23.19: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/23.19.E1 23.19.E1] || [[Item:Q7368|<math>\modularlambdatau@{\tau} = 16\left(\frac{\Dedekindeta^{2}@{2\tau}\Dedekindeta@{\tfrac{1}{2}\tau}}{\Dedekindeta^{3}@{\tau}}\right)^{8}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modularlambdatau@{\tau} = 16\left(\frac{\Dedekindeta^{2}@{2\tau}\Dedekindeta@{\tfrac{1}{2}\tau}}{\Dedekindeta^{3}@{\tau}}\right)^{8}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ModularLambda[\[Tau]] == 16*(Divide[(DedekindEta[2*\[Tau]])^(2)* DedekindEta[Divide[1,2]*\[Tau]],(DedekindEta[\[Tau]])^(3)])^(8)</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 10]
| [https://dlmf.nist.gov/23.19.E1 23.19.E1] || <math qid="Q7368">\modularlambdatau@{\tau} = 16\left(\frac{\Dedekindeta^{2}@{2\tau}\Dedekindeta@{\tfrac{1}{2}\tau}}{\Dedekindeta^{3}@{\tau}}\right)^{8}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modularlambdatau@{\tau} = 16\left(\frac{\Dedekindeta^{2}@{2\tau}\Dedekindeta@{\tfrac{1}{2}\tau}}{\Dedekindeta^{3}@{\tau}}\right)^{8}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ModularLambda[\[Tau]] == 16*(Divide[(DedekindEta[2*\[Tau]])^(2)* DedekindEta[Divide[1,2]*\[Tau]],(DedekindEta[\[Tau]])^(3)])^(8)</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 10]
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| [https://dlmf.nist.gov/23.19.E2 23.19.E2] || [[Item:Q7369|<math>\KleincompinvarJtau@{\tau} = \frac{4}{27}\frac{\left(1-\modularlambdatau@{\tau}+\modularlambdatau^{2}@{\tau}\right)^{3}}{\left(\modularlambdatau@{\tau}\left(1-\modularlambdatau@{\tau}\right)\right)^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\KleincompinvarJtau@{\tau} = \frac{4}{27}\frac{\left(1-\modularlambdatau@{\tau}+\modularlambdatau^{2}@{\tau}\right)^{3}}{\left(\modularlambdatau@{\tau}\left(1-\modularlambdatau@{\tau}\right)\right)^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>KleinInvariantJ[\[Tau]] == Divide[4,27]*Divide[(1 - ModularLambda[\[Tau]]+ (ModularLambda[\[Tau]])^(2))^(3),(ModularLambda[\[Tau]]*(1 - ModularLambda[\[Tau]]))^(2)]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 10]
| [https://dlmf.nist.gov/23.19.E2 23.19.E2] || <math qid="Q7369">\KleincompinvarJtau@{\tau} = \frac{4}{27}\frac{\left(1-\modularlambdatau@{\tau}+\modularlambdatau^{2}@{\tau}\right)^{3}}{\left(\modularlambdatau@{\tau}\left(1-\modularlambdatau@{\tau}\right)\right)^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\KleincompinvarJtau@{\tau} = \frac{4}{27}\frac{\left(1-\modularlambdatau@{\tau}+\modularlambdatau^{2}@{\tau}\right)^{3}}{\left(\modularlambdatau@{\tau}\left(1-\modularlambdatau@{\tau}\right)\right)^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>KleinInvariantJ[\[Tau]] == Divide[4,27]*Divide[(1 - ModularLambda[\[Tau]]+ (ModularLambda[\[Tau]])^(2))^(3),(ModularLambda[\[Tau]]*(1 - ModularLambda[\[Tau]]))^(2)]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 10]
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| [https://dlmf.nist.gov/23.19.E4 23.19.E4] || [[Item:Q7371|<math>\Delta = (2\pi)^{12}\Dedekindeta^{24}@{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Delta = (2\pi)^{12}\Dedekindeta^{24}@{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[CapitalDelta] == (2*Pi)^(12)* (DedekindEta[\[Tau]])^(24)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-8.27953934969212*^7, 0.49999990438754693]
| [https://dlmf.nist.gov/23.19.E4 23.19.E4] || <math qid="Q7371">\Delta = (2\pi)^{12}\Dedekindeta^{24}@{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Delta = (2\pi)^{12}\Dedekindeta^{24}@{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[CapitalDelta] == (2*Pi)^(12)* (DedekindEta[\[Tau]])^(24)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-8.27953934969212*^7, 0.49999990438754693]
Test Values: {Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.8191325291713696*^7, 0.49999997450648886]
Test Values: {Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.8191325291713696*^7, 0.49999997450648886]
Test Values: {Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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Latest revision as of 12:01, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
23.19.E1 λ ⁡ ( τ ) = 16 ⁢ ( η 2 ⁡ ( 2 ⁢ τ ) ⁢ η ⁡ ( 1 2 ⁢ τ ) η 3 ⁡ ( τ ) ) 8 modular-Lambda 𝜏 16 superscript Dedekind-modular-Eta 2 2 𝜏 Dedekind-modular-Eta 1 2 𝜏 Dedekind-modular-Eta 3 𝜏 8 {\displaystyle{\displaystyle\lambda\left(\tau\right)=16\left(\frac{{\eta^{2}}% \left(2\tau\right)\eta\left(\tfrac{1}{2}\tau\right)}{{\eta^{3}}\left(\tau% \right)}\right)^{8}}}
\modularlambdatau@{\tau} = 16\left(\frac{\Dedekindeta^{2}@{2\tau}\Dedekindeta@{\tfrac{1}{2}\tau}}{\Dedekindeta^{3}@{\tau}}\right)^{8}		 

Error

ModularLambda[\[Tau]] == 16*(Divide[(DedekindEta[2*\[Tau]])^(2)* DedekindEta[Divide[1,2]*\[Tau]],(DedekindEta[\[Tau]])^(3)])^(8)
Missing Macro Error Failure - Successful [Tested: 10]
23.19.E2 J ⁡ ( τ ) = 4 27 ⁢ ( 1 - λ ⁡ ( τ ) + λ 2 ⁡ ( τ ) ) 3 ( λ ⁡ ( τ ) ⁢ ( 1 - λ ⁡ ( τ ) ) ) 2 Kleins-invariant-modular-J 𝜏 4 27 superscript 1 modular-Lambda 𝜏 modular-Lambda 2 𝜏 3 superscript modular-Lambda 𝜏 1 modular-Lambda 𝜏 2 {\displaystyle{\displaystyle J\left(\tau\right)=\frac{4}{27}\frac{\left(1-% \lambda\left(\tau\right)+{\lambda^{2}}\left(\tau\right)\right)^{3}}{\left(% \lambda\left(\tau\right)\left(1-\lambda\left(\tau\right)\right)\right)^{2}}}}
\KleincompinvarJtau@{\tau} = \frac{4}{27}\frac{\left(1-\modularlambdatau@{\tau}+\modularlambdatau^{2}@{\tau}\right)^{3}}{\left(\modularlambdatau@{\tau}\left(1-\modularlambdatau@{\tau}\right)\right)^{2}}		 

Error

KleinInvariantJ[\[Tau]] == Divide[4,27]*Divide[(1 - ModularLambda[\[Tau]]+ (ModularLambda[\[Tau]])^(2))^(3),(ModularLambda[\[Tau]]*(1 - ModularLambda[\[Tau]]))^(2)]
Missing Macro Error Failure - Successful [Tested: 10]
23.19.E4 Δ = ( 2 ⁢ π ) 12 ⁢ η 24 ⁡ ( τ ) Δ superscript 2 𝜋 12 Dedekind-modular-Eta 24 𝜏 {\displaystyle{\displaystyle\Delta=(2\pi)^{12}{\eta^{24}}\left(\tau\right)}}
\Delta = (2\pi)^{12}\Dedekindeta^{24}@{\tau}		 

Error

\[CapitalDelta] == (2*Pi)^(12)* (DedekindEta[\[Tau]])^(24)
Missing Macro Error Failure -
Failed [20 / 100]
Result: Complex[-8.27953934969212*^7, 0.49999990438754693]
Test Values: {Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[1.8191325291713696*^7, 0.49999997450648886]
Test Values: {Rule[Δ, 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
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