34.2: Difference between revisions
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Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/34.2.E1 34.2.E1] | | | [https://dlmf.nist.gov/34.2.E1 34.2.E1] || <math qid="Q9710">|j_{r}-j_{s}| \leq j_{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>|j_{r}-j_{s}| \leq j_{t}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">abs(j[r]- j[s]) <= j[t]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Abs[Subscript[j, r]- Subscript[j, s]] <= Subscript[j, t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/34.2.E3 34.2.E3] | | | [https://dlmf.nist.gov/34.2.E3 34.2.E3] || <math qid="Q9712">m_{1}+m_{2}+m_{3} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>m_{1}+m_{2}+m_{3} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">m[1]+ m[2]+ m[3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[m, 1]+ Subscript[m, 2]+ Subscript[m, 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
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| [https://dlmf.nist.gov/34.2.E4 34.2.E4] | | | [https://dlmf.nist.gov/34.2.E4 34.2.E4] || <math qid="Q9713">\Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{1}-j_{2}-m_{3}}}\Delta(j_{1}j_{2}j_{3})\left((j_{1}+m_{1})!(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!(j_{3}-m_{3})!\right)^{\frac{1}{2}}\*\sum_{s}\frac{(-1)^{s}}{s!(j_{1}+j_{2}-j_{3}-s)!(j_{1}-m_{1}-s)!(j_{2}+m_{2}-s)!(j_{3}-j_{2}+m_{1}+s)!(j_{3}-j_{1}-m_{2}+s)!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{1}-j_{2}-m_{3}}}\Delta(j_{1}j_{2}j_{3})\left((j_{1}+m_{1})!(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!(j_{3}-m_{3})!\right)^{\frac{1}{2}}\*\sum_{s}\frac{(-1)^{s}}{s!(j_{1}+j_{2}-j_{3}-s)!(j_{1}-m_{1}-s)!(j_{2}+m_{2}-s)!(j_{3}-j_{2}+m_{1}+s)!(j_{3}-j_{1}-m_{2}+s)!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[m, 1], Subscript[m, 3]}] == (- 1)^(Subscript[j, 1]- Subscript[j, 2]- Subscript[m, 3])*((Divide[(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3])!*(Subscript[j, 1]- Subscript[j, 2]+ Subscript[j, 3])!*(- Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])!,(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!])^(Divide[1,2]))*((Subscript[j, 1]+ Subscript[m, 1])!*(Subscript[j, 1]- Subscript[m, 1])!*(Subscript[j, 2]+ Subscript[m, 2])!*(Subscript[j, 2]- Subscript[m, 2])!*(Subscript[j, 3]+ Subscript[m, 3])!*(Subscript[j, 3]- Subscript[m, 3])!)^(Divide[1,2])* Sum[Divide[(- 1)^(s),(s)!*(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3]- s)!*(Subscript[j, 1]- Subscript[m, 1]- s)!*(Subscript[j, 2]+ Subscript[m, 2]- s)!*(Subscript[j, 3]- Subscript[j, 2]+ Subscript[m, 1]+ s)!*(Subscript[j, 3]- Subscript[j, 1]- Subscript[m, 2]+ s)!], {s, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Translation Error || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/34.2.E6 34.2.E6] | | | [https://dlmf.nist.gov/34.2.E6 34.2.E6] || <math qid="Q9715">\Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{2}-m_{1}+m_{3}}}\frac{(j_{1}+j_{2}+m_{3})!(j_{2}+j_{3}-m_{1})!}{\Delta(j_{1}j_{2}j_{3})(j_{1}+j_{2}+j_{3}+1)!}\left(\frac{(j_{1}+m_{1})!(j_{3}-m_{3})!}{(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!}\right)^{\frac{1}{2}}\*{\genhyperF{3}{2}@{-j_{1}-j_{2}-j_{3}-1,-j_{1}+m_{1},-j_{3}-m_{3}}{-j_{1}-j_{2}-m_{3},-j_{2}-j_{3}+m_{1}}{1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{2}-m_{1}+m_{3}}}\frac{(j_{1}+j_{2}+m_{3})!(j_{2}+j_{3}-m_{1})!}{\Delta(j_{1}j_{2}j_{3})(j_{1}+j_{2}+j_{3}+1)!}\left(\frac{(j_{1}+m_{1})!(j_{3}-m_{3})!}{(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!}\right)^{\frac{1}{2}}\*{\genhyperF{3}{2}@{-j_{1}-j_{2}-j_{3}-1,-j_{1}+m_{1},-j_{3}-m_{3}}{-j_{1}-j_{2}-m_{3},-j_{2}-j_{3}+m_{1}}{1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[m, 1], Subscript[m, 3]}] == (- 1)^(Subscript[j, 2]- Subscript[m, 1]+ Subscript[m, 3])*Divide[(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[m, 3])!*(Subscript[j, 2]+ Subscript[j, 3]- Subscript[m, 1])!,((Divide[(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3])!*(Subscript[j, 1]- Subscript[j, 2]+ Subscript[j, 3])!*(- Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])!,(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!])^(Divide[1,2]))*(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!]*(Divide[(Subscript[j, 1]+ Subscript[m, 1])!*(Subscript[j, 3]- Subscript[m, 3])!,(Subscript[j, 1]- Subscript[m, 1])!*(Subscript[j, 2]+ Subscript[m, 2])!*(Subscript[j, 2]- Subscript[m, 2])!*(Subscript[j, 3]+ Subscript[m, 3])!])^(Divide[1,2])*HypergeometricPFQ[{- Subscript[j, 1]- Subscript[j, 2]- Subscript[j, 3]- 1 , - Subscript[j, 1]+ Subscript[m, 1], - Subscript[j, 3]- Subscript[m, 3]}, {- Subscript[j, 1]- Subscript[j, 2]- Subscript[m, 3], - Subscript[j, 2]- Subscript[j, 3]+ Subscript[m, 1]}, 1]</syntaxhighlight> || Missing Macro Error || Translation Error || - || - | ||
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</div> | </div> | ||
Latest revision as of 13:14, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 34.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |j_{r}-j_{s}| \leq j_{t}}
|j_{r}-j_{s}| \leq j_{t} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(j[r]- j[s]) <= j[t] |
Abs[Subscript[j, r]- Subscript[j, s]] <= Subscript[j, t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 34.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m_{1}+m_{2}+m_{3} = 0}
m_{1}+m_{2}+m_{3} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | m[1]+ m[2]+ m[3] = 0 |
Subscript[m, 1]+ Subscript[m, 2]+ Subscript[m, 3] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 34.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{1}-j_{2}-m_{3}}}\Delta(j_{1}j_{2}j_{3})\left((j_{1}+m_{1})!(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!(j_{3}-m_{3})!\right)^{\frac{1}{2}}\*\sum_{s}\frac{(-1)^{s}}{s!(j_{1}+j_{2}-j_{3}-s)!(j_{1}-m_{1}-s)!(j_{2}+m_{2}-s)!(j_{3}-j_{2}+m_{1}+s)!(j_{3}-j_{1}-m_{2}+s)!}}
\Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{1}-j_{2}-m_{3}}}\Delta(j_{1}j_{2}j_{3})\left((j_{1}+m_{1})!(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!(j_{3}-m_{3})!\right)^{\frac{1}{2}}\*\sum_{s}\frac{(-1)^{s}}{s!(j_{1}+j_{2}-j_{3}-s)!(j_{1}-m_{1}-s)!(j_{2}+m_{2}-s)!(j_{3}-j_{2}+m_{1}+s)!(j_{3}-j_{1}-m_{2}+s)!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[m, 1], Subscript[m, 3]}] == (- 1)^(Subscript[j, 1]- Subscript[j, 2]- Subscript[m, 3])*((Divide[(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3])!*(Subscript[j, 1]- Subscript[j, 2]+ Subscript[j, 3])!*(- Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])!,(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!])^(Divide[1,2]))*((Subscript[j, 1]+ Subscript[m, 1])!*(Subscript[j, 1]- Subscript[m, 1])!*(Subscript[j, 2]+ Subscript[m, 2])!*(Subscript[j, 2]- Subscript[m, 2])!*(Subscript[j, 3]+ Subscript[m, 3])!*(Subscript[j, 3]- Subscript[m, 3])!)^(Divide[1,2])* Sum[Divide[(- 1)^(s),(s)!*(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3]- s)!*(Subscript[j, 1]- Subscript[m, 1]- s)!*(Subscript[j, 2]+ Subscript[m, 2]- s)!*(Subscript[j, 3]- Subscript[j, 2]+ Subscript[m, 1]+ s)!*(Subscript[j, 3]- Subscript[j, 1]- Subscript[m, 2]+ s)!], {s, - Infinity, Infinity}, GenerateConditions->None]
|
Missing Macro Error | Translation Error | - | - |
| 34.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{2}-m_{1}+m_{3}}}\frac{(j_{1}+j_{2}+m_{3})!(j_{2}+j_{3}-m_{1})!}{\Delta(j_{1}j_{2}j_{3})(j_{1}+j_{2}+j_{3}+1)!}\left(\frac{(j_{1}+m_{1})!(j_{3}-m_{3})!}{(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!}\right)^{\frac{1}{2}}\*{\genhyperF{3}{2}@{-j_{1}-j_{2}-j_{3}-1,-j_{1}+m_{1},-j_{3}-m_{3}}{-j_{1}-j_{2}-m_{3},-j_{2}-j_{3}+m_{1}}{1}}}
\Wignerthreejsym{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}} = {(-1)^{j_{2}-m_{1}+m_{3}}}\frac{(j_{1}+j_{2}+m_{3})!(j_{2}+j_{3}-m_{1})!}{\Delta(j_{1}j_{2}j_{3})(j_{1}+j_{2}+j_{3}+1)!}\left(\frac{(j_{1}+m_{1})!(j_{3}-m_{3})!}{(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!}\right)^{\frac{1}{2}}\*{\genhyperF{3}{2}@{-j_{1}-j_{2}-j_{3}-1,-j_{1}+m_{1},-j_{3}-m_{3}}{-j_{1}-j_{2}-m_{3},-j_{2}-j_{3}+m_{1}}{1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ThreeJSymbol[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[m, 1], Subscript[m, 3]}] == (- 1)^(Subscript[j, 2]- Subscript[m, 1]+ Subscript[m, 3])*Divide[(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[m, 3])!*(Subscript[j, 2]+ Subscript[j, 3]- Subscript[m, 1])!,((Divide[(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3])!*(Subscript[j, 1]- Subscript[j, 2]+ Subscript[j, 3])!*(- Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])!,(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!])^(Divide[1,2]))*(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1)!]*(Divide[(Subscript[j, 1]+ Subscript[m, 1])!*(Subscript[j, 3]- Subscript[m, 3])!,(Subscript[j, 1]- Subscript[m, 1])!*(Subscript[j, 2]+ Subscript[m, 2])!*(Subscript[j, 2]- Subscript[m, 2])!*(Subscript[j, 3]+ Subscript[m, 3])!])^(Divide[1,2])*HypergeometricPFQ[{- Subscript[j, 1]- Subscript[j, 2]- Subscript[j, 3]- 1 , - Subscript[j, 1]+ Subscript[m, 1], - Subscript[j, 3]- Subscript[m, 3]}, {- Subscript[j, 1]- Subscript[j, 2]- Subscript[m, 3], - Subscript[j, 2]- Subscript[j, 3]+ Subscript[m, 1]}, 1]
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Missing Macro Error | Translation Error | - | - |