19.10: 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 | ||
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| [https://dlmf.nist.gov/19.10#Ex1 19.10#Ex1] | | | [https://dlmf.nist.gov/19.10#Ex1 19.10#Ex1] || <math qid="Q6263">\ln@{x/y} = (x-y)\CarlsonellintRC@{\tfrac{1}{4}(x+y)^{2}}{xy}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ln@{x/y} = (x-y)\CarlsonellintRC@{\tfrac{1}{4}(x+y)^{2}}{xy}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Log[x/y] == (x - y)*1/Sqrt[x*y]*Hypergeometric2F1[1/2,1/2,3/2,1-(Divide[1,4]*(x + y)^(2))/(x*y)]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 6.283185307179586] | ||
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/19.10#Ex2 19.10#Ex2] | | | [https://dlmf.nist.gov/19.10#Ex2 19.10#Ex2] || <math qid="Q6264">\atan@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}+x^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}+x^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[x/y] == x*1/Sqrt[(y)^(2)+ (x)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2))/((y)^(2)+ (x)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.5707963267948966 | ||
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.498091544796509 | Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.498091544796509 | ||
Test Values: {Rule[x, 1.5], Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[x, 1.5], Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/19.10#Ex3 19.10#Ex3] | | | [https://dlmf.nist.gov/19.10#Ex3 19.10#Ex3] || <math qid="Q6265">\atanh@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}-x^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atanh@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}-x^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTanh[x/y] == x*1/Sqrt[(y)^(2)- (x)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2))/((y)^(2)- (x)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/19.10#Ex4 19.10#Ex4] | | | [https://dlmf.nist.gov/19.10#Ex4 19.10#Ex4] || <math qid="Q6266">\asin@{x/y} = x\CarlsonellintRC@{y^{2}-x^{2}}{y^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asin@{x/y} = x\CarlsonellintRC@{y^{2}-x^{2}}{y^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[x/y] == x*1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2)- (x)^(2))/((y)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.141592653589793 | ||
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.141592653589793, 3.525494348078172] | Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.141592653589793, 3.525494348078172] | ||
Test Values: {Rule[x, 1.5], Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[x, 1.5], Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/19.10#Ex5 19.10#Ex5] | | | [https://dlmf.nist.gov/19.10#Ex5 19.10#Ex5] || <math qid="Q6267">\asinh@{x/y} = x\CarlsonellintRC@{y^{2}+x^{2}}{y^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\asinh@{x/y} = x\CarlsonellintRC@{y^{2}+x^{2}}{y^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSinh[x/y] == x*1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2)+ (x)^(2))/((y)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.7627471740390859, 0.0] | ||
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.6368929184641337, 0.0] | Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.6368929184641337, 0.0] | ||
Test Values: {Rule[x, 1.5], Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[x, 1.5], Rule[y, -0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
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| [https://dlmf.nist.gov/19.10#Ex6 19.10#Ex6] | | | [https://dlmf.nist.gov/19.10#Ex6 19.10#Ex6] || <math qid="Q6268">\acos@{x/y} = (y^{2}-x^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@{x/y} = (y^{2}-x^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[x/y] == ((y)^(2)- (x)^(2))^(1/2)* 1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/19.10#Ex7 19.10#Ex7] | | | [https://dlmf.nist.gov/19.10#Ex7 19.10#Ex7] || <math qid="Q6269">\acosh@{x/y} = (x^{2}-y^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acosh@{x/y} = (x^{2}-y^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCosh[x/y] == ((x)^(2)- (y)^(2))^(1/2)* 1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/19.10.E2 19.10.E2] | | | [https://dlmf.nist.gov/19.10.E2 19.10.E2] || <math qid="Q6270">(\sinh@@{\phi})\CarlsonellintRC@{1}{\cosh^{2}@@{\phi}} = \Gudermannian@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\sinh@@{\phi})\CarlsonellintRC@{1}{\cosh^{2}@@{\phi}} = \Gudermannian@{\phi}</syntaxhighlight> || <math>-\infty < (\phi), (\phi) < \infty</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Sinh[\[Phi]])*1/Sqrt[(Cosh[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cosh[\[Phi]])^(2))] == Gudermannian[\[Phi]]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 6] | ||
|} | |} | ||
</div> | </div> |
Latest revision as of 12:50, 28 June 2021
DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
---|---|---|---|---|---|---|---|---|
19.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@{x/y} = (x-y)\CarlsonellintRC@{\tfrac{1}{4}(x+y)^{2}}{xy}}
\ln@{x/y} = (x-y)\CarlsonellintRC@{\tfrac{1}{4}(x+y)^{2}}{xy} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
Log[x/y] == (x - y)*1/Sqrt[x*y]*Hypergeometric2F1[1/2,1/2,3/2,1-(Divide[1,4]*(x + y)^(2))/(x*y)]
|
Missing Macro Error | Failure | - | Failed [12 / 18]
Result: Complex[0.0, 6.283185307179586]
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}
Result: Indeterminate
Test Values: {Rule[x, 1.5], Rule[y, 1.5]}
... skip entries to safe data |
19.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}+x^{2}}}
\atan@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}+x^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ArcTan[x/y] == x*1/Sqrt[(y)^(2)+ (x)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2))/((y)^(2)+ (x)^(2))]
|
Missing Macro Error | Failure | - | Failed [9 / 18]
Result: -1.5707963267948966
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}
Result: -2.498091544796509
Test Values: {Rule[x, 1.5], Rule[y, -0.5]}
... skip entries to safe data |
19.10#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atanh@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}-x^{2}}}
\atanh@{x/y} = x\CarlsonellintRC@{y^{2}}{y^{2}-x^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ArcTanh[x/y] == x*1/Sqrt[(y)^(2)- (x)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2))/((y)^(2)- (x)^(2))]
|
Missing Macro Error | Failure | - | Failed [15 / 18]
Result: Indeterminate
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}
Result: Indeterminate
Test Values: {Rule[x, 1.5], Rule[y, 1.5]}
... skip entries to safe data |
19.10#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@{x/y} = x\CarlsonellintRC@{y^{2}-x^{2}}{y^{2}}}
\asin@{x/y} = x\CarlsonellintRC@{y^{2}-x^{2}}{y^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ArcSin[x/y] == x*1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2)- (x)^(2))/((y)^(2))]
|
Missing Macro Error | Failure | - | Failed [9 / 18]
Result: -3.141592653589793
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}
Result: Complex[-3.141592653589793, 3.525494348078172]
Test Values: {Rule[x, 1.5], Rule[y, -0.5]}
... skip entries to safe data |
19.10#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@{x/y} = x\CarlsonellintRC@{y^{2}+x^{2}}{y^{2}}}
\asinh@{x/y} = x\CarlsonellintRC@{y^{2}+x^{2}}{y^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ArcSinh[x/y] == x*1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((y)^(2)+ (x)^(2))/((y)^(2))]
|
Missing Macro Error | Failure | - | Failed [9 / 18]
Result: Complex[-1.7627471740390859, 0.0]
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}
Result: Complex[-3.6368929184641337, 0.0]
Test Values: {Rule[x, 1.5], Rule[y, -0.5]}
... skip entries to safe data |
19.10#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@{x/y} = (y^{2}-x^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}}}
\acos@{x/y} = (y^{2}-x^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ArcCos[x/y] == ((y)^(2)- (x)^(2))^(1/2)* 1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))]
|
Missing Macro Error | Failure | - | Failed [12 / 18]
Result: Indeterminate
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}
Result: Indeterminate
Test Values: {Rule[x, 1.5], Rule[y, 1.5]}
... skip entries to safe data |
19.10#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@{x/y} = (x^{2}-y^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}}}
\acosh@{x/y} = (x^{2}-y^{2})^{1/2}\CarlsonellintRC@{x^{2}}{y^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ArcCosh[x/y] == ((x)^(2)- (y)^(2))^(1/2)* 1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))]
|
Missing Macro Error | Failure | - | Failed [12 / 18]
Result: Indeterminate
Test Values: {Rule[x, 1.5], Rule[y, -1.5]}
Result: Indeterminate
Test Values: {Rule[x, 1.5], Rule[y, 1.5]}
... skip entries to safe data |
19.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sinh@@{\phi})\CarlsonellintRC@{1}{\cosh^{2}@@{\phi}} = \Gudermannian@{\phi}}
(\sinh@@{\phi})\CarlsonellintRC@{1}{\cosh^{2}@@{\phi}} = \Gudermannian@{\phi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\infty < (\phi), (\phi) < \infty} | Error
|
(Sinh[\[Phi]])*1/Sqrt[(Cosh[\[Phi]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(1)/((Cosh[\[Phi]])^(2))] == Gudermannian[\[Phi]]
|
Missing Macro Error | Failure | - | Successful [Tested: 6] |