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| <div style="width: 100%; height: 75vh; overflow: auto;"> | | <div style="-moz-column-count:2; column-count:2;"> |
| {| class="wikitable sortable" style="margin: 0;"
| | ; Notation : [[36.1|36.1 Special Notation]]<br> |
| |- | | ; Properties : [[36.2|36.2 Catastrophes and Canonical Integrals]]<br>[[36.3|36.3 Visualizations of Canonical Integrals]]<br>[[36.4|36.4 Bifurcation Sets]]<br>[[36.5|36.5 Stokes Sets]]<br>[[36.6|36.6 Scaling Relations]]<br>[[36.7|36.7 Zeros]]<br>[[36.8|36.8 Convergent Series Expansions]]<br>[[36.9|36.9 Integral Identities]]<br>[[36.10|36.10 Differential Equations]]<br>[[36.11|36.11 Leading-Order Asymptotics]]<br> |
| ! scope="col" style="position: sticky; top: 0;" | DLMF
| | ; Applications : [[36.12|36.12 Uniform Approximation of Integrals]]<br>[[36.13|36.13 Kelvin’s Ship-Wave Pattern]]<br>[[36.14|36.14 Other Physical Applications]]<br> |
| ! scope="col" style="position: sticky; top: 0;" | Formula
| | ; Computation : [[36.15|36.15 Methods of Computation]]<br> |
| ! scope="col" style="position: sticky; top: 0;" | Constraints
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| ! scope="col" style="position: sticky; top: 0;" | Maple
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| ! scope="col" style="position: sticky; top: 0;" | Mathematica
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| ! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
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| ! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
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| ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
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| ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| | [https://dlmf.nist.gov/36.2#Ex2 36.2#Ex2] || [[Item:Q9843|<math>\mathrm{F}_{+}(\mathbf{x}) = \int_{0}^{\infty}\cos@{ry\exp@{+ i\dfrac{\pi}{6}}}\exp@{2ir^{2}z\exp@{+ i\dfrac{\pi}{3}}}\AiryAi@{3^{2/3}r^{2}+3^{-1/3}\exp@{- i\dfrac{\pi}{3}}\left(\tfrac{1}{3}z^{2}-x\right)}\diff{r}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathrm{F}_{+}(\mathbf{x}) = \int_{0}^{\infty}\cos@{ry\exp@{+ i\dfrac{\pi}{6}}}\exp@{2ir^{2}z\exp@{+ i\dfrac{\pi}{3}}}\AiryAi@{3^{2/3}r^{2}+3^{-1/3}\exp@{- i\dfrac{\pi}{3}}\left(\tfrac{1}{3}z^{2}-x\right)}\diff{r}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>F[+](x) = int(cos(r*y*exp(+ I*(Pi)/(6)))*exp(2*I*(r)^(2)*(x + y*I)*exp(+ I*(Pi)/(3)))*AiryAi((3)^(2/3)* (r)^(2)+ (3)^(- 1/3)* exp(- I*(Pi)/(3))*((1)/(3)*(x + y*I)^(2)- x)), r = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[F, +][x] == Integrate[Cos[r*y*Exp[+ I*Divide[Pi,6]]]*Exp[2*I*(r)^(2)*(x + y*I)*Exp[+ I*Divide[Pi,3]]]*AiryAi[(3)^(2/3)* (r)^(2)+ (3)^(- 1/3)* Exp[- I*Divide[Pi,3]]*(Divide[1,3]*(x + y*I)^(2)- x)], {r, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Error
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| | [https://dlmf.nist.gov/36.2#Ex2 36.2#Ex2] || [[Item:Q9843|<math>\mathrm{F}_{-}(\mathbf{x}) = \int_{0}^{\infty}\cos@{ry\exp@{- i\dfrac{\pi}{6}}}\exp@{2ir^{2}z\exp@{- i\dfrac{\pi}{3}}}\AiryAi@{3^{2/3}r^{2}+3^{-1/3}\exp@{+ i\dfrac{\pi}{3}}\left(\tfrac{1}{3}z^{2}-x\right)}\diff{r}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathrm{F}_{-}(\mathbf{x}) = \int_{0}^{\infty}\cos@{ry\exp@{- i\dfrac{\pi}{6}}}\exp@{2ir^{2}z\exp@{- i\dfrac{\pi}{3}}}\AiryAi@{3^{2/3}r^{2}+3^{-1/3}\exp@{+ i\dfrac{\pi}{3}}\left(\tfrac{1}{3}z^{2}-x\right)}\diff{r}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>F[-](x) = int(cos(r*y*exp(- I*(Pi)/(6)))*exp(2*I*(r)^(2)*(x + y*I)*exp(- I*(Pi)/(3)))*AiryAi((3)^(2/3)* (r)^(2)+ (3)^(- 1/3)* exp(+ I*(Pi)/(3))*((1)/(3)*(x + y*I)^(2)- x)), r = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[F, -][x] == Integrate[Cos[r*y*Exp[- I*Divide[Pi,6]]]*Exp[2*I*(r)^(2)*(x + y*I)*Exp[- I*Divide[Pi,3]]]*AiryAi[(3)^(2/3)* (r)^(2)+ (3)^(- 1/3)* Exp[+ I*Divide[Pi,3]]*(Divide[1,3]*(x + y*I)^(2)- x)], {r, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Error
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| | [https://dlmf.nist.gov/36.2.E14 36.2.E14] || [[Item:Q9850|<math>P(x_{2},x_{1}) = \int_{-\infty}^{\infty}\exp@{\iunit(t^{4}+x_{2}t^{2}+x_{1}t)}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>P(x_{2},x_{1}) = \int_{-\infty}^{\infty}\exp@{\iunit(t^{4}+x_{2}t^{2}+x_{1}t)}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>P(x[2], x[1]) = int(exp(I*((t)^(4)+ x[2]*(t)^(2)+ x[1]*t)), t = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>P[Subscript[x, 2], Subscript[x, 1]] == Integrate[Exp[I*((t)^(4)+ Subscript[x, 2]*(t)^(2)+ Subscript[x, 1]*t)], {t, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Error
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| | [https://dlmf.nist.gov/36.2#Ex10 36.2#Ex10] || [[Item:Q9859|<math>\tfrac{1}{3}\sqrt{\pi}\EulerGamma@{\tfrac{1}{6}} = 3.28868</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{3}\sqrt{\pi}\EulerGamma@{\tfrac{1}{6}} = 3.28868</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(3)*sqrt(Pi)*GAMMA((1)/(6)) = 3.28868</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,3]*Sqrt[Pi]*Gamma[Divide[1,6]] == 3.28868</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || Successful [Tested: 1]
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| | [https://dlmf.nist.gov/36.2#Ex11 36.2#Ex11] || [[Item:Q9860|<math>\tfrac{1}{3}\EulerGamma^{2}@{\tfrac{1}{3}} = 2.39224</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{3}\EulerGamma^{2}@{\tfrac{1}{3}} = 2.39224</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(3)*(GAMMA((1)/(3)))^(2) = 2.39224</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,3]*(Gamma[Divide[1,3]])^(2) == 2.39224</syntaxhighlight> || Failure || Failure || Successful [Tested: 0] || Successful [Tested: 1]
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4.E5 36.4.E5] || [[Item:Q9877|<math>x = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4.E6 36.4.E6] || [[Item:Q9878|<math>27x^{2} = -8y^{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>27x^{2} = -8y^{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">27*(x)^(2) = - 8*(y)^(3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">27*(x)^(2) == - 8*(y)^(3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4#Ex3 36.4#Ex3] || [[Item:Q9879|<math>x = 3t^{2}(z+5t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = 3t^{2}(z+5t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = 3*(t)^(2)*((x + y*I)+ 5*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == 3*(t)^(2)*((x + y*I)+ 5*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4#Ex4 36.4#Ex4] || [[Item:Q9880|<math>y = -t(3z+10t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>y = -t(3z+10t^{2})</syntaxhighlight> || <math>-\infty < t, t < \infty</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">y = - t*(3*(x + y*I)+ 10*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">y == - t*(3*(x + y*I)+ 10*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4#Ex5 36.4#Ex5] || [[Item:Q9881|<math>y = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>y = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">y = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">y == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4#Ex6 36.4#Ex6] || [[Item:Q9882|<math>z \leq 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z \leq 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z <= 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z <= 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4#Ex7 36.4#Ex7] || [[Item:Q9883|<math>x = \tfrac{9}{20}z^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = \tfrac{9}{20}z^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = (9)/(20)*(x + y*I)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == Divide[9,20]*(x + y*I)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4#Ex8 36.4#Ex8] || [[Item:Q9884|<math>z \leq 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z \leq 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z <= 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z <= 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4#Ex9 36.4#Ex9] || [[Item:Q9885|<math>x = -\tfrac{3}{20}z^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = -\tfrac{3}{20}z^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = -(3)/(20)*(x + y*I)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == -Divide[3,20]*(x + y*I)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.4#Ex10 36.4#Ex10] || [[Item:Q9886|<math>10y^{2} = -4z^{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>10y^{2} = -4z^{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">10*(y)^(2) = - 4*(x + y*I)^(3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">10*(y)^(2) == - 4*(x + y*I)^(3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/36.4#Ex11 36.4#Ex11] || [[Item:Q9887|<math>x = \tfrac{1}{3}z^{2}(-\cos@{2\phi}-2\cos@@{\phi})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = \tfrac{1}{3}z^{2}(-\cos@{2\phi}-2\cos@@{\phi})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = (1)/(3)*(x + y*I)^(2)*(- cos(2*phi)- 2*cos(phi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == Divide[1,3]*(x + y*I)^(2)*(- Cos[2*\[Phi]]- 2*Cos[\[Phi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.430780988-1.820001528*I
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| Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 4.430780988+1.820001528*I
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| Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.4307809877134479, -1.8200015289703178]
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| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[6.36271355956067, -6.045425917929804]
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| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/36.4#Ex12 36.4#Ex12] || [[Item:Q9888|<math>y = \tfrac{1}{3}z^{2}(\sin@{2\phi}-2\sin@@{\phi})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = \tfrac{1}{3}z^{2}(\sin@{2\phi}-2\sin@@{\phi})</syntaxhighlight> || <math>0 \leq \phi, \phi \leq 2\pi</math> || <syntaxhighlight lang=mathematica>y = (1)/(3)*(x + y*I)^(2)*(sin(2*phi)- 2*sin(phi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == Divide[1,3]*(x + y*I)^(2)*(Sin[2*\[Phi]]- 2*Sin[\[Phi]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [54 / 54]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.500000000-2.780804948*I
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| Test Values: {phi = 3/2, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.500000000+2.780804948*I
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| Test Values: {phi = 3/2, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [54 / 54]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.5, -2.7808049477223626]
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| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.5, -0.17607013860076426]
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| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/36.4.E11 36.4.E11] || [[Item:Q9889|<math>x+iy = -z^{2}\exp@{\tfrac{2}{3}i\pi m}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x+iy = -z^{2}\exp@{\tfrac{2}{3}i\pi m}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x + I*y = -(x + y*I)^(2)* exp((2)/(3)*I*Pi*m)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x + I*y == -(x + y*I)^(2)* Exp[Divide[2,3]*I*Pi*m]</syntaxhighlight> || Error || Failure || - || Skip - No test values generated
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| | [https://dlmf.nist.gov/36.4#Ex13 36.4#Ex13] || [[Item:Q9890|<math>x = -\tfrac{1}{12}z^{2}(\exp@{2\tau}+ 2\exp@{-\tau})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = -\tfrac{1}{12}z^{2}(\exp@{2\tau}+ 2\exp@{-\tau})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = -(1)/(12)*(x + y*I)^(2)*(exp(2*tau)+ 2*exp(- tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == -Divide[1,12]*(x + y*I)^(2)*(Exp[2*\[Tau]]+ 2*Exp[- \[Tau]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.132329502-1.422064683*I
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| Test Values: {tau = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.132329502+1.422064683*I
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| Test Values: {tau = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.1323295016161525, -1.4220646828050367]
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| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.694217640570763, -0.7789550680773418]
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| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/36.4#Ex13 36.4#Ex13] || [[Item:Q9890|<math>x = -\tfrac{1}{12}z^{2}(\exp@{2\tau}- 2\exp@{-\tau})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = -\tfrac{1}{12}z^{2}(\exp@{2\tau}- 2\exp@{-\tau})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = -(1)/(12)*(x + y*I)^(2)*(exp(2*tau)- 2*exp(- tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == -Divide[1,12]*(x + y*I)^(2)*(Exp[2*\[Tau]]- 2*Exp[- \[Tau]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.434813476-.8683714834*I
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| Test Values: {tau = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.434813476+.8683714834*I
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| Test Values: {tau = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.4348134754242143, -0.8683714827345889]
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| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.578112467364518, 0.8232541553428006]
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| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/36.4#Ex14 36.4#Ex14] || [[Item:Q9891|<math>y = -\tfrac{1}{12}z^{2}(\exp@{-2\tau}+ 2\exp@{\tau})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = -\tfrac{1}{12}z^{2}(\exp@{-2\tau}+ 2\exp@{\tau})</syntaxhighlight> || <math>-\infty \leq \tau, \tau < \infty.</math> || <syntaxhighlight lang=mathematica>y = -(1)/(12)*(x + y*I)^(2)*(exp(- 2*tau)+ 2*exp(tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == -Divide[1,12]*(x + y*I)^(2)*(Exp[- 2*\[Tau]]+ 2*Exp[\[Tau]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.500000000-7.699423965*I
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| Test Values: {tau = -3/2, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.500000000+7.699423965*I
| |
| Test Values: {tau = -3/2, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.5, -7.699423966306697]
| |
| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.5, -3.3799369533914976]
| |
| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/36.4#Ex14 36.4#Ex14] || [[Item:Q9891|<math>y = -\tfrac{1}{12}z^{2}(\exp@{-2\tau}- 2\exp@{\tau})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = -\tfrac{1}{12}z^{2}(\exp@{-2\tau}- 2\exp@{\tau})</syntaxhighlight> || <math>-\infty \leq \tau, \tau < \infty.</math> || <syntaxhighlight lang=mathematica>y = -(1)/(12)*(x + y*I)^(2)*(exp(- 2*tau)- 2*exp(tau))</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == -Divide[1,12]*(x + y*I)^(2)*(Exp[- 2*\[Tau]]- 2*Exp[\[Tau]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.500000000-7.364728725*I
| |
| Test Values: {tau = -3/2, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.500000000+7.364728725*I
| |
| Test Values: {tau = -3/2, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.5, -7.364728726084054]
| |
| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.5, 3.3425966521155988]
| |
| Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.4.E13 36.4.E13] || [[Item:Q9892|<math>x = y</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = y</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E2 36.5.E2] || [[Item:Q9895|<math>y^{3} = \tfrac{27}{4}\left(\sqrt{27}-5\right)x^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>y^{3} = \tfrac{27}{4}\left(\sqrt{27}-5\right)x^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(y)^(3) = (27)/(4)*(sqrt(27)- 5)*(x)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(y)^(3) == Divide[27,4]*(Sqrt[27]- 5)*(x)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5#Ex3 36.5#Ex3] || [[Item:Q9896|<math>x = B_{+}|y|^{4/3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = B_{+}|y|^{4/3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = B[+]*(abs(y))^(4/3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == Subscript[B, +]*(Abs[y])^(4/3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5#Ex4 36.5#Ex4] || [[Item:Q9897|<math>B_{+} = 10^{-1/3}\left(2x_{+}^{4/3}-\tfrac{1}{2}x_{+}^{-2/3}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{+} = 10^{-1/3}\left(2x_{+}^{4/3}-\tfrac{1}{2}x_{+}^{-2/3}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[+] = (10)^(- 1/3)*(2*(x[+])^(4/3)-(1)/(2)*(x[+])^(- 2/3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, +] == (10)^(- 1/3)*(2*(Subscript[x, +])^(4/3)-Divide[1,2]*(Subscript[x, +])^(- 2/3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E4 36.5.E4] || [[Item:Q9898|<math>80x^{5}-40x^{4}-55x^{3}+5x^{2}+20x-1 = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>80x^{5}-40x^{4}-55x^{3}+5x^{2}+20x-1 = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">80*(x)^(5)- 40*(x)^(4)- 55*(x)^(3)+ 5*(x)^(2)+ 20*x - 1 = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">80*(x)^(5)- 40*(x)^(4)- 55*(x)^(3)+ 5*(x)^(2)+ 20*x - 1 == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5#Ex5 36.5#Ex5] || [[Item:Q9899|<math>B_{-} = -1.69916</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-} = -1.69916</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[-] = - 1.69916</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, -] == - 1.69916</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5#Ex6 36.5#Ex6] || [[Item:Q9900|<math>B_{+} = 0.33912</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{+} = 0.33912</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[+] = 0.33912</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, +] == 0.33912</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/36.5.E7 36.5.E7] || [[Item:Q9903|<math>X = \dfrac{9}{20}+20u^{4}-\frac{Y^{2}}{20u^{2}}+6u^{2}\sign@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>X = \dfrac{9}{20}+20u^{4}-\frac{Y^{2}}{20u^{2}}+6u^{2}\sign@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>X = (9)/(20)+ 20*(u)^(4)-((y/(abs(x + y*I))^(3/2))^(2))/(20*(u)^(2))+ 6*(u)^(2)* signum(x + y*I)</syntaxhighlight> || <syntaxhighlight lang=mathematica>X == Divide[9,20]+ 20*(u)^(4)-Divide[(y/(Abs[x + y*I])^(3/2))^(2),20*(u)^(2)]+ 6*(u)^(2)* Sign[x + y*I]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.626363000-18.38362857*I
| |
| Test Values: {X = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 11.97483223-22.62626926*I
| |
| Test Values: {X = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[4.626363002559913, -18.383628553565494]
| |
| Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[X, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[11.974832230909447, -22.62626924068478]
| |
| Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[X, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/36.5.E8 36.5.E8] || [[Item:Q9904|<math>16u^{5}-\frac{Y^{2}}{10u}+4u^{3}\sign@{z}-\frac{3}{10}|Y|\sign@{z}+4t^{5}+2t^{3}\sign@{z}+|Y|t^{2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>16u^{5}-\frac{Y^{2}}{10u}+4u^{3}\sign@{z}-\frac{3}{10}|Y|\sign@{z}+4t^{5}+2t^{3}\sign@{z}+|Y|t^{2} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>16*(u)^(5)-((y/(abs(x + y*I))^(3/2))^(2))/(10*u)+ 4*(u)^(3)* signum(x + y*I)-(3)/(10)*abs(y/(abs(x + y*I))^(3/2))*signum(x + y*I)+ 4*(t)^(5)+ 2*(t)^(3)* signum(x + y*I)+abs(y/(abs(x + y*I))^(3/2))*(t)^(2) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>16*(u)^(5)-Divide[(y/(Abs[x + y*I])^(3/2))^(2),10*u]+ 4*(u)^(3)* Sign[x + y*I]-Divide[3,10]*Abs[y/(Abs[x + y*I])^(3/2)]*Sign[x + y*I]+ 4*(t)^(5)+ 2*(t)^(3)* Sign[x + y*I]+Abs[y/(Abs[x + y*I])^(3/2)]*(t)^(2) == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -45.20699439+15.71617138*I
| |
| Test Values: {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -50.86384865+5.964253129*I
| |
| Test Values: {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-45.20699439419109, 15.716171367970516]
| |
| Test Values: {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-50.863848643683475, 5.964253107561413]
| |
| Test Values: {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/36.5.E9 36.5.E9] || [[Item:Q9905|<math>t = -u+\left(\dfrac{|Y|}{10u}-u^{2}-\dfrac{3}{10}\sign@{z}\right)^{1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>t = -u+\left(\dfrac{|Y|}{10u}-u^{2}-\dfrac{3}{10}\sign@{z}\right)^{1/2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>t = - u +((abs(y/(abs(x + y*I))^(3/2)))/(10*u)- (u)^(2)-(3)/(10)*signum(x + y*I))^(1/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>t == - u +(Divide[Abs[y/(Abs[x + y*I])^(3/2)],10*u]- (u)^(2)-Divide[3,10]*Sign[x + y*I])^(1/2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.010332328+1.400961906*I
| |
| Test Values: {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.190759425+1.489998263*I
| |
| Test Values: {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.0103323276990124, 1.4009619057655258]
| |
| Test Values: {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.1907594253432556, 1.489998262392432]
| |
| Test Values: {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E10 36.5.E10] || [[Item:Q9906|<math>160u^{6}+40u^{4} = Y^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>160u^{6}+40u^{4} = Y^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">160*(u)^(6)+ 40*(u)^(4) = (y/(abs(x + y*I))^(3/2))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">160*(u)^(6)+ 40*(u)^(4) == (y/(Abs[x + y*I])^(3/2))^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E11 36.5.E11] || [[Item:Q9907|<math>\frac{x}{z^{2}} = -1-12u^{2}+8u-\left|\frac{y}{z^{2}}\right|\dfrac{\frac{1}{3}-u}{\left(u\left(\frac{2}{3}-u\right)\right)^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\frac{x}{z^{2}} = -1-12u^{2}+8u-\left|\frac{y}{z^{2}}\right|\dfrac{\frac{1}{3}-u}{\left(u\left(\frac{2}{3}-u\right)\right)^{1/2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x)/((x + y*I)^(2)) = - 1 - 12*(u)^(2)+ 8*u -abs((y)/((x + y*I)^(2)))*((1)/(3)- u)/((u*((2)/(3)- u))^(1/2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[x,(x + y*I)^(2)] == - 1 - 12*(u)^(2)+ 8*u -Abs[Divide[y,(x + y*I)^(2)]]*Divide[Divide[1,3]- u,(u*(Divide[2,3]- u))^(1/2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E12 36.5.E12] || [[Item:Q9908|<math>8u^{3}-4u^{2}-\left|\frac{y}{3z^{2}}\right|\left(\frac{u}{\tfrac{2}{3}-u}\right)^{1/2} = \frac{y^{2}}{6wz^{4}}-2w^{3}-2w^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>8u^{3}-4u^{2}-\left|\frac{y}{3z^{2}}\right|\left(\frac{u}{\tfrac{2}{3}-u}\right)^{1/2} = \frac{y^{2}}{6wz^{4}}-2w^{3}-2w^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">8*(u)^(3)- 4*(u)^(2)-abs((y)/(3*(x + y*I)^(2)))*((u)/((2)/(3)- u))^(1/2) = ((y)^(2))/(6*w*(x + y*I)^(4))- 2*(u -(2)/(3)+(((2)/(3)- u)^(2)+abs((y)/(6*(x + y*I)^(2)))*(((2)/(3)- u)/(u))^(1/2))^(1/2))^(3)- 2*(u -(2)/(3)+(((2)/(3)- u)^(2)+abs((y)/(6*(x + y*I)^(2)))*(((2)/(3)- u)/(u))^(1/2))^(1/2))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">8*(u)^(3)- 4*(u)^(2)-Abs[Divide[y,3*(x + y*I)^(2)]]*(Divide[u,Divide[2,3]- u])^(1/2) == Divide[(y)^(2),6*w*(x + y*I)^(4)]- 2*(u -Divide[2,3]+((Divide[2,3]- u)^(2)+Abs[Divide[y,6*(x + y*I)^(2)]]*(Divide[Divide[2,3]- u,u])^(1/2))^(1/2))^(3)- 2*(u -Divide[2,3]+((Divide[2,3]- u)^(2)+Abs[Divide[y,6*(x + y*I)^(2)]]*(Divide[Divide[2,3]- u,u])^(1/2))^(1/2))^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E14 36.5.E14] || [[Item:Q9910|<math>0 < u</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 < u</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < u</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < u</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5#Ex11 36.5#Ex11] || [[Item:Q9913|<math>Y(u,X) = 8u-24u^{2}+X\dfrac{u-\tfrac{1}{6}}{\left(u\left(u-\tfrac{1}{3}\right)\right)^{1/2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Y(u,X) = 8u-24u^{2}+X\dfrac{u-\tfrac{1}{6}}{\left(u\left(u-\tfrac{1}{3}\right)\right)^{1/2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Y(u ,((x - y)/(x + y*I)^(2))) = 8*u - 24*(u)^(2)+((x - y)/(x + y*I)^(2))*(u -(1)/(6))/((u*(u -(1)/(3)))^(1/2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Y[u ,((x - y)/(x + y*I)^(2))] == 8*u - 24*(u)^(2)+((x - y)/(x + y*I)^(2))*Divide[u -Divide[1,6],(u*(u -Divide[1,3]))^(1/2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E17 36.5.E17] || [[Item:Q9915|<math>Y_{\mathrm{S}}(X) = Y(u,|X|)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Y_{\mathrm{S}}(X) = Y(u,|X|)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Y[S](((x - y)/(x + y*I)^(2))) = Y(u ,abs((x - y)/(x + y*I)^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Y, S][((x - y)/(x + y*I)^(2))] == Y[u ,Abs[(x - y)/(x + y*I)^(2)]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E19 36.5.E19] || [[Item:Q9917|<math>Y_{\mathrm{S}}(X) = Y(-u,-|X|)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Y_{\mathrm{S}}(X) = Y(-u,-|X|)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Y[S](((x - y)/(x + y*I)^(2))) = Y(- u , -abs((x - y)/(x + y*I)^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Y, S][((x - y)/(x + y*I)^(2))] == Y[- u , -Abs[(x - y)/(x + y*I)^(2)]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.5.E21 36.5.E21] || [[Item:Q9919|<math>w = (\tfrac{1}{3}+u)\left(1-\left(1-\dfrac{|X|}{12u^{1/2}(\tfrac{1}{3}+u)^{3/2}}\right)^{1/2}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w = (\tfrac{1}{3}+u)\left(1-\left(1-\dfrac{|X|}{12u^{1/2}(\tfrac{1}{3}+u)^{3/2}}\right)^{1/2}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(u -(2)/(3)+(((2)/(3)- u)^(2)+abs((y)/(6*(x + y*I)^(2)))*(((2)/(3)- u)/(u))^(1/2))^(1/2)) = ((1)/(3)+ u)*(1 -(1 -(abs((x - y)/(x + y*I)^(2)))/(12*(u)^(1/2)*((1)/(3)+ u)^(3/2)))^(1/2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(u -Divide[2,3]+((Divide[2,3]- u)^(2)+Abs[Divide[y,6*(x + y*I)^(2)]]*(Divide[Divide[2,3]- u,u])^(1/2))^(1/2)) == (Divide[1,3]+ u)*(1 -(1 -Divide[Abs[(x - y)/(x + y*I)^(2)],12*(u)^(1/2)*(Divide[1,3]+ u)^(3/2)])^(1/2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.6#Ex9 36.6#Ex9] || [[Item:Q9928|<math>\gamma_{y}^{(\mathrm{U})} = \tfrac{2}{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{y}^{(\mathrm{U})} = \tfrac{2}{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(gamma[y])^(U) = (2)/(3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Gamma], y])^(U) == Divide[2,3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.6#Ex10 36.6#Ex10] || [[Item:Q9929|<math>\gamma_{z}^{(\mathrm{U})} = \tfrac{1}{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{z}^{(\mathrm{U})} = \tfrac{1}{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(gamma[z])^(U) = (1)/(3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Gamma], z])^(U) == Divide[1,3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.7#Ex1 36.7#Ex1] || [[Item:Q9932|<math>y_{m} = -\sqrt{2\pi(2m+1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>y_{m} = -\sqrt{2\pi(2m+1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">y[m] = -sqrt(2*Pi*(2*m + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[y, m] == -Sqrt[2*Pi*(2*m + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.7#Ex2 36.7#Ex2] || [[Item:Q9933|<math>x_{m,n}^{+} = \sqrt{\dfrac{2}{-y_{m}}}\left(2n+\tfrac{1}{2}+(-1)^{m}\tfrac{1}{2}+\tfrac{1}{4}\right)\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{m,n}^{+} = \sqrt{\dfrac{2}{-y_{m}}}\left(2n+\tfrac{1}{2}+(-1)^{m}\tfrac{1}{2}+\tfrac{1}{4}\right)\pi</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x[m , n])^(+) = sqrt((2)/(- y[m]))*(2*n +(1)/(2)+(- 1)^(m)*(1)/(2)+(1)/(4))*Pi</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[x, m , n])^(+) == Sqrt[Divide[2,- Subscript[y, m]]]*(2*n +Divide[1,2]+(- 1)^(m)*Divide[1,2]+Divide[1,4])*Pi</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.7#Ex3 36.7#Ex3] || [[Item:Q9934|<math>x_{n} = +\left(\dfrac{8}{27}\right)^{1/2}|y_{n}|^{3/2}(1+\xi_{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{n} = +\left(\dfrac{8}{27}\right)^{1/2}|y_{n}|^{3/2}(1+\xi_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[n] = +((8)/(27))^(1/2)*(abs(y[n]))^(3/2)*(1 + xi[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, n] == +(Divide[8,27])^(1/2)*(Abs[Subscript[y, n]])^(3/2)*(1 + Subscript[\[Xi], n])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.7#Ex4 36.7#Ex4] || [[Item:Q9935|<math>y_{n} = -\left(\frac{3\pi(8n+5)}{9+8\xi_{n}}\right)^{1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>y_{n} = -\left(\frac{3\pi(8n+5)}{9+8\xi_{n}}\right)^{1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">y[n] = -((3*Pi*(8*n + 5))/(9 + 8*xi[n]))^(1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[y, n] == -(Divide[3*Pi*(8*n + 5),9 + 8*Subscript[\[Xi], n]])^(1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/36.7.E3 36.7.E3] || [[Item:Q9936|<math>\frac{3\pi(8n+5)}{9+8\xi_{n}}\xi_{n}^{3/2} = \dfrac{27}{16}\left(\dfrac{3}{2}\right)^{1/2}\left(\ln@{\frac{1}{\xi_{n}}}+3\ln@{\dfrac{3}{2}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{3\pi(8n+5)}{9+8\xi_{n}}\xi_{n}^{3/2} = \dfrac{27}{16}\left(\dfrac{3}{2}\right)^{1/2}\left(\ln@{\frac{1}{\xi_{n}}}+3\ln@{\dfrac{3}{2}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(3*Pi*(8*n + 5))/(9 + 8*xi[n])*(xi[n])^(3/2) = (27)/(16)*((3)/(2))^(1/2)*(ln((1)/(xi[n]))+ 3*ln((3)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[3*Pi*(8*n + 5),9 + 8*Subscript[\[Xi], n]]*(Subscript[\[Xi], n])^(3/2) == Divide[27,16]*(Divide[3,2])^(1/2)*(Log[Divide[1,Subscript[\[Xi], n]]]+ 3*Log[Divide[3,2]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.887397376+4.913760852*I
| |
| Test Values: {xi = 1/2*3^(1/2)+1/2*I, xi[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 7.826714845+7.271674350*I
| |
| Test Values: {xi = 1/2*3^(1/2)+1/2*I, xi[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.8873973728456934, 4.913760851775014]
| |
| Test Values: {Rule[n, 1], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[7.826714842534605, 7.271674348744825]
| |
| Test Values: {Rule[n, 2], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.7.E4 36.7.E4] || [[Item:Q9937|<math>z_{n} = + 3(\tfrac{1}{4}\pi(2n-\tfrac{1}{2}))^{1/3}\\</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n} = + 3(\tfrac{1}{4}\pi(2n-\tfrac{1}{2}))^{1/3}\\</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n] = + 3*((1)/(4)*Pi*(2*n -(1)/(2)))^(1/3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n] == + 3*(Divide[1,4]*Pi*(2*n -Divide[1,2]))^(1/3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.7#Ex5 36.7#Ex5] || [[Item:Q9938|<math>\Delta z = \frac{9\pi}{2z_{n}^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\Delta z = \frac{9\pi}{2z_{n}^{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Delta*z = (9*Pi)/(2*(z[n])^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[CapitalDelta]*z == Divide[9*Pi,2*(Subscript[z, n])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.7#Ex6 36.7#Ex6] || [[Item:Q9939|<math>\Delta x = \frac{6\pi}{z_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\Delta x = \frac{6\pi}{z_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Delta*x = (6*Pi)/(x + y*I[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[CapitalDelta]*x == Divide[6*Pi,Subscript[x + y*I, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/36.7.E6 36.7.E6] || [[Item:Q9940|<math>\exp@{-2\pi i\left(\frac{z-z_{n}}{\Delta z}+\frac{2x}{\Delta x}\right)}\*{\left(2\exp@{\frac{-6\pi ix}{\Delta x}}\cos@{\frac{2\sqrt{3}\pi y}{\Delta x}}+1\right)} = \sqrt{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\exp@{-2\pi i\left(\frac{z-z_{n}}{\Delta z}+\frac{2x}{\Delta x}\right)}\*{\left(2\exp@{\frac{-6\pi ix}{\Delta x}}\cos@{\frac{2\sqrt{3}\pi y}{\Delta x}}+1\right)} = \sqrt{3}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(- 2*Pi*I*(((x + y*I)-x + y*I[n])/(Delta*(x + y*I))+(2*x)/(Delta*x)))*(2*exp((- 6*Pi*I*x)/(Delta*x))*cos((2*sqrt(3)*Pi*y)/(Delta*x))+ 1) = sqrt(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- 2*Pi*I*(Divide[(x + y*I)-Subscript[x + y*I, n],\[CapitalDelta]*(x + y*I)]+Divide[2*x,\[CapitalDelta]*x])]*(2*Exp[Divide[- 6*Pi*I*x,\[CapitalDelta]*x]]*Cos[Divide[2*Sqrt[3]*Pi*y,\[CapitalDelta]*x]]+ 1) == Sqrt[3]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-1.7320508075688772, Times[Complex[1.0151974851172445, -0.010763380729874927], Power[2.718281828459045, Times[Complex[0.0, -6.283185307179586], Plus[Complex[1.7320508075688774, -0.9999999999999999], Times[Complex[0.4553418012614795, 0.12200846792814624], Plus[Complex[1.5, -1.5], Times[-1.0, Subscript[Complex[1.5, -1.5], 1]]]]]]]]]
| |
| Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[-1.7320508075688772, Times[Complex[1.0151974851172445, -0.010763380729874927], Power[2.718281828459045, Times[Complex[0.0, -6.283185307179586], Plus[Complex[1.7320508075688774, -0.9999999999999999], Times[Complex[0.4553418012614795, 0.12200846792814624], Plus[Complex[1.5, -1.5], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]]]]]]]]
| |
| Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[Δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/36.9.E2 36.9.E2] || [[Item:Q9955|<math>(\AiryAi@{x})^{2} = \frac{2^{2/3}}{\pi}\int_{0}^{\infty}\AiryAi@{2^{2/3}(u^{2}+x)}\diff{u}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\AiryAi@{x})^{2} = \frac{2^{2/3}}{\pi}\int_{0}^{\infty}\AiryAi@{2^{2/3}(u^{2}+x)}\diff{u}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(AiryAi(x))^(2) = ((2)^(2/3))/(Pi)*int(AiryAi((2)^(2/3)*((u)^(2)+ x)), u = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(AiryAi[x])^(2) == Divide[(2)^(2/3),Pi]*Integrate[AiryAi[(2)^(2/3)*((u)^(2)+ x)], {u, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.11.E1 36.11.E1] || [[Item:Q9984|<math>t_{1}(\mathbf{x}) < t_{2}(\mathbf{x})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{1}(\mathbf{x}) < t_{2}(\mathbf{x})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[1](x) < t[2](x)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, 1][x] < Subscript[t, 2][x]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |-
| |
| | [https://dlmf.nist.gov/36.12.E9 36.12.E9] || [[Item:Q10001|<math>P_{mn}(\mathbf{y}) = (t_{n}(\mathbf{x}(\mathbf{y})))^{K+1}+\sum_{l=m+2}^{K}\frac{l}{K+2}x_{l}(\mathbf{y})(t_{n}(\mathbf{x}(\mathbf{y})))^{l-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>P_{mn}(\mathbf{y}) = (t_{n}(\mathbf{x}(\mathbf{y})))^{K+1}+\sum_{l=m+2}^{K}\frac{l}{K+2}x_{l}(\mathbf{y})(t_{n}(\mathbf{x}(\mathbf{y})))^{l-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>P[m, n](y) = (t[n](x(y)))^(K + 1)+ sum((l)/(K + 2)*x[l](y)*(t[n](x(y)))^(l - 1), l = m + 2..K)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[P, m, n][y] == (Subscript[t, n][x[y]])^(K + 1)+ Sum[Divide[l,K + 2]*Subscript[x, l][y]*(Subscript[t, n][x[y]])^(l - 1), {l, m + 2, K}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/36.13.E1 36.13.E1] || [[Item:Q10008|<math>z(\phi,\rho) = \int_{-\pi/2}^{\pi/2}\cos@{\rho\frac{\cos@{\theta+\phi}}{\cos^{2}@@{\theta}}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z(\phi,\rho) = \int_{-\pi/2}^{\pi/2}\cos@{\rho\frac{\cos@{\theta+\phi}}{\cos^{2}@@{\theta}}}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z(phi , rho) = int(cos(rho*(cos(theta + phi))/((cos(theta))^(2))), theta = - Pi/2..Pi/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z[\[Phi], \[Rho]] == Integrate[Cos[\[Rho]*Divide[Cos[\[Theta]+ \[Phi]],(Cos[\[Theta]])^(2)]], {\[Theta], - Pi/2, Pi/2}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Error
| |
| |- style="background: #dfe6e9;"
| |
| | [https://dlmf.nist.gov/36.13.E2 36.13.E2] || [[Item:Q10009|<math>\rho = \ifrac{gr}{V^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho = \ifrac{gr}{V^{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho = (g*r)/((V)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Rho] == Divide[g*r,(V)^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |-
| |
| | [https://dlmf.nist.gov/36.13#Ex1 36.13#Ex1] || [[Item:Q10011|<math>\theta_{+}(\phi) = \tfrac{1}{2}(\asin@{3\sin@@{\phi}}-\phi)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\theta_{+}(\phi) = \tfrac{1}{2}(\asin@{3\sin@@{\phi}}-\phi)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>theta[+](phi) = (1)/(2)*(arcsin(3*sin(phi))- phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Theta], +][\[Phi]] == Divide[1,2]*(ArcSin[3*Sin[\[Phi]]]- \[Phi])</syntaxhighlight> || Error || Failure || - || Error
| |
| |-
| |
| | [https://dlmf.nist.gov/36.13#Ex2 36.13#Ex2] || [[Item:Q10012|<math>\theta_{-}(\phi) = \tfrac{1}{2}(\pi-\phi-\asin@{3\sin@@{\phi}})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\theta_{-}(\phi) = \tfrac{1}{2}(\pi-\phi-\asin@{3\sin@@{\phi}})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>theta[-](phi) = (1)/(2)*(Pi - phi - arcsin(3*sin(phi)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Theta], -][\[Phi]] == Divide[1,2]*(Pi - \[Phi]- ArcSin[3*Sin[\[Phi]]])</syntaxhighlight> || Error || Failure || - || Error
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| |-
| |
| | [https://dlmf.nist.gov/36.13.E5 36.13.E5] || [[Item:Q10013|<math>|\phi| = \phi_{c}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\phi| = \phi_{c}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>abs(phi) = phi[c]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[\[Phi]] == Subscript[\[Phi], c]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [282 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1339745960-.5000000000*I
| |
| Test Values: {c = -3/2, phi = 1/2*3^(1/2)+1/2*I, phi[c] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.500000000-.8660254040*I
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| Test Values: {c = -3/2, phi = 1/2*3^(1/2)+1/2*I, phi[c] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [282 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.1339745962155613, -0.49999999999999994]
| |
| Test Values: {Rule[c, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, c], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.4999999999999998, -0.8660254037844387]
| |
| Test Values: {Rule[c, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, c], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
| |
| |-
| |
| | [https://dlmf.nist.gov/36.13.E5 36.13.E5] || [[Item:Q10013|<math>\phi_{c} = \asin@{\tfrac{1}{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi_{c} = \asin@{\tfrac{1}{3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi[c] = arcsin((1)/(3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Phi], c] == ArcSin[Divide[1,3]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5261884946+.5000000000*I
| |
| Test Values: {c = -3/2, phi = 1/2*3^(1/2)+1/2*I, phi[c] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8398369094+.8660254040*I
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| Test Values: {c = -3/2, phi = 1/2*3^(1/2)+1/2*I, phi[c] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5261884943303168, 0.49999999999999994]
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| Test Values: {Rule[c, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, c], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.8398369094541217, 0.8660254037844387]
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| Test Values: {Rule[c, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, c], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |- style="background: #dfe6e9;"
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| | [https://dlmf.nist.gov/36.13.E6 36.13.E6] || [[Item:Q10014|<math>\omega(\mathbf{k}) = \sqrt{gk}+\mathbf{V}\cdot\mathbf{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\omega(\mathbf{k}) = \sqrt{gk}+\mathbf{V}\cdot\mathbf{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">omega(k) = sqrt(g*k)+ V * k</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Omega][k] == Sqrt[g*k]+ V * k</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| |}
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| </div> | | </div> |