33.12: 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/33.12#Ex6 33.12#Ex6] | | | [https://dlmf.nist.gov/33.12#Ex6 33.12#Ex6] || <math qid="Q9601">B_{1} = -\tfrac{1}{5}x</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1} = -\tfrac{1}{5}x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[1] = -(1)/(5)*x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 1] == -Divide[1,5]*x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/33.12#Ex7 33.12#Ex7] | | | [https://dlmf.nist.gov/33.12#Ex7 33.12#Ex7] || <math qid="Q9602">B_{2} = \tfrac{1}{350}(7x^{5}-30x^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2} = \tfrac{1}{350}(7x^{5}-30x^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[2] = (1)/(350)*(7*(x)^(5)- 30*(x)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 2] == Divide[1,350]*(7*(x)^(5)- 30*(x)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/33.12#Ex8 33.12#Ex8] | | | [https://dlmf.nist.gov/33.12#Ex8 33.12#Ex8] || <math qid="Q9603">B_{3} = \tfrac{1}{15750}(264x^{6}-290x^{3}-560)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3} = \tfrac{1}{15750}(264x^{6}-290x^{3}-560)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[3] = (1)/(15750)*(264*(x)^(6)- 290*(x)^(3)- 560)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 3] == Divide[1,15750]*(264*(x)^(6)- 290*(x)^(3)- 560)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/33.12.E8 33.12.E8] | | | [https://dlmf.nist.gov/33.12.E8 33.12.E8] || <math qid="Q9606">\deriv[2]{w}{z} = \left(4\eta^{2}\left(\frac{1-z}{z}\right)+\frac{\ell(\ell+1)}{z^{2}}\right)w</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z} = \left(4\eta^{2}\left(\frac{1-z}{z}\right)+\frac{\ell(\ell+1)}{z^{2}}\right)w</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)]) = (4*(eta((1 - z)/(z)))^(2)+(ell*(ell + 1))/((z)^(2)))*w</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}] == (4*(\[Eta][Divide[1 - z,z]])^(2)+Divide[\[ScriptL]*(\[ScriptL]+ 1),(z)^(2)])*w</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [296 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.7320508075688767, 1.5358983848622458] | ||
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-7.196152422706632, 3.535898384862246] | Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-7.196152422706632, 3.535898384862246] | ||
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
|} | |} | ||
</div> | </div> | ||
Latest revision as of 12:14, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 33.12#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1} = -\tfrac{1}{5}x}
B_{1} = -\tfrac{1}{5}x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | B[1] = -(1)/(5)*x |
Subscript[B, 1] == -Divide[1,5]*x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 33.12#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2} = \tfrac{1}{350}(7x^{5}-30x^{2})}
B_{2} = \tfrac{1}{350}(7x^{5}-30x^{2}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | B[2] = (1)/(350)*(7*(x)^(5)- 30*(x)^(2)) |
Subscript[B, 2] == Divide[1,350]*(7*(x)^(5)- 30*(x)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 33.12#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{3} = \tfrac{1}{15750}(264x^{6}-290x^{3}-560)}
B_{3} = \tfrac{1}{15750}(264x^{6}-290x^{3}-560) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | B[3] = (1)/(15750)*(264*(x)^(6)- 290*(x)^(3)- 560) |
Subscript[B, 3] == Divide[1,15750]*(264*(x)^(6)- 290*(x)^(3)- 560) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 33.12.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = \left(4\eta^{2}\left(\frac{1-z}{z}\right)+\frac{\ell(\ell+1)}{z^{2}}\right)w}
\deriv[2]{w}{z} = \left(4\eta^{2}\left(\frac{1-z}{z}\right)+\frac{\ell(\ell+1)}{z^{2}}\right)w |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(w, [z$(2)]) = (4*(eta((1 - z)/(z)))^(2)+(ell*(ell + 1))/((z)^(2)))*w
|
D[w, {z, 2}] == (4*(\[Eta][Divide[1 - z,z]])^(2)+Divide[\[ScriptL]*(\[ScriptL]+ 1),(z)^(2)])*w
|
Failure | Failure | Error | Failed [296 / 300]
Result: Complex[-3.7320508075688767, 1.5358983848622458]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-7.196152422706632, 3.535898384862246]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |