3.12: 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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{{DISPLAYTITLE:Numerical Methods - 3.12 Mathematical Constants}} | |||
<div style="width: 100%; height: 75vh; overflow: auto;"> | <div style="width: 100%; height: 75vh; overflow: auto;"> | ||
{| class="wikitable sortable" style="margin: 0;" | {| class="wikitable sortable" style="margin: 0;" | ||
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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ||
|- | |- | ||
| [https://dlmf.nist.gov/3.12.E1 3.12.E1] | | | [https://dlmf.nist.gov/3.12.E1 3.12.E1] || <math qid="Q1493">\cpi = 3.14159\;26535\;89793\;23846\;\ldots</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cpi = 3.14159\;26535\;89793\;23846\;\ldots</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Pi = 3.14159265358979323846</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pi == 3.14159265358979323846</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1] | ||
|- | |- | ||
| [https://dlmf.nist.gov/3.12.E2 3.12.E2] | | | [https://dlmf.nist.gov/3.12.E2 3.12.E2] || <math qid="Q1494">\cpi = 4\int_{0}^{1}\frac{\diff{t}}{1+t^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cpi = 4\int_{0}^{1}\frac{\diff{t}}{1+t^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Pi = 4*int((1)/(1 + (t)^(2)), t = 0..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pi == 4*Integrate[Divide[1,1 + (t)^(2)], {t, 0, 1}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1] | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/3.12.E3 3.12.E3] | | | [https://dlmf.nist.gov/3.12.E3 3.12.E3] || <math qid="Q1495">e = 2.71828\;18284\;59045\;23536\;\ldots</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e = 2.71828\;18284\;59045\;23536\;\ldots</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">exp(1) = 2.71828182845904523536</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">E == 2.71828182845904523536</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/3.12.E4 3.12.E4] | | | [https://dlmf.nist.gov/3.12.E4 3.12.E4] || <math qid="Q1496">\EulerConstant = 0.57721\;56649\;01532\;86060\;\ldots</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerConstant = 0.57721\;56649\;01532\;86060\;\ldots</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>gamma = 0.57721566490153286060</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerGamma == 0.57721566490153286060</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1] | ||
|} | |} | ||
</div> | </div> | ||
Latest revision as of 11:04, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 3.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi = 3.14159\;26535\;89793\;23846\;\ldots}
\cpi = 3.14159\;26535\;89793\;23846\;\ldots |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Pi = 3.14159265358979323846
|
Pi == 3.14159265358979323846
|
Successful | Successful | - | Successful [Tested: 1] |
| 3.12.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi = 4\int_{0}^{1}\frac{\diff{t}}{1+t^{2}}}
\cpi = 4\int_{0}^{1}\frac{\diff{t}}{1+t^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Pi = 4*int((1)/(1 + (t)^(2)), t = 0..1)
|
Pi == 4*Integrate[Divide[1,1 + (t)^(2)], {t, 0, 1}, GenerateConditions->None]
|
Successful | Successful | - | Successful [Tested: 1] |
| 3.12.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e = 2.71828\;18284\;59045\;23536\;\ldots}
e = 2.71828\;18284\;59045\;23536\;\ldots |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | exp(1) = 2.71828182845904523536 |
E == 2.71828182845904523536 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.12.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerConstant = 0.57721\;56649\;01532\;86060\;\ldots}
\EulerConstant = 0.57721\;56649\;01532\;86060\;\ldots |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | gamma = 0.57721566490153286060
|
EulerGamma == 0.57721566490153286060
|
Successful | Successful | - | Successful [Tested: 1] |