5.20: 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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| [https://dlmf.nist.gov/5.20.E1 5.20.E1] | | | [https://dlmf.nist.gov/5.20.E1 5.20.E1] || <math qid="Q2206">W = \frac{1}{2}\sum_{\ell=1}^{n}x_{\ell}^{2}-\sum_{1\leq\ell<j\leq n}\ln@@{|x_{\ell}-x_{j}|}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>W = \frac{1}{2}\sum_{\ell=1}^{n}x_{\ell}^{2}-\sum_{1\leq\ell<j\leq n}\ln@@{|x_{\ell}-x_{j}|}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>W = (1)/(2)*sum((x[ell])^(2), ell = 1..n)- sum(sum(ln(abs(x[ell]- x[j])), j = ell + 1..n), ell = 1..j - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>W == Divide[1,2]*Sum[(Subscript[x, \[ScriptL]])^(2), {\[ScriptL], 1, n}, GenerateConditions->None]- Sum[Sum[Log[Abs[Subscript[x, \[ScriptL]]- Subscript[x, j]]], {j, [ScriptL] + 1, n}, GenerateConditions->None], {\[ScriptL], 1, j - 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || Error | ||
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| [https://dlmf.nist.gov/5.20.E4 5.20.E4] | | | [https://dlmf.nist.gov/5.20.E4 5.20.E4] || <math qid="Q2209">W = -\sum_{1\leq\ell<j\leq n}\ln@@{|e^{i\theta_{\ell}}-e^{i\theta_{j}}|}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>W = -\sum_{1\leq\ell<j\leq n}\ln@@{|e^{i\theta_{\ell}}-e^{i\theta_{j}}|}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>W = - sum(sum(ln(abs(exp(I*theta[ell])- exp(I*theta[j]))), j = ell + 1..n), ell = 1..j - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>W == - Sum[Sum[Log[Abs[Exp[I*Subscript[\[Theta], \[ScriptL]]]- Exp[I*Subscript[\[Theta], j]]]], {j, [ScriptL] + 1, n}, GenerateConditions->None], {\[ScriptL], 1, j - 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || Error | ||
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</div> | </div> | ||
Latest revision as of 11:13, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 5.20.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W = \frac{1}{2}\sum_{\ell=1}^{n}x_{\ell}^{2}-\sum_{1\leq\ell<j\leq n}\ln@@{|x_{\ell}-x_{j}|}}
W = \frac{1}{2}\sum_{\ell=1}^{n}x_{\ell}^{2}-\sum_{1\leq\ell<j\leq n}\ln@@{|x_{\ell}-x_{j}|} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | W = (1)/(2)*sum((x[ell])^(2), ell = 1..n)- sum(sum(ln(abs(x[ell]- x[j])), j = ell + 1..n), ell = 1..j - 1)
|
W == Divide[1,2]*Sum[(Subscript[x, \[ScriptL]])^(2), {\[ScriptL], 1, n}, GenerateConditions->None]- Sum[Sum[Log[Abs[Subscript[x, \[ScriptL]]- Subscript[x, j]]], {j, [ScriptL] + 1, n}, GenerateConditions->None], {\[ScriptL], 1, j - 1}, GenerateConditions->None]
|
Failure | Failure | Error | Error |
| 5.20.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W = -\sum_{1\leq\ell<j\leq n}\ln@@{|e^{i\theta_{\ell}}-e^{i\theta_{j}}|}}
W = -\sum_{1\leq\ell<j\leq n}\ln@@{|e^{i\theta_{\ell}}-e^{i\theta_{j}}|} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | W = - sum(sum(ln(abs(exp(I*theta[ell])- exp(I*theta[j]))), j = ell + 1..n), ell = 1..j - 1)
|
W == - Sum[Sum[Log[Abs[Exp[I*Subscript[\[Theta], \[ScriptL]]]- Exp[I*Subscript[\[Theta], j]]]], {j, [ScriptL] + 1, n}, GenerateConditions->None], {\[ScriptL], 1, j - 1}, GenerateConditions->None]
|
Failure | Failure | Error | Error |