22.17: 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/22.17.E1 22.17.E1] || [[Item:Q7155|<math>\genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k</syntaxhighlight> || <syntaxhighlight lang=mathematica>genJacobiellk[p]*q* z*k == genJacobiellk[p]*q* z- k</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.0
| [https://dlmf.nist.gov/22.17.E1 22.17.E1] || <math qid="Q7155">\genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k</syntaxhighlight> || <syntaxhighlight lang=mathematica>genJacobiellk[p]*q* z*k == genJacobiellk[p]*q* z- k</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.0
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[2.0, Times[Complex[0.0, 1.0], genJacobiellk]]
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[2.0, Times[Complex[0.0, 1.0], genJacobiellk]]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/22.17.E2 22.17.E2] || [[Item:Q7156|<math>\Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, 1/k) = k*JacobiSN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (1/k)^2] == k*JacobiSN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
| [https://dlmf.nist.gov/22.17.E2 22.17.E2] || <math qid="Q7156">\Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, 1/k) = k*JacobiSN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (1/k)^2] == k*JacobiSN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
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| [https://dlmf.nist.gov/22.17.E3 22.17.E3] || [[Item:Q7157|<math>\Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, 1/k) = JacobiDN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (1/k)^2] == JacobiDN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
| [https://dlmf.nist.gov/22.17.E3 22.17.E3] || <math qid="Q7157">\Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, 1/k) = JacobiDN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (1/k)^2] == JacobiDN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
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| [https://dlmf.nist.gov/22.17.E4 22.17.E4] || [[Item:Q7158|<math>\Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, 1/k) = JacobiCN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (1/k)^2] == JacobiCN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
| [https://dlmf.nist.gov/22.17.E4 22.17.E4] || <math qid="Q7158">\Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, 1/k) = JacobiCN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (1/k)^2] == JacobiCN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
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Latest revision as of 12:00, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
22.17.E1 p ⁣ q ⁡ ( z , k ) = p ⁣ q ⁡ ( z , - k ) abstract-Jacobi-elliptic p q 𝑧 𝑘 abstract-Jacobi-elliptic p q 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{pq}\left(z,k\right)=\operatorname{pq% }\left(z,-k\right)}}
\genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}		 

genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k

genJacobiellk[p]*q* z*k == genJacobiellk[p]*q* z- k
Failure Failure Error
Failed [300 / 300]
Result: 1.0
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Plus[2.0, Times[Complex[0.0, 1.0], genJacobiellk]]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
22.17.E2 sn ⁡ ( z , 1 / k ) = k ⁢ sn ⁡ ( z / k , k ) Jacobi-elliptic-sn 𝑧 1 𝑘 𝑘 Jacobi-elliptic-sn 𝑧 𝑘 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(z,1/k\right)=k\operatorname% {sn}\left(z/k,k\right)}}
\Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}		 

JacobiSN(z, 1/k) = k*JacobiSN(z/k, k)

JacobiSN[z, (1/k)^2] == k*JacobiSN[z/k, (k)^2]
Failure Failure Successful [Tested: 21] Successful [Tested: 21]
22.17.E3 cn ⁡ ( z , 1 / k ) = dn ⁡ ( z / k , k ) Jacobi-elliptic-cn 𝑧 1 𝑘 Jacobi-elliptic-dn 𝑧 𝑘 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(z,1/k\right)=\operatorname{% dn}\left(z/k,k\right)}}
\Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}		 

JacobiCN(z, 1/k) = JacobiDN(z/k, k)

JacobiCN[z, (1/k)^2] == JacobiDN[z/k, (k)^2]
Failure Failure Successful [Tested: 21] Successful [Tested: 21]
22.17.E4 dn ⁡ ( z , 1 / k ) = cn ⁡ ( z / k , k ) Jacobi-elliptic-dn 𝑧 1 𝑘 Jacobi-elliptic-cn 𝑧 𝑘 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(z,1/k\right)=\operatorname{% cn}\left(z/k,k\right)}}
\Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}		 

JacobiDN(z, 1/k) = JacobiCN(z/k, k)

JacobiDN[z, (1/k)^2] == JacobiCN[z/k, (k)^2]
Failure Failure Successful [Tested: 21] Successful [Tested: 21]
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