27.2: Difference between revisions

From testwiki
Jump to navigation Jump to search
VisualWikitext
 
 
Line 14: Line 14:
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-  
|-  
| [https://dlmf.nist.gov/27.2.E1 27.2.E1] || [[Item:Q7988|<math>n = \prod_{r=1}^{\nprimesdiv@{n}}p^{a_{r}}_{r}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>n = \prod_{r=1}^{\nprimesdiv@{n}}p^{a_{r}}_{r}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>n = product((p[r])^(a[r]), r = 1..ifactor(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Translation Error || - || -
| [https://dlmf.nist.gov/27.2.E1 27.2.E1] || <math qid="Q7988">n = \prod_{r=1}^{\nprimesdiv@{n}}p^{a_{r}}_{r}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>n = \prod_{r=1}^{\nprimesdiv@{n}}p^{a_{r}}_{r}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>n = product((p[r])^(a[r]), r = 1..ifactor(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Translation Error || - || -
|-  
|-  
| [https://dlmf.nist.gov/27.2.E7 27.2.E7] || [[Item:Q7994|<math>\Eulertotientphi[]@{n} = \Eulertotientphi[0]@{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Eulertotientphi[]@{n} = \Eulertotientphi[0]@{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerPhi[n] == Sum[If[CoprimeQ[n, m], m^(0), 0], {m, 1, n}]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.0
| [https://dlmf.nist.gov/27.2.E7 27.2.E7] || <math qid="Q7994">\Eulertotientphi[]@{n} = \Eulertotientphi[0]@{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Eulertotientphi[]@{n} = \Eulertotientphi[0]@{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerPhi[n] == Sum[If[CoprimeQ[n, m], m^(0), 0], {m, 1, n}]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.0
Test Values: {Rule[n, 1]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.0
Test Values: {Rule[n, 1]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.0
Test Values: {Rule[n, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[n, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/27.2.E9 27.2.E9] || [[Item:Q7996|<math>\ndivisors[]@{n} = \sum_{d\divides n}1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ndivisors[]@{n} = \sum_{d\divides n}1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>numelems(Divisors(n)) = sum(1, d**n in - infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Translation Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/27.2.E9 27.2.E9] || <math qid="Q7996">\ndivisors[]@{n} = \sum_{d\divides n}1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ndivisors[]@{n} = \sum_{d\divides n}1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>numelems(Divisors(n)) = sum(1, d**n in - infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Translation Error || Missing Macro Error || - || -
|-  
|-  
| [https://dlmf.nist.gov/27.2.E10 27.2.E10] || [[Item:Q7997|<math>\sumdivisors{\alpha}@{n} = \sum_{d\divides n}d^{\alpha}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sumdivisors{\alpha}@{n} = \sum_{d\divides n}d^{\alpha}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>add(divisors(alpha)) = sum((d)^(alpha), d**n in - infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Translation Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/27.2.E10 27.2.E10] || <math qid="Q7997">\sumdivisors{\alpha}@{n} = \sum_{d\divides n}d^{\alpha}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sumdivisors{\alpha}@{n} = \sum_{d\divides n}d^{\alpha}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>add(divisors(alpha)) = sum((d)^(alpha), d**n in - infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Translation Error || Missing Macro Error || - || -
|}
|}
</div>
</div>

Latest revision as of 12:06, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
27.2.E1 n = ∏ r = 1 ν ⁡ ( n ) p r a r 𝑛 superscript subscript product 𝑟 1 number-of-primes-dividing-nu 𝑛 subscript superscript 𝑝 subscript 𝑎 𝑟 𝑟 {\displaystyle{\displaystyle n=\prod_{r=1}^{\nu\left(n\right)}p^{a_{r}}_{r}}}
n = \prod_{r=1}^{\nprimesdiv@{n}}p^{a_{r}}_{r}		 

n = product((p[r])^(a[r]), r = 1..ifactor(n))

Error
Error Translation Error - -
27.2.E7 ϕ ⁡ ( n ) = ϕ 0 ⁡ ( n ) Euler-totient-phi 𝑛 Euler-totient-phi-n 0 𝑛 {\displaystyle{\displaystyle\phi\left(n\right)=\phi_{0}\left(n\right)}}
\Eulertotientphi[]@{n} = \Eulertotientphi[0]@{n}		 

Error

EulerPhi[n] == Sum[If[CoprimeQ[n, m], m^(0), 0], {m, 1, n}]
Missing Macro Error Failure -
Failed [3 / 3]
Result: 1.0
Test Values: {Rule[n, 1]}


Result: 1.0
Test Values: {Rule[n, 2]}

... skip entries to safe data
27.2.E9 d ⁡ ( n ) = ∑ d | n 1 divisor-function-D 𝑛 subscript divides 𝑑 𝑛 1 {\displaystyle{\displaystyle d\left(n\right)=\sum_{d\mathbin{|}n}1}}
\ndivisors[]@{n} = \sum_{d\divides n}1		 

numelems(Divisors(n)) = sum(1, d**n in - infinity)

Error
Translation Error Missing Macro Error - -
27.2.E10 σ α ⁡ ( n ) = ∑ d | n d α divisor-sigma 𝛼 𝑛 subscript divides 𝑑 𝑛 superscript 𝑑 𝛼 {\displaystyle{\displaystyle\sigma_{\alpha}\left(n\right)=\sum_{d\mathbin{|}n}% d^{\alpha}}}
\sumdivisors{\alpha}@{n} = \sum_{d\divides n}d^{\alpha}		 

add(divisors(alpha)) = sum((d)^(alpha), d**n in - infinity)

Error
Translation Error Missing Macro Error - -
Retrieved from "https://lct.wmflabs.org/w/index.php?title=27.2&oldid=58471"