27.9: 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/27.9.E1 27.9.E1] || [[Item:Q8055|<math>\Legendresym{-1}{p} = (-1)^{(p-1)/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Legendresym{-1}{p} = (-1)^{(p-1)/2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreSymbol(- 1, p) = (- 1)^((p - 1)/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
| [https://dlmf.nist.gov/27.9.E1 27.9.E1] || <math qid="Q8055">\Legendresym{-1}{p} = (-1)^{(p-1)/2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Legendresym{-1}{p} = (-1)^{(p-1)/2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreSymbol(- 1, p) = (- 1)^((p - 1)/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
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| [https://dlmf.nist.gov/27.9.E2 27.9.E2] || [[Item:Q8056|<math>\Legendresym{2}{p} = (-1)^{(p^{2}-1)/8}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Legendresym{2}{p} = (-1)^{(p^{2}-1)/8}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreSymbol(2, p) = (- 1)^(((p)^(2)- 1)/8)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
| [https://dlmf.nist.gov/27.9.E2 27.9.E2] || <math qid="Q8056">\Legendresym{2}{p} = (-1)^{(p^{2}-1)/8}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Legendresym{2}{p} = (-1)^{(p^{2}-1)/8}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreSymbol(2, p) = (- 1)^(((p)^(2)- 1)/8)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
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| [https://dlmf.nist.gov/27.9.E3 27.9.E3] || [[Item:Q8057|<math>\Legendresym{p}{q}\Legendresym{q}{p} = (-1)^{(p-1)(q-1)/4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Legendresym{p}{q}\Legendresym{q}{p} = (-1)^{(p-1)(q-1)/4}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreSymbol(p, q)*LegendreSymbol(q, p) = (- 1)^((p - 1)*(q - 1)/4)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
| [https://dlmf.nist.gov/27.9.E3 27.9.E3] || <math qid="Q8057">\Legendresym{p}{q}\Legendresym{q}{p} = (-1)^{(p-1)(q-1)/4}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Legendresym{p}{q}\Legendresym{q}{p} = (-1)^{(p-1)(q-1)/4}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LegendreSymbol(p, q)*LegendreSymbol(q, p) = (- 1)^((p - 1)*(q - 1)/4)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
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Latest revision as of 12:06, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
27.9.E1 ( - 1 | p ) = ( - 1 ) ( p - 1 ) / 2 Legendre-symbol 1 𝑝 superscript 1 𝑝 1 2 {\displaystyle{\displaystyle(-1|p)=(-1)^{(p-1)/2}}}
\Legendresym{-1}{p} = (-1)^{(p-1)/2}		 

LegendreSymbol(- 1, p) = (- 1)^((p - 1)/2)

Error
Failure Missing Macro Error Error -
27.9.E2 ( 2 | p ) = ( - 1 ) ( p 2 - 1 ) / 8 Legendre-symbol 2 𝑝 superscript 1 superscript 𝑝 2 1 8 {\displaystyle{\displaystyle(2|p)=(-1)^{(p^{2}-1)/8}}}
\Legendresym{2}{p} = (-1)^{(p^{2}-1)/8}		 

LegendreSymbol(2, p) = (- 1)^(((p)^(2)- 1)/8)

Error
Failure Missing Macro Error Error -
27.9.E3 ( p | q ) ⁢ ( q | p ) = ( - 1 ) ( p - 1 ) ⁢ ( q - 1 ) / 4 Legendre-symbol 𝑝 𝑞 Legendre-symbol 𝑞 𝑝 superscript 1 𝑝 1 𝑞 1 4 {\displaystyle{\displaystyle(p|q)(q|p)=(-1)^{(p-1)(q-1)/4}}}
\Legendresym{p}{q}\Legendresym{q}{p} = (-1)^{(p-1)(q-1)/4}		 

LegendreSymbol(p, q)*LegendreSymbol(q, p) = (- 1)^((p - 1)*(q - 1)/4)

Error
Failure Missing Macro Error Error -
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