4.32: 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/4.32.E1 4.32.E1] | | | [https://dlmf.nist.gov/4.32.E1 4.32.E1] || <math qid="Q1854">\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cosh(x) <= ((sinh(x))/(x))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cosh[x] <= (Divide[Sinh[x],x])^(3)</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | ||
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| [https://dlmf.nist.gov/4.32.E2 4.32.E2] | | | [https://dlmf.nist.gov/4.32.E2 4.32.E2] || <math qid="Q1855">\sin@@{x}\cos@@{x} < \tanh@@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@@{x}\cos@@{x} < \tanh@@{x}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>sin(x)*cos(x) < tanh(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[x]*Cos[x] < Tanh[x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | ||
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| [https://dlmf.nist.gov/4.32.E2 4.32.E2] | | | [https://dlmf.nist.gov/4.32.E2 4.32.E2] || <math qid="Q1855">\tanh@@{x} < x</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tanh@@{x} < x</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>tanh(x) < x</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tanh[x] < x</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | ||
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| [https://dlmf.nist.gov/4.32.E3 4.32.E3] | | | [https://dlmf.nist.gov/4.32.E3 4.32.E3] || <math qid="Q1856">|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}</syntaxhighlight> || <math>x > 0, y > 0</math> || <syntaxhighlight lang=mathematica>abs(cosh(x)- cosh(y)) >= abs(x - y)*sqrt(sinh(x)*sinh(y))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[Cosh[x]- Cosh[y]] >= Abs[x - y]*Sqrt[Sinh[x]*Sinh[y]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9] | ||
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| [https://dlmf.nist.gov/4.32.E4 4.32.E4] | | | [https://dlmf.nist.gov/4.32.E4 4.32.E4] || <math qid="Q1857">\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}</syntaxhighlight> || <math>x \geq 0</math> || <syntaxhighlight lang=mathematica>arctan(x) <= (1)/(2)*Pi*tanh(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[x] <= Divide[1,2]*Pi*Tanh[x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | ||
|} | |} | ||
</div> | </div> | ||
Latest revision as of 11:09, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 4.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}}
\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cosh(x) <= ((sinh(x))/(x))^(3)
|
Cosh[x] <= (Divide[Sinh[x],x])^(3)
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 4.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{x}\cos@@{x} < \tanh@@{x}}
\sin@@{x}\cos@@{x} < \tanh@@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0} | sin(x)*cos(x) < tanh(x)
|
Sin[x]*Cos[x] < Tanh[x]
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 4.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{x} < x}
\tanh@@{x} < x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0} | tanh(x) < x
|
Tanh[x] < x
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 4.32.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}}
|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, y > 0} | abs(cosh(x)- cosh(y)) >= abs(x - y)*sqrt(sinh(x)*sinh(y))
|
Abs[Cosh[x]- Cosh[y]] >= Abs[x - y]*Sqrt[Sinh[x]*Sinh[y]]
|
Failure | Failure | Successful [Tested: 9] | Successful [Tested: 9] |
| 4.32.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}}
\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \geq 0} | arctan(x) <= (1)/(2)*Pi*tanh(x)
|
ArcTan[x] <= Divide[1,2]*Pi*Tanh[x]
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Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |