Weierstrass Elliptic and Modular Functions - 23.22 Methods of Computation

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
23.22.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\omega_{1} = -2i\omega_{3}}
2\omega_{1} = -2i\omega_{3}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -2i\omega_{3} = \frac{\left(\EulerGamma@{\frac{1}{4}}\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}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
- 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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\omega_{1} = 2e^{-\pi i/3}\omega_{3}}
2\omega_{1} = 2e^{-\pi i/3}\omega_{3}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2e^{-\pi i/3}\omega_{3} = \frac{\left(\EulerGamma@{\frac{1}{3}}\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}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\omega_{1} = 0.867568+i1.466607}
2\omega_{1} = 0.867568+i1.466607		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\omega_{3} = -1.223741+i1.328694}
2\omega_{3} = -1.223741+i1.328694		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
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 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau = 0.305480+i1.015109}
\tau = 0.305480+i1.015109		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
tau = 0.305480 + I*1.015109
 
\[Tau] == 0.305480 + I*1.015109
 Skipped - no semantic math Skipped - no semantic math - -
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