27.3: 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/27.3.E3 27.3.E3] | | | [https://dlmf.nist.gov/27.3.E3 27.3.E3] || <math qid="Q8004">\Eulertotientphi[]@{n} = n\prod_{p\divides n}(1-p^{-1})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Eulertotientphi[]@{n} = n\prod_{p\divides n}(1-p^{-1})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(n) = n*product(1 - (p)^(- 1), p**n in - infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerPhi[n] == n*Product[1 - (p)^(- 1), {p**n, - Infinity}, GenerateConditions->None]</syntaxhighlight> || Translation Error || Translation Error || - || - | ||
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| [https://dlmf.nist.gov/27.3.E5 27.3.E5] | | | [https://dlmf.nist.gov/27.3.E5 27.3.E5] || <math qid="Q8006">\ndivisors[]@{n} = \prod_{r=1}^{\nprimesdiv@{n}}(1+a_{r})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ndivisors[]@{n} = \prod_{r=1}^{\nprimesdiv@{n}}(1+a_{r})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>numelems(Divisors(n)) = product(1 + a[r], r = 1..ifactor(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Missing Macro Error || - || - | ||
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| [https://dlmf.nist.gov/27.3.E6 27.3.E6] | | | [https://dlmf.nist.gov/27.3.E6 27.3.E6] || <math qid="Q8007">\sumdivisors{\alpha}@{n} = \prod_{r=1}^{\nprimesdiv@{n}}\frac{p^{\alpha(1+a_{r})}_{r}-1}{p^{\alpha}_{r}-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sumdivisors{\alpha}@{n} = \prod_{r=1}^{\nprimesdiv@{n}}\frac{p^{\alpha(1+a_{r})}_{r}-1}{p^{\alpha}_{r}-1}</syntaxhighlight> || <math>\alpha \neq 0</math> || <syntaxhighlight lang=mathematica>add(divisors(alpha)) = product(((p[r])^(alpha*(1 + a[r]))- 1)/((p[r])^(alpha)- 1), r = 1..ifactor(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || - | ||
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| [https://dlmf.nist.gov/27.3.E8 27.3.E8] | | | [https://dlmf.nist.gov/27.3.E8 27.3.E8] || <math qid="Q8009">\Eulertotientphi[]@{m}\Eulertotientphi[]@{n} = \Eulertotientphi[]@{mn}\Eulertotientphi[]@{\pgcd{m,n}}/\pgcd{m,n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Eulertotientphi[]@{m}\Eulertotientphi[]@{n} = \Eulertotientphi[]@{mn}\Eulertotientphi[]@{\pgcd{m,n}}/\pgcd{m,n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(m)*phi(n) = phi(m*n)*phi(gcd(m , n))/gcd(m , n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerPhi[m]*EulerPhi[n] == EulerPhi[m*n]*EulerPhi[GCD[m , n]]/GCD[m , n]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1. | ||
Test Values: {m = 2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2. | Test Values: {m = 2, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2. | ||
Test Values: {m = 3, n = 3}</syntaxhighlight><br></div></div> || Successful [Tested: 9] | Test Values: {m = 3, n = 3}</syntaxhighlight><br></div></div> || Successful [Tested: 9] | ||
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</div> | </div> | ||
Latest revision as of 12:06, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 27.3.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Eulertotientphi[]@{n} = n\prod_{p\divides n}(1-p^{-1})}
\Eulertotientphi[]@{n} = n\prod_{p\divides n}(1-p^{-1}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | phi(n) = n*product(1 - (p)^(- 1), p**n in - infinity)
|
EulerPhi[n] == n*Product[1 - (p)^(- 1), {p**n, - Infinity}, GenerateConditions->None]
|
Translation Error | Translation Error | - | - |
| 27.3.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ndivisors[]@{n} = \prod_{r=1}^{\nprimesdiv@{n}}(1+a_{r})}
\ndivisors[]@{n} = \prod_{r=1}^{\nprimesdiv@{n}}(1+a_{r}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | numelems(Divisors(n)) = product(1 + a[r], r = 1..ifactor(n))
|
Error
|
Error | Missing Macro Error | - | - |
| 27.3.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sumdivisors{\alpha}@{n} = \prod_{r=1}^{\nprimesdiv@{n}}\frac{p^{\alpha(1+a_{r})}_{r}-1}{p^{\alpha}_{r}-1}}
\sumdivisors{\alpha}@{n} = \prod_{r=1}^{\nprimesdiv@{n}}\frac{p^{\alpha(1+a_{r})}_{r}-1}{p^{\alpha}_{r}-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha \neq 0} | add(divisors(alpha)) = product(((p[r])^(alpha*(1 + a[r]))- 1)/((p[r])^(alpha)- 1), r = 1..ifactor(n))
|
Error
|
Failure | Missing Macro Error | Error | - |
| 27.3.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Eulertotientphi[]@{m}\Eulertotientphi[]@{n} = \Eulertotientphi[]@{mn}\Eulertotientphi[]@{\pgcd{m,n}}/\pgcd{m,n}}
\Eulertotientphi[]@{m}\Eulertotientphi[]@{n} = \Eulertotientphi[]@{mn}\Eulertotientphi[]@{\pgcd{m,n}}/\pgcd{m,n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | phi(m)*phi(n) = phi(m*n)*phi(gcd(m , n))/gcd(m , n)
|
EulerPhi[m]*EulerPhi[n] == EulerPhi[m*n]*EulerPhi[GCD[m , n]]/GCD[m , n]
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Failure | Failure | Failed [2 / 9] Result: -1.
Test Values: {m = 2, n = 2}
Result: -2.
Test Values: {m = 3, n = 3}
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Successful [Tested: 9] |