4.14: Difference between revisions

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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/4.14.E1 4.14.E1] || [[Item:Q1653|<math>\sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(z) = (exp(I*z)- exp(- I*z))/(2*I)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[z] == Divide[Exp[I*z]- Exp[- I*z],2*I]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E1 4.14.E1] || <math qid="Q1653">\sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(z) = (exp(I*z)- exp(- I*z))/(2*I)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[z] == Divide[Exp[I*z]- Exp[- I*z],2*I]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E2 4.14.E2] || [[Item:Q1654|<math>\cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(z) = (exp(I*z)+ exp(- I*z))/(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[z] == Divide[Exp[I*z]+ Exp[- I*z],2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E2 4.14.E2] || <math qid="Q1654">\cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(z) = (exp(I*z)+ exp(- I*z))/(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[z] == Divide[Exp[I*z]+ Exp[- I*z],2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
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| [https://dlmf.nist.gov/4.14.E3 4.14.E3] || [[Item:Q1655|<math>\cos@@{z}+ i\sin@@{z} = e^{+ iz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{z}+ i\sin@@{z} = e^{+ iz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(z)+ I*sin(z) = exp(+ I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[z]+ I*Sin[z] == Exp[+ I*z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E3 4.14.E3] || <math qid="Q1655">\cos@@{z}+ i\sin@@{z} = e^{+ iz}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{z}+ i\sin@@{z} = e^{+ iz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(z)+ I*sin(z) = exp(+ I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[z]+ I*Sin[z] == Exp[+ I*z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E3 4.14.E3] || [[Item:Q1655|<math>\cos@@{z}- i\sin@@{z} = e^{- iz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{z}- i\sin@@{z} = e^{- iz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(z)- I*sin(z) = exp(- I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[z]- I*Sin[z] == Exp[- I*z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E3 4.14.E3] || <math qid="Q1655">\cos@@{z}- i\sin@@{z} = e^{- iz}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{z}- i\sin@@{z} = e^{- iz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(z)- I*sin(z) = exp(- I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[z]- I*Sin[z] == Exp[- I*z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E4 4.14.E4] || [[Item:Q1656|<math>\tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>tan(z) = (sin(z))/(cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tan[z] == Divide[Sin[z],Cos[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E4 4.14.E4] || <math qid="Q1656">\tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>tan(z) = (sin(z))/(cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tan[z] == Divide[Sin[z],Cos[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E5 4.14.E5] || [[Item:Q1657|<math>\csc@@{z} = \frac{1}{\sin@@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\csc@@{z} = \frac{1}{\sin@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>csc(z) = (1)/(sin(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Csc[z] == Divide[1,Sin[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E5 4.14.E5] || <math qid="Q1657">\csc@@{z} = \frac{1}{\sin@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\csc@@{z} = \frac{1}{\sin@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>csc(z) = (1)/(sin(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Csc[z] == Divide[1,Sin[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E6 4.14.E6] || [[Item:Q1658|<math>\sec@@{z} = \frac{1}{\cos@@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sec@@{z} = \frac{1}{\cos@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sec(z) = (1)/(cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sec[z] == Divide[1,Cos[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E6 4.14.E6] || <math qid="Q1658">\sec@@{z} = \frac{1}{\cos@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sec@@{z} = \frac{1}{\cos@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sec(z) = (1)/(cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sec[z] == Divide[1,Cos[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E7 4.14.E7] || [[Item:Q1659|<math>\cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cot(z) = (cos(z))/(sin(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cot[z] == Divide[Cos[z],Sin[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E7 4.14.E7] || <math qid="Q1659">\cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cot(z) = (cos(z))/(sin(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cot[z] == Divide[Cos[z],Sin[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E7 4.14.E7] || [[Item:Q1659|<math>\frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(cos(z))/(sin(z)) = (1)/(tan(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Cos[z],Sin[z]] == Divide[1,Tan[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
| [https://dlmf.nist.gov/4.14.E7 4.14.E7] || <math qid="Q1659">\frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(cos(z))/(sin(z)) = (1)/(tan(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Cos[z],Sin[z]] == Divide[1,Tan[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
|-  
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| [https://dlmf.nist.gov/4.14.E8 4.14.E8] || [[Item:Q1660|<math>\sin@{z+2k\pi} = \sin@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{z+2k\pi} = \sin@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(z + 2*k*Pi) = sin(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[z + 2*k*Pi] == Sin[z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 21]
| [https://dlmf.nist.gov/4.14.E8 4.14.E8] || <math qid="Q1660">\sin@{z+2k\pi} = \sin@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{z+2k\pi} = \sin@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(z + 2*k*Pi) = sin(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[z + 2*k*Pi] == Sin[z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 21]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E9 4.14.E9] || [[Item:Q1661|<math>\cos@{z+2k\pi} = \cos@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@{z+2k\pi} = \cos@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(z + 2*k*Pi) = cos(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[z + 2*k*Pi] == Cos[z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 21]
| [https://dlmf.nist.gov/4.14.E9 4.14.E9] || <math qid="Q1661">\cos@{z+2k\pi} = \cos@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@{z+2k\pi} = \cos@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(z + 2*k*Pi) = cos(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[z + 2*k*Pi] == Cos[z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 21]
|-  
|-  
| [https://dlmf.nist.gov/4.14.E10 4.14.E10] || [[Item:Q1662|<math>\tan@{z+k\pi} = \tan@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tan@{z+k\pi} = \tan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>tan(z + k*Pi) = tan(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tan[z + k*Pi] == Tan[z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 21]
| [https://dlmf.nist.gov/4.14.E10 4.14.E10] || <math qid="Q1662">\tan@{z+k\pi} = \tan@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tan@{z+k\pi} = \tan@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>tan(z + k*Pi) = tan(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tan[z + k*Pi] == Tan[z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 21]
|}
|}
</div>
</div>

Latest revision as of 11:06, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
4.14.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit}}
\sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sin(z) = (exp(I*z)- exp(- I*z))/(2*I)

Sin[z] == Divide[Exp[I*z]- Exp[- I*z],2*I]
Successful Successful - Successful [Tested: 7]
4.14.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2}}
\cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
cos(z) = (exp(I*z)+ exp(- I*z))/(2)

Cos[z] == Divide[Exp[I*z]+ Exp[- I*z],2]
Successful Successful - Successful [Tested: 7]
4.14.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z}+ i\sin@@{z} = e^{+ iz}}
\cos@@{z}+ i\sin@@{z} = e^{+ iz}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
cos(z)+ I*sin(z) = exp(+ I*z)

Cos[z]+ I*Sin[z] == Exp[+ I*z]
Successful Successful - Successful [Tested: 7]
4.14.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z}- i\sin@@{z} = e^{- iz}}
\cos@@{z}- i\sin@@{z} = e^{- iz}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
cos(z)- I*sin(z) = exp(- I*z)

Cos[z]- I*Sin[z] == Exp[- I*z]
Successful Successful - Successful [Tested: 7]
4.14.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}}}
\tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
tan(z) = (sin(z))/(cos(z))

Tan[z] == Divide[Sin[z],Cos[z]]
Successful Successful - Successful [Tested: 7]
4.14.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc@@{z} = \frac{1}{\sin@@{z}}}
\csc@@{z} = \frac{1}{\sin@@{z}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
csc(z) = (1)/(sin(z))

Csc[z] == Divide[1,Sin[z]]
Successful Successful - Successful [Tested: 7]
4.14.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@@{z} = \frac{1}{\cos@@{z}}}
\sec@@{z} = \frac{1}{\cos@@{z}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sec(z) = (1)/(cos(z))

Sec[z] == Divide[1,Cos[z]]
Successful Successful - Successful [Tested: 7]
4.14.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}}}
\cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
cot(z) = (cos(z))/(sin(z))

Cot[z] == Divide[Cos[z],Sin[z]]
Successful Successful - Successful [Tested: 7]
4.14.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}}}
\frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(cos(z))/(sin(z)) = (1)/(tan(z))

Divide[Cos[z],Sin[z]] == Divide[1,Tan[z]]
Successful Successful - Successful [Tested: 7]
4.14.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z+2k\pi} = \sin@@{z}}
\sin@{z+2k\pi} = \sin@@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sin(z + 2*k*Pi) = sin(z)

Sin[z + 2*k*Pi] == Sin[z]
Successful Failure - Successful [Tested: 21]
4.14.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z+2k\pi} = \cos@@{z}}
\cos@{z+2k\pi} = \cos@@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
cos(z + 2*k*Pi) = cos(z)

Cos[z + 2*k*Pi] == Cos[z]
Successful Failure - Successful [Tested: 21]
4.14.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{z+k\pi} = \tan@@{z}}
\tan@{z+k\pi} = \tan@@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
tan(z + k*Pi) = tan(z)

Tan[z + k*Pi] == Tan[z]
Successful Failure - Successful [Tested: 21]
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