Weierstrass Elliptic and Modular Functions - 23.18 Modular Transformations
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 23.18.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modularlambdatau@{\mathcal{A}\tau} = \modularlambdatau@{\tau}}
\modularlambdatau@{\mathcal{A}\tau} = \modularlambdatau@{\tau} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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ModularLambda[A*\[Tau]] == ModularLambda[\[Tau]]
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Missing Macro Error | Failure | - | Failed [10 / 100]
Result: Complex[-5.551115123125783*^-17, -21.100969873679457]
Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-4.440892098500626*^-16, -21.100969873679432]
Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 23.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KleincompinvarJtau@{\mathcal{A}\tau} = \KleincompinvarJtau@{\tau}}
\KleincompinvarJtau@{\mathcal{A}\tau} = \KleincompinvarJtau@{\tau} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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KleinInvariantJ[A*\[Tau]] == KleinInvariantJ[\[Tau]]
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Missing Macro Error | Failure | - | Failed [8 / 100]
Result: Complex[71.08223570333668, 2.1851275073468844*^-14]
Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-71.08223570333656, -1.2998925520285436*^-13]
Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 23.18.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{\mathcal{A}\tau} = \varepsilon(\mathcal{A})\left(-i(c\tau+d)\right)^{1/2}\Dedekindeta@{\tau}}
\Dedekindeta@{\mathcal{A}\tau} = \varepsilon(\mathcal{A})\left(-i(c\tau+d)\right)^{1/2}\Dedekindeta@{\tau} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
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DedekindEta[A*\[Tau]] == \[CurlyEpsilon][A]*(- I*(c*\[Tau]+ d))^(1/2)* DedekindEta[\[Tau]]
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Missing Macro Error | Failure | - | Failed [180 / 300]
Result: Complex[0.11245781368984653, 0.4581664384510718]
Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 1], Rule[τ, Complex[0, 1]]}
Result: Complex[-0.5688147076679476, 1.020829457922046]
Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 2], Rule[τ, Complex[0, 1]]}
... skip entries to safe data |
| 23.18.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon(\mathcal{A}) = \exp@{\pi i\left(\frac{a+d}{12c}+s(-d,c)\right)}}
\varepsilon(\mathcal{A}) = \exp@{\pi i\left(\frac{a+d}{12c}+s(-d,c)\right)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | varepsilon(A) = exp(Pi*I*((a + d)/(12*c)+ s(- d , c)))
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\[CurlyEpsilon][A] == Exp[Pi*I*(Divide[a + d,12*c]+ s[- d , c])]
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Failure | Failure | Error | Error |
| 23.18.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s(d,c) = \sum_{r=1}^{c-1}\frac{r}{c}\left(\frac{dr}{c}-\floor{\frac{dr}{c}}-\frac{1}{2}\right),}
s(d,c) = \sum_{r=1}^{c-1}\frac{r}{c}\left(\frac{dr}{c}-\floor{\frac{dr}{c}}-\frac{1}{2}\right), |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c > 0} | s(d , c) = sum((r)/(c)*((d*r)/(c)- floor((d*r)/(c))-(1)/(2)), r = 1..c - 1)
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s[d , c] == Sum[Divide[r,c]*(Divide[d*r,c]- Floor[Divide[d*r,c]]-Divide[1,2]), {r, 1, c - 1}, GenerateConditions->None]
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Skipped - Unable to analyze test case: Null | Skipped - Unable to analyze test case: Null | - | - |