 3}` `1.414213562+.242640688I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 1}` `0.+1.656854250I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 2}` `-1.414213562+3.071067812I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 3}` `2.828427124+1.656854250I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 1}` `1.414213562+3.071067812I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 2}` `0.+4.485281374I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 3}` `-3.999999998+2.828427124I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 1}` `-5.414213560+4.242640686I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 2}` `-6.828427122+5.656854248I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 3}` `-2.585786436+4.242640686I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 1}` `-3.999999998+5.656854248I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 2}` `-5.414213560+7.071067810I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 3}` `-1.171572874+5.656854248I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 1}` `-2.585786436+7.071067810I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 2}` `-3.999999998+8.485281372I <- {Phi = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 3}` `0.+6.828427122I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 1}` `-1.414213562+8.242640684I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 2}` `-2.828427124+9.656854246I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 3}` `1.414213562+8.242640684I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 1}` `0.+9.656854246I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 2}` `-1.414213562+11.07106781I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 3}` `2.828427124+9.656854246I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 1}` `1.414213562+11.07106781I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 2}` `0.+12.48528137I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 3}` `3.999999998+2.828427124I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 1}` `2.585786436+4.242640686I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 2}` `1.171572874+5.656854248I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 3}` `5.414213560+4.242640686I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 1}` `3.999999998+5.656854248I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 2}` `2.585786436+7.071067810I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 3}` `6.828427122+5.656854248I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 1}` `5.414213560+7.071067810I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 2}` `3.999999998+8.485281372I <- {Phi = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 3}` `-1.171572874+0.I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 1}` `.242640688+1.414213562I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 2}` `1.656854250+2.828427124I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 1, y = 3}` `.242640688-1.414213562I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 1}` `1.656854250+0.I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 2}` `3.071067812+1.414213562I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 2, y = 3}` `1.656854250-2.828427124I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 1}` `3.071067812-1.414213562I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 2}` `4.485281374+0.I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), x = 3, y = 3}` `2.828427124+3.999999998I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 1}` `4.242640686+5.414213560I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 2}` `5.656854248+6.828427122I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 1, y = 3}` `4.242640686+2.585786436I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 1}` `5.656854248+3.999999998I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 2}` `7.071067810+5.414213560I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 2, y = 3}` `5.656854248+1.171572874I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 1}` `7.071067810+2.585786436I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 2}` `8.485281372+3.999999998I <- {Phi = -2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), x = 3, y = 3}` `6.828427122+0.I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 1}` `8.242640684+1.414213562I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 2}` `9.656854246+2.828427124I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 1, y = 3}` `8.242640684-1.414213562I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 1}` `9.656854246+0.I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 2}` `11.07106781+1.414213562I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 2, y = 3}` `9.656854246-2.828427124I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 1}` `11.07106781-1.414213562I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 2}` `12.48528137+0.I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2), x = 3, y = 3}` `2.828427124-3.999999998I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 1}` `4.242640686-2.585786436I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 2}` `5.656854248-1.171572874I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 1, y = 3}` `4.242640686-5.414213560I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 1}` `5.656854248-3.999999998I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 2}` `7.071067810-2.585786436I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 2, y = 3}` `5.656854248-6.828427122I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 1}` `7.071067810-5.414213560I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 2}` `8.485281372-3.999999998I <- {Phi = -2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2), x = 3, y = 3}`	Fail `Complex[0.0, 1.1715728752538097] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[1.4142135623730951, -0.24264068711928566] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[2.8284271247461903, -1.6568542494923806] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4142135623730951, -0.24264068711928566] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, -1.6568542494923806] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[1.4142135623730951, -3.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.8284271247461903, -1.6568542494923806] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4142135623730951, -3.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, -4.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `1.1715728752538097 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.24264068711928566, -1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6568542494923806, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.24264068711928566, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `-1.6568542494923806 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.0710678118654755, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.6568542494923806, 2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-3.0710678118654755, 1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `-4.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, -1.1715728752538097] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4142135623730951, 0.24264068711928566] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.8284271247461903, 1.6568542494923806] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[1.4142135623730951, 0.24264068711928566] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, 1.6568542494923806] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4142135623730951, 3.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.8284271247461903, 1.6568542494923806] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[1.4142135623730951, 3.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, 4.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `-1.1715728752538097 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.24264068711928566, 1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[1.6568542494923806, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.24264068711928566, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `1.6568542494923806 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.0710678118654755, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[1.6568542494923806, -2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.0710678118654755, -1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `4.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.0, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.414213562373095, -4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[6.82842712474619, -5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[2.585786437626905, -4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.0, -5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.414213562373095, -7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[1.1715728752538097, -5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[2.585786437626905, -7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.0, -8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.8284271247461903, -4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.242640687119286, -5.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -6.82842712474619] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.242640687119286, -2.585786437626905] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.0710678118654755, -5.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, -1.1715728752538097] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.0710678118654755, -2.585786437626905] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-8.485281374238571, -4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.0, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.414213562373095, 4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.82842712474619, 5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.585786437626905, 4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.0, 5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.414213562373095, 7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.1715728752538097, 5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.585786437626905, 7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.0, 8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.8284271247461903, 4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.242640687119286, 5.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 6.82842712474619] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.242640687119286, 2.585786437626905] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.0710678118654755, 5.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, 1.1715728752538097] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.0710678118654755, 2.585786437626905] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.485281374238571, 4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, -6.82842712474619] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[1.4142135623730951, -8.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[2.8284271247461903, -9.65685424949238] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4142135623730951, -8.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, -9.65685424949238] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[1.4142135623730951, -11.071067811865476] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.8284271247461903, -9.65685424949238] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4142135623730951, -11.071067811865476] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, -12.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `-6.82842712474619 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-8.242640687119286, -1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-9.65685424949238, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-8.242640687119286, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `-9.65685424949238 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-11.071067811865476, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-9.65685424949238, 2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-11.071067811865476, 1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `-12.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, 6.82842712474619] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4142135623730951, 8.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.8284271247461903, 9.65685424949238] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[1.4142135623730951, 8.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, 9.65685424949238] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.4142135623730951, 11.071067811865476] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.8284271247461903, 9.65685424949238] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[1.4142135623730951, 11.071067811865476] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, 12.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `6.82842712474619 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.242640687119286, 1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.65685424949238, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.242640687119286, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `9.65685424949238 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[11.071067811865476, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[9.65685424949238, -2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[11.071067811865476, -1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `12.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.0, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.585786437626905, -4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-1.1715728752538097, -5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.414213562373095, -4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.0, -5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.585786437626905, -7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.82842712474619, -5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-5.414213562373095, -7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-4.0, -8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.8284271247461903, 4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.242640687119286, 2.585786437626905] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 1.1715728752538097] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.242640687119286, 5.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.0710678118654755, 2.585786437626905] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-5.656854249492381, 6.82842712474619] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-7.0710678118654755, 5.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-8.485281374238571, 4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.0, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.585786437626905, 4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[1.1715728752538097, 5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.414213562373095, 4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.0, 5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.585786437626905, 7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[6.82842712474619, 5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.414213562373095, 7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[4.0, 8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.8284271247461903, -4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.242640687119286, -2.585786437626905] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -1.1715728752538097] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[4.242640687119286, -5.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.0710678118654755, -2.585786437626905] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[5.656854249492381, -6.82842712474619] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[7.0710678118654755, -5.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[8.485281374238571, -4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
1.15.E42	${\displaystyle{\displaystyle\int^{\infty}_{-\infty}K_{R}(s)\mathrm{d}s=1}}$	`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	${\displaystyle{\displaystyle\sigma_{R}(\theta)=\frac{1}{\sqrt{2\pi}}\int^{R}_{% -R}\left(1-\frac{\|t\|}{R}\right)e^{-i\theta t}F(t)\mathrm{d}t}}$	`sigma[R](theta)=(1)/(sqrt(2Pi))int((1 -(abs(t))/(R)) exp(- Ithetat)F(t), t = - R..R)`	`Subscript[\[Sigma], R](\[Theta])=Divide[1,Sqrt[2Pi]]Integrate[(1 -Divide[Abs[t],R]) Exp[- I\[Theta]t]F(t), {t, - R, R}]`	Failure	Failure	Skip	Successful
1.16.E19	${\displaystyle{\displaystyle x^{\alpha}_{+}=x^{\alpha}H\left(x\right)}}$	`(x[+])^(alpha)= (x)^(alpha)* Heaviside(x)`	`(Subscript[x, +])^(\[Alpha])= (x)^(\[Alpha])* HeavisideTheta[x]`	Error	Failure	-	Error
1.16#Ex1	${\displaystyle{\displaystyle F(\mathbf{x})=F}}$	`F*(x)= F`	`F*(x)= F`	Failure	Failure	Fail `1.414213562+1.414213562I <- {F = 2^(1/2)+I2^(1/2), x = 2}` `2.828427124+2.828427124I <- {F = 2^(1/2)+I2^(1/2), x = 3}` `1.414213562-1.414213562I <- {F = 2^(1/2)-I2^(1/2), x = 2}` `2.828427124-2.828427124I <- {F = 2^(1/2)-I2^(1/2), x = 3}` `-1.414213562-1.414213562I <- {F = -2^(1/2)-I2^(1/2), x = 2}` `-2.828427124-2.828427124I <- {F = -2^(1/2)-I2^(1/2), x = 3}` `-1.414213562+1.414213562I <- {F = -2^(1/2)+I2^(1/2), x = 2}` `-2.828427124+2.828427124I <- {F = -2^(1/2)+I2^(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	${\displaystyle{\displaystyle D_{\boldsymbol{{\alpha}}}={\mathrm{i}^{-\|% \boldsymbol{{\alpha}}\|}}D^{\boldsymbol{{\alpha}}}}}$	`D[alpha]= (I)^(-abs(alpha))* (D)^(alpha)`	`Subscript[D, \[Alpha]]= (I)^(-Abs[\[Alpha]])* (D)^(\[Alpha])`	Failure	Failure	Fail `.9779681321+2.175809568I <- {D = 2^(1/2)+I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `.9779681321-.6526175556I <- {D = 2^(1/2)+I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.850458992-.6526175556I <- {D = 2^(1/2)+I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.850458992+2.175809568I <- {D = 2^(1/2)+I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `9.438272386+2.467033025I <- {D = 2^(1/2)+I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `9.438272386-.361394099I <- {D = 2^(1/2)+I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `6.609845262-.361394099I <- {D = 2^(1/2)+I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `6.609845262+2.467033025I <- {D = 2^(1/2)+I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `.8479100469+.4255625275I <- {D = 2^(1/2)+I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `.8479100469-2.402864596I <- {D = 2^(1/2)+I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.980517077-2.402864596I <- {D = 2^(1/2)+I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.980517077+.4255625275I <- {D = 2^(1/2)+I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `1.536729595+1.398138497I <- {D = 2^(1/2)+I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `1.536729595-1.430288627I <- {D = 2^(1/2)+I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.291697529-1.430288627I <- {D = 2^(1/2)+I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.291697529+1.398138497I <- {D = 2^(1/2)+I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `9.438272386+.361394099I <- {D = 2^(1/2)-I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `9.438272386-2.467033025I <- {D = 2^(1/2)-I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `6.609845262-2.467033025I <- {D = 2^(1/2)-I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `6.609845262+.361394099I <- {D = 2^(1/2)-I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `.9779681321+.6526175556I <- {D = 2^(1/2)-I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `.9779681321-2.175809568I <- {D = 2^(1/2)-I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.850458992-2.175809568I <- {D = 2^(1/2)-I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.850458992+.6526175556I <- {D = 2^(1/2)-I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `1.536729595+1.430288627I <- {D = 2^(1/2)-I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `1.536729595-1.398138497I <- {D = 2^(1/2)-I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.291697529-1.398138497I <- {D = 2^(1/2)-I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.291697529+1.430288627I <- {D = 2^(1/2)-I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `.8479100469+2.402864596I <- {D = 2^(1/2)-I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `.8479100469-.4255625275I <- {D = 2^(1/2)-I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.980517077-.4255625275I <- {D = 2^(1/2)-I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.980517077+2.402864596I <- {D = 2^(1/2)-I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `-51.12384670-51.57661382I <- {D = -2^(1/2)-I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `-51.12384670-54.40504094I <- {D = -2^(1/2)-I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-53.95227382-54.40504094I <- {D = -2^(1/2)-I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-53.95227382-51.57661382I <- {D = -2^(1/2)-I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `1.377148458+1.501888445I <- {D = -2^(1/2)-I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `1.377148458-1.326538679I <- {D = -2^(1/2)-I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.451278666-1.326538679I <- {D = -2^(1/2)-I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.451278666+1.501888445I <- {D = -2^(1/2)-I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `1.404778314+1.423730122I <- {D = -2^(1/2)-I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `1.404778314-1.404697002I <- {D = -2^(1/2)-I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.423648810-1.404697002I <- {D = -2^(1/2)-I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.423648810+1.423730122I <- {D = -2^(1/2)-I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `-2.676538322-8.262170665I <- {D = -2^(1/2)-I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `-2.676538322-11.09059779I <- {D = -2^(1/2)-I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-5.504965446-11.09059779I <- {D = -2^(1/2)-I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-5.504965446-8.262170665I <- {D = -2^(1/2)-I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `1.377148458+1.326538679I <- {D = -2^(1/2)+I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `1.377148458-1.501888445I <- {D = -2^(1/2)+I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.451278666-1.501888445I <- {D = -2^(1/2)+I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.451278666+1.326538679I <- {D = -2^(1/2)+I2^(1/2), alpha = 2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `-51.12384670+54.40504094I <- {D = -2^(1/2)+I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `-51.12384670+51.57661382I <- {D = -2^(1/2)+I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-53.95227382+51.57661382I <- {D = -2^(1/2)+I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-53.95227382+54.40504094I <- {D = -2^(1/2)+I2^(1/2), alpha = 2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `-2.676538322+11.09059779I <- {D = -2^(1/2)+I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `-2.676538322+8.262170665I <- {D = -2^(1/2)+I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-5.504965446+8.262170665I <- {D = -2^(1/2)+I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-5.504965446+11.09059779I <- {D = -2^(1/2)+I2^(1/2), alpha = -2^(1/2)-I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}` `1.404778314+1.404697002I <- {D = -2^(1/2)+I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)+I2^(1/2)}` `1.404778314-1.423730122I <- {D = -2^(1/2)+I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = 2^(1/2)-I2^(1/2)}` `-1.423648810-1.423730122I <- {D = -2^(1/2)+I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)-I2^(1/2)}` `-1.423648810+1.404697002I <- {D = -2^(1/2)+I2^(1/2), alpha = -2^(1/2)+I2^(1/2), D[alpha] = -2^(1/2)+I2^(1/2)}`	Successful
1.16.E32	${\displaystyle{\displaystyle P(\mathbf{D})=\sum_{\boldsymbol{{\alpha}}}c_{% \boldsymbol{{\alpha}}}\mathbf{D}^{\alpha}}}$	`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	${\displaystyle{\displaystyle\int^{\infty}_{-\infty}\delta\left(t\right){% \mathrm{e}^{\mathrm{i}xt}}\mathrm{d}t=1}}$	`int(Dirac(t)exp(Ix*t), t = - infinity..infinity)= 1`	`Integrate[DiracDelta[t]Exp[Ix*t], {t, - Infinity, Infinity}]= 1`	Successful	Successful	-	-
1.16.E43	${\displaystyle{\displaystyle\frac{1}{2\pi}\int^{\infty}_{-\infty}{\mathrm{e}^{% \mathrm{i}xt}}\mathrm{d}t=\delta\left(x\right)}}$	`(1)/(2Pi)int(exp(Ixt), t = - infinity..infinity)= Dirac(x)`	`Divide[1,2Pi]Integrate[Exp[Ixt], {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	${\displaystyle{\displaystyle\operatorname{sign}\left(x\right)=2H\left(x\right)% -1}}$	`signum(x)= 2*Heaviside(x)- 1`	`Sign[x]= 2*HeavisideTheta[x]- 1`	Failure	Failure	Skip	Successful
1.17.E1	${\displaystyle{\displaystyle\delta\left(x\right)=0}}$	`Dirac(x)= 0`	`DiracDelta[x]= 0`	Error	Failure	-	Successful
1.17.E2	${\displaystyle{\displaystyle\int_{-\infty}^{\infty}\delta\left(x-a\right)\phi(% x)\mathrm{d}x=\phi(a)}}$	`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	${\displaystyle{\displaystyle\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty% }^{\infty}e^{-n(x-a)^{2}}\phi(x)\mathrm{d}x=\phi(a)}}$	`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	${\displaystyle{\displaystyle\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty% }^{\infty}e^{-n(x-a)^{2}}\phi(x)\mathrm{d}x=\tfrac{1}{2}\phi(a-)+\tfrac{1}{2}% \phi(a+)}}$	`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	${\displaystyle{\displaystyle\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left% (\int_{-\infty}^{\infty}\phi(x)e^{itx}\mathrm{d}x\right)\mathrm{d}t=\phi(a)}}$	`(1)/(2Pi)int(exp(- Iat)(int(phi(x)* exp(Itx), x = - infinity..infinity)), t = - infinity..infinity)= phi*(a)`	`Divide[1,2Pi]Integrate[Exp[- Iat](Integrate[\[Phi](x)* Exp[Itx], {x, - Infinity, Infinity}]), {t, - Infinity, Infinity}]= \[Phi]*(a)`	Failure	Failure	Skip	Skip
1.17.E9	${\displaystyle{\displaystyle\int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-% \infty}^{\infty}e^{i(x-a)t}\mathrm{d}t\right)\phi(x)\mathrm{d}x=\phi(a)}}$	`int(((1)/(2Pi)int(exp(I(x - a) t), t = - infinity..infinity))* phi(x), x = - infinity..infinity)= phi(a)`	`Integrate[(Divide[1,2Pi]Integrate[Exp[I(x - a) t], {t, - Infinity, Infinity}])* \[Phi](x), {x, - Infinity, Infinity}]= \[Phi](a)`	Failure	Failure	Skip	Skip
1.17.E10	${\displaystyle{\displaystyle\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n% )}e^{i(x-a)t}\mathrm{d}t=\sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}}}$	`(1)/(2Pi)int(exp(- (t)^(2)/(4n))exp(I(x - a) t), t = - infinity..infinity)=sqrt((n)/(Pi))exp(- n(x - a)^(2))`	`Divide[1,2Pi]Integrate[Exp[- (t)^(2)/(4n)]Exp[I(x - a) t], {t, - Infinity, Infinity}]=Sqrt[Divide[n,Pi]]Exp[- n(x - a)^(2)]`	Failure	Failure	Skip	Skip
1.17.E12	${\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{1}{2\pi}\int_{-\infty% }^{\infty}e^{i(x-a)t}\mathrm{d}t}}$	`Dirac(x - a)=(1)/(2Pi)int(exp(I(x - a) t), t = - infinity..infinity)`	`DiracDelta[x - a]=Divide[1,2Pi]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	${\displaystyle{\displaystyle\delta\left(x-a\right)=x\int_{0}^{\infty}tJ_{\nu}% \left(xt\right)J_{\nu}\left(at\right)\mathrm{d}t}}$	`Dirac(x - a)= xint(tBesselJ(nu, xt)BesselJ(nu, a*t), t = 0..infinity)`	`DiracDelta[x - a]= xIntegrate[tBesselJ[\[Nu], xt]BesselJ[\[Nu], a*t], {t, 0, Infinity}]`	Failure	Failure	Skip	Successful
1.17.E14	${\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{2xa}{\pi}\int_{0}^{% \infty}t^{2}\mathsf{j}_{\ell}\left(xt\right)\mathsf{j}_{\ell}\left(at\right)% \mathrm{d}t}}$	`Error`	`DiracDelta[x - a]=Divide[2xa,Pi]Integrate[(t)^(2) SphericalBesselJ[\[ScriptL], xt]SphericalBesselJ[\[ScriptL], a*t], {t, 0, Infinity}]`	Error	Failure	-	Successful
1.17.E17	${\displaystyle{\displaystyle\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}% \left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\mathrm{d}x\right)=\phi(a)}}$	`(1)/(2Pi)sum(exp(- Ika)(int(phi(x)* exp(Ikx), x = - Pi..Pi)), k = - infinity..infinity)= phi*(a)`	`Divide[1,2Pi]Sum[Exp[- Ika](Integrate[\[Phi](x)* Exp[Ikx], {x, - Pi, Pi}]), {k, - Infinity, Infinity}]= \[Phi]*(a)`	Error	Failure	-	Successful
1.17.E18	${\displaystyle{\displaystyle\int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{% k=-\infty}^{\infty}e^{ik(x-a)}\right)\mathrm{d}x=\phi(a)}}$	`int(phi(x)((1)/(2Pi)sum(exp(Ik(x - a)), k = - infinity..infinity)), x = - Pi..Pi)= phi*(a)`	`Integrate[\[Phi](x)(Divide[1,2Pi]Sum[Exp[Ik(x - a)], {k, - Infinity, Infinity}]), {x, - Pi, Pi}]= \[Phi]*(a)`	Failure	Failure	Skip	Error
1.17.E21	${\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{1}{2\pi}\sum_{k=-% \infty}^{\infty}e^{ik(x-a)}}}$	`Dirac(x - a)=(1)/(2Pi)sum(exp(Ik(x - a)), k = - infinity..infinity)`	`DiracDelta[x - a]=Divide[1,2Pi]Sum[Exp[Ik(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	${\displaystyle{\displaystyle\delta\left(x-a\right)=\sum_{k=0}^{\infty}(k+% \tfrac{1}{2})P_{k}\left(x\right)P_{k}\left(a\right)}}$	`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	${\displaystyle{\displaystyle\delta\left(x-a\right)=e^{-(x+a)/2}\sum_{k=0}^{% \infty}L_{k}\left(x\right)L_{k}\left(a\right)}}$	`Dirac(x - a)= exp(-(x + a)/ 2)sum(LaguerreL(k, x)LaguerreL(k, a), k = 0..infinity)`	`Error`	Failure	Error	-	-
1.17.E24	${\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{e^{-(x^{2}+a^{2})/2}}% {\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{H_{k}\left(x\right)H_{k}\left(a\right)}{2% ^{k}k!}}}$	`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

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