Weierstrass Elliptic and Modular Functions - 23.22 Methods of Computation

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
23.22.E2	${\displaystyle{\displaystyle 2\omega_{1}=-2i\omega_{3}}}$ 2\omega_{1} = -2i\omega_{3}		2*omega[1] = - 2*I*omega[3]	2*Subscript[\[Omega], 1] == - 2*I*Subscript[\[Omega], 3]	Failure	Failure	Failed [288 / 300] Result: .732050808+2.732050808*I Test Values: {omega = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I} Result: 3.464101616+2.000000000*I Test Values: {omega = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2-1/2*I*3^(1/2)} ... skip entries to safe data	Failed [288 / 300] Result: Complex[0.7320508075688775, 2.732050807568877] Test Values: {Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[3.4641016151377544, 2.0] Test Values: {Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} ... skip entries to safe data
23.22.E2	${\displaystyle{\displaystyle-2i\omega_{3}=\frac{\left(\Gamma\left(\frac{1}{4}\right)\right)^{2}}{2\sqrt{\pi}c^{1/4}}}}$ -2i\omega_{3} = \frac{\left(\EulerGamma@{\frac{1}{4}}\right)^{2}}{2\sqrt{\pi}c^{1/4}}		- 2*I*omega[3] = ((GAMMA((1)/(4)))^(2))/(2*sqrt(Pi)*(c)^(1/4))	- 2*I*Subscript[\[Omega], 3] == Divide[(Gamma[Divide[1,4]])^(2),2*Sqrt[Pi]*(c)^(1/4)]	Failure	Failure	Failed [300 / 300] Result: -1.369296462+.637245654*I Test Values: {c = -3/2, omega = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I} Result: -.637245654+3.369296462*I Test Values: {c = -3/2, omega = 1/2*3^(1/2)+1/2*I, omega[3] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-1.3692964596386887, 0.6372456520698113] Test Values: {Rule[c, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.6372456520698113, 3.3692964596386883] Test Values: {Rule[c, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
23.22.E3	${\displaystyle{\displaystyle 2\omega_{1}=2e^{-\pi i/3}\omega_{3}}}$ 2\omega_{1} = 2e^{-\pi i/3}\omega_{3}		2*omega[1] = 2*exp(- Pi*I/3)*omega[3]	2*Subscript[\[Omega], 1] == 2*Exp[- Pi*I/3]*Subscript[\[Omega], 3]	Failure	Failure	Failed [300 / 300] Result: 0.+2.000000001*I Test Values: {omega = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I} Result: .732050807-.732050808*I Test Values: {omega = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.0, 1.9999999999999998] Test Values: {Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.7320508075688772, -0.7320508075688773] Test Values: {Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
23.22.E3	${\displaystyle{\displaystyle 2e^{-\pi i/3}\omega_{3}=\frac{\left(\Gamma\left(\frac{1}{3}\right)\right)^{3}}{2\pi d^{1/6}}}}$ 2e^{-\pi i/3}\omega_{3} = \frac{\left(\EulerGamma@{\frac{1}{3}}\right)^{3}}{2\pi d^{1/6}}		2*exp(- Pi*I/3)*omega[3] = ((GAMMA((1)/(3)))^(3))/(2*Pi*(d)^(1/6))	2*Exp[- Pi*I/3]*Subscript[\[Omega], 3] == Divide[(Gamma[Divide[1,3]])^(3),2*Pi*(d)^(1/6)]	Failure	Failure	Failed [300 / 300] Result: -1.316213396-.7333114397*I Test Values: {d = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I} Result: -2.048264203+1.998739369*I Test Values: {d = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, omega[3] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-1.3162133925119985, -0.7333114390610043] Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.048264200080876, 1.9987393685078727] Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
23.22#Ex1	${\displaystyle{\displaystyle 2\omega_{1}=0.867568+i1.466607}}$ 2\omega_{1} = 0.867568+i1.466607		2*omega[1] = 0.867568 + I*1.466607	2*Subscript[\[Omega], 1] == 0.867568 + I*1.466607	Skipped - no semantic math	Skipped - no semantic math	-	-
23.22#Ex2	${\displaystyle{\displaystyle 2\omega_{3}=-1.223741+i1.328694}}$ 2\omega_{3} = -1.223741+i1.328694		2*omega[3] = - 1.223741 + I*1.328694	2*Subscript[\[Omega], 3] == - 1.223741 + I*1.328694	Skipped - no semantic math	Skipped - no semantic math	-	-
23.22#Ex3	${\displaystyle{\displaystyle\tau=0.305480+i1.015109}}$ \tau = 0.305480+i1.015109		tau = 0.305480 + I*1.015109	\[Tau] == 0.305480 + I*1.015109	Skipped - no semantic math	Skipped - no semantic math	-	-