1.5: 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/1.5.E4 1.5.E4] || [[Item:Q121|<math>\pderiv{f}{y} = D_{y}f</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv{f}{y} = D_{y}f</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, y) = D[y]*f</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, y] == Subscript[D, y]*f</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5000000004-.8660254040*I
| [https://dlmf.nist.gov/1.5.E4 1.5.E4] || <math qid="Q121">\pderiv{f}{y} = D_{y}f</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv{f}{y} = D_{y}f</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, y) = D[y]*f</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, y] == Subscript[D, y]*f</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5000000004-.8660254040*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040-.5000000004*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040-.5000000004*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8660254040+.5000000004*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8660254040+.5000000004*I
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Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], 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/1.5.E4 1.5.E4] || [[Item:Q121|<math>D_{y}f = f_{y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>D_{y}f = f_{y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>D[y]*f = f[y]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[D, y]*f == Subscript[f, y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3660254036+.3660254040*I
| [https://dlmf.nist.gov/1.5.E4 1.5.E4] || <math qid="Q121">D_{y}f = f_{y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>D_{y}f = f_{y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>D[y]*f = f[y]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[D, y]*f == Subscript[f, y]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3660254036+.3660254040*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.000000000+0.*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.000000000+0.*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4e-9+1.732050808*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4e-9+1.732050808*I
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Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], 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/1.5#Ex3 1.5#Ex3] || [[Item:Q128|<math>x = r\cos@@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = r\cos@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = r*cos(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == r*Cos[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.595814528-.5954243254*I
| [https://dlmf.nist.gov/1.5#Ex3 1.5#Ex3] || <math qid="Q128">x = r\cos@@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = r\cos@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = r*cos(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == r*Cos[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.095814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.095814528-.5954243254*I
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Test Values: {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[r, -1.5], Rule[x, 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/1.5#Ex4 1.5#Ex4] || [[Item:Q129|<math>y = r\sin@@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = r\sin@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = r*sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == r*Sin[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.211529498+.5063946946*I
| [https://dlmf.nist.gov/1.5#Ex4 1.5#Ex4] || <math qid="Q129">y = r\sin@@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = r\sin@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = r*sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == r*Sin[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.211529498+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .788470502+.5063946946*I
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Test Values: {Rule[r, -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>
Test Values: {Rule[r, -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/1.5.E13 1.5.E13] || [[Item:Q132|<math>\pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, [x$(2)])+ diff(f, [y$(2)]) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, {x, 2}]+ D[f, {y, 2}] == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
| [https://dlmf.nist.gov/1.5.E13 1.5.E13] || <math qid="Q132">\pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, [x$(2)])+ diff(f, [y$(2)]) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, {x, 2}]+ D[f, {y, 2}] == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
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| [https://dlmf.nist.gov/1.5#Ex5 1.5#Ex5] || [[Item:Q133|<math>x = r\cos@@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = r\cos@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = r*cos(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == r*Cos[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.595814528-.5954243254*I
| [https://dlmf.nist.gov/1.5#Ex5 1.5#Ex5] || <math qid="Q133">x = r\cos@@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = r\cos@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = r*cos(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == r*Cos[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.095814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.095814528-.5954243254*I
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Test Values: {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[r, -1.5], Rule[x, 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/1.5#Ex6 1.5#Ex6] || [[Item:Q134|<math>y = r\sin@@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = r\sin@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = r*sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == r*Sin[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.211529498+.5063946946*I
| [https://dlmf.nist.gov/1.5#Ex6 1.5#Ex6] || <math qid="Q134">y = r\sin@@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = r\sin@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = r*sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == r*Sin[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.211529498+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .788470502+.5063946946*I
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Test Values: {Rule[r, -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>
Test Values: {Rule[r, -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>
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5#Ex7 1.5#Ex7] || [[Item:Q135|<math>z = z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5#Ex7 1.5#Ex7] || <math qid="Q135">z = z</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/1.5.E15 1.5.E15] || [[Item:Q136|<math>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}+\pderiv[2]{f}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}+\pderiv[2]{f}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
| [https://dlmf.nist.gov/1.5.E15 1.5.E15] || <math qid="Q136">\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}+\pderiv[2]{f}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}+\pderiv[2]{f}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) )</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
|-  
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| [https://dlmf.nist.gov/1.5#Ex8 1.5#Ex8] || [[Item:Q137|<math>x = \rho\sin@@{\theta}\cos@@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = \rho\sin@@{\theta}\cos@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = rho*sin(theta)*cos(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == \[Rho]*Sin[\[Theta]]*Cos[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7933233780-.2990618885*I
| [https://dlmf.nist.gov/1.5#Ex8 1.5#Ex8] || <math qid="Q137">x = \rho\sin@@{\theta}\cos@@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = \rho\sin@@{\theta}\cos@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = rho*sin(theta)*cos(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == \[Rho]*Sin[\[Theta]]*Cos[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7933233780-.2990618885*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2066766220-.2990618885*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2066766220-.2990618885*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.293323378-.2990618885*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.293323378-.2990618885*I
Line 76: Line 76:
Test Values: {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/1.5#Ex9 1.5#Ex9] || [[Item:Q138|<math>y = \rho\sin@@{\theta}\sin@@{\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = \rho\sin@@{\theta}\sin@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = rho*sin(theta)*sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == \[Rho]*Sin[\[Theta]]*Sin[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.750303606-.8142131232*I
| [https://dlmf.nist.gov/1.5#Ex9 1.5#Ex9] || <math qid="Q138">y = \rho\sin@@{\theta}\sin@@{\phi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = \rho\sin@@{\theta}\sin@@{\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = rho*sin(theta)*sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == \[Rho]*Sin[\[Theta]]*Sin[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.750303606-.8142131232*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.249696394-.8142131232*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = -1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.249696394-.8142131232*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7503036064-.8142131232*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7503036064-.8142131232*I
Line 84: Line 84:
Test Values: {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/1.5#Ex10 1.5#Ex10] || [[Item:Q139|<math>z = \rho\cos@@{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \rho\cos@@{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = rho*cos(theta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == \[Rho]*Cos[\[Theta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .348818158e-1+.4784968852*I
| [https://dlmf.nist.gov/1.5#Ex10 1.5#Ex10] || <math qid="Q139">z = \rho\cos@@{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \rho\cos@@{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = rho*cos(theta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == \[Rho]*Cos[\[Theta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .348818158e-1+.4784968852*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.331143588+.8445222892*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.331143588+.8445222892*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3311435882-.8875285188*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3311435882-.8875285188*I
Line 92: Line 92:
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/1.5.E17 1.5.E17] || [[Item:Q140|<math>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = (1)/((rho)^(2))*diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))*diff(f, [phi$(2)]), rho)+(1)/((rho)^(2)* sin(theta))*diff(sin(theta)*diff(f, theta), theta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == Divide[1,\[Rho]^(2)]*D[(\[Rho]^(2)* D[f, \[Rho]])+Divide[1,\[Rho]^(2)* (Sin[\[Theta]])^(2)]*D[f, {\[Phi], 2}], \[Rho]]+Divide[1,\[Rho]^(2)* Sin[\[Theta]]]*D[Sin[\[Theta]]*D[f, \[Theta]], \[Theta]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
| [https://dlmf.nist.gov/1.5.E17 1.5.E17] || <math qid="Q140">\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = (1)/((rho)^(2))*diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))*diff(f, [phi$(2)]), rho)+(1)/((rho)^(2)* sin(theta))*diff(sin(theta)*diff(f, theta), theta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == Divide[1,\[Rho]^(2)]*D[(\[Rho]^(2)* D[f, \[Rho]])+Divide[1,\[Rho]^(2)* (Sin[\[Theta]])^(2)]*D[f, {\[Phi], 2}], \[Rho]]+Divide[1,\[Rho]^(2)* Sin[\[Theta]]]*D[Sin[\[Theta]]*D[f, \[Theta]], \[Theta]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
|-  
|-  
| [https://dlmf.nist.gov/1.5.E19 1.5.E19] || [[Item:Q142|<math>\pderiv{f}{x} = \pderiv{f}{y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv{f}{x} = \pderiv{f}{y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, x) = diff(f, y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, x] == D[f, y]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 180]
| [https://dlmf.nist.gov/1.5.E19 1.5.E19] || <math qid="Q142">\pderiv{f}{x} = \pderiv{f}{y}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv{f}{x} = \pderiv{f}{y}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, x) = diff(f, y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, x] == D[f, y]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 180]
|-  
|-  
| [https://dlmf.nist.gov/1.5.E23 1.5.E23] || [[Item:Q146|<math>\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>abs(int(diff(f, x), y = c[1]..d)) < epsilon</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[Integrate[D[f, x], {y, Subscript[c, 1], d}, GenerateConditions->None]] < \[Epsilon]</syntaxhighlight> || Failure || Failure || Successful [Tested: 300] || Successful [Tested: 300]
| [https://dlmf.nist.gov/1.5.E23 1.5.E23] || <math qid="Q146">\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>abs(int(diff(f, x), y = c[1]..d)) < epsilon</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[Integrate[D[f, x], {y, Subscript[c, 1], d}, GenerateConditions->None]] < \[Epsilon]</syntaxhighlight> || Failure || Failure || Successful [Tested: 300] || Successful [Tested: 300]
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5.E25 1.5.E25] || [[Item:Q148|<math>a = x_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a = x_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = x[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == Subscript[x, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5.E25 1.5.E25] || <math qid="Q148">a = x_{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a = x_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = x[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == Subscript[x, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5.E26 1.5.E26] || [[Item:Q149|<math>c = y_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c = y_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c = y[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c == Subscript[y, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5.E26 1.5.E26] || <math qid="Q149">c = y_{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c = y_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c = y[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c == Subscript[y, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5#Ex11 1.5#Ex11] || [[Item:Q153|<math>a \leq x</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a \leq x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a <= x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a <= x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5#Ex11 1.5#Ex11] || <math qid="Q153">a \leq x</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a \leq x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a <= x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a <= x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5#Ex12 1.5#Ex12] || [[Item:Q154|<math>\phi_{1}(x) \leq y</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\phi_{1}(x) \leq y</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">phi[1](x) <= y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Phi], 1][x] <= y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5#Ex12 1.5#Ex12] || <math qid="Q154">\phi_{1}(x) \leq y</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\phi_{1}(x) \leq y</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">phi[1](x) <= y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Phi], 1][x] <= y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5#Ex13 1.5#Ex13] || [[Item:Q157|<math>c \leq y</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c \leq y</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c <= y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c <= y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5#Ex13 1.5#Ex13] || <math qid="Q157">c \leq y</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c \leq y</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c <= y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c <= y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5#Ex14 1.5#Ex14] || [[Item:Q158|<math>\psi_{1}(y) \leq x</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\psi_{1}(y) \leq x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">psi[1](y) <= x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Psi], 1][y] <= x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5#Ex14 1.5#Ex14] || <math qid="Q158">\psi_{1}(y) \leq x</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\psi_{1}(y) \leq x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">psi[1](y) <= x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Psi], 1][y] <= x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5#Ex15 1.5#Ex15] || [[Item:Q162|<math>a \leq x</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a \leq x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a <= x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a <= x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5#Ex15 1.5#Ex15] || <math qid="Q162">a \leq x</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a \leq x</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a <= x</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a <= x</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5#Ex16 1.5#Ex16] || [[Item:Q163|<math>\phi_{1}(x) \leq y</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\phi_{1}(x) \leq y</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">phi[1](x) <= y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Phi], 1][x] <= y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5#Ex16 1.5#Ex16] || <math qid="Q163">\phi_{1}(x) \leq y</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\phi_{1}(x) \leq y</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">phi[1](x) <= y</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Phi], 1][x] <= y</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.5#Ex17 1.5#Ex17] || [[Item:Q164|<math>\psi_{1}(x,y) \leq z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\psi_{1}(x,y) \leq z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">psi[1](x , y) <= (x + y*I)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Psi], 1][x , y] <= (x + y*I)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.5#Ex17 1.5#Ex17] || <math qid="Q164">\psi_{1}(x,y) \leq z</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\psi_{1}(x,y) \leq z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">psi[1](x , y) <= (x + y*I)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Psi], 1][x , y] <= (x + y*I)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|}
|}
</div>
</div>

Latest revision as of 10:58, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
1.5.E4 ∂ ⁡ f ∂ ⁡ y = D y ⁢ f partial-derivative 𝑓 𝑦 subscript 𝐷 𝑦 𝑓 {\displaystyle{\displaystyle\frac{\partial f}{\partial y}=D_{y}f}}
\pderiv{f}{y} = D_{y}f		 

diff(f, y) = D[y]*f

D[f, y] == Subscript[D, y]*f
Failure Failure
Failed [300 / 300]
Result: -.5000000004-.8660254040*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I}


Result: .8660254040-.5000000004*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2+1/2*I*3^(1/2)}


Result: -.8660254040+.5000000004*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2-1/2*I*3^(1/2)}


Result: .5000000004+.8660254040*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2*3^(1/2)-1/2*I}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-0.5000000000000001, -0.8660254037844386]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.8660254037844387, -0.49999999999999994]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5.E4 D y ⁢ f = f y subscript 𝐷 𝑦 𝑓 subscript 𝑓 𝑦 {\displaystyle{\displaystyle D_{y}f=f_{y}}}
D_{y}f = f_{y}		 

D[y]*f = f[y]

Subscript[D, y]*f == Subscript[f, y]
Failure Failure
Failed [300 / 300]
Result: -.3660254036+.3660254040*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = 1/2*3^(1/2)+1/2*I}


Result: 1.000000000+0.*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = -1/2+1/2*I*3^(1/2)}


Result: .4e-9+1.732050808*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = 1/2-1/2*I*3^(1/2)}


Result: 1.366025404+1.366025404*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = -1/2*3^(1/2)-1/2*I}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-0.3660254037844386, 0.36602540378443865]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.9999999999999999, -1.1102230246251565*^-16]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5#Ex3 x = r ⁢ cos ⁡ ϕ 𝑥 𝑟 italic-ϕ {\displaystyle{\displaystyle x=r\cos\phi}}
x = r\cos@@{\phi}		 

x = r*cos(phi)

x == r*Cos[\[Phi]]
Failure Failure
Failed [180 / 180]
Result: 2.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}


Result: 1.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}


Result: 3.095814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 2}


Result: .404185472+.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = 1.5, x = 1.5}

... skip entries to safe data
Failed [180 / 180]
Result: Complex[2.595814528585838, -0.5954243253435487]
Test Values: {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[3.3416482752961656, 0.7036130644027555]
Test Values: {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5#Ex4 y = r ⁢ sin ⁡ ϕ 𝑦 𝑟 italic-ϕ {\displaystyle{\displaystyle y=r\sin\phi}}
y = r\sin@@{\phi}		 

y = r*sin(phi)

y == r*Sin[\[Phi]]
Failure Failure
Failed [300 / 300]
Result: -.211529498+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}


Result: 2.788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}


Result: .788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -.5}


Result: 1.788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = .5}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-0.21152949854979308, 0.506394694834305]
Test Values: {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-2.506097038210817, 1.2879550752257174]
Test Values: {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5.E13 ∂ 2 ⁡ f ∂ ⁡ x 2 + ∂ 2 ⁡ f ∂ ⁡ y 2 = ∂ 2 ⁡ f ∂ ⁡ r 2 + 1 r ⁢ ∂ ⁡ f ∂ ⁡ r + 1 r 2 ⁢ ∂ 2 ⁡ f ∂ ⁡ ϕ 2 partial-derivative 𝑓 𝑥 2 partial-derivative 𝑓 𝑦 2 partial-derivative 𝑓 𝑟 2 1 𝑟 partial-derivative 𝑓 𝑟 1 superscript 𝑟 2 partial-derivative 𝑓 italic-ϕ 2 {\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}=\frac{{\partial}^{2}f}{{\partial r}^{2}}+% \frac{1}{r}\frac{\partial f}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}f}% {{\partial\phi}^{2}}}}
\pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}		 

diff(f, [x$(2)])+ diff(f, [y$(2)]) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])

D[f, {x, 2}]+ D[f, {y, 2}] == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]
Successful Successful - Successful [Tested: 300]
1.5#Ex5 x = r ⁢ cos ⁡ ϕ 𝑥 𝑟 italic-ϕ {\displaystyle{\displaystyle x=r\cos\phi}}
x = r\cos@@{\phi}		 

x = r*cos(phi)

x == r*Cos[\[Phi]]
Failure Failure
Failed [180 / 180]
Result: 2.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}


Result: 1.595814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}


Result: 3.095814528-.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 2}


Result: .404185472+.5954243254*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = 1.5, x = 1.5}

... skip entries to safe data
Failed [180 / 180]
Result: Complex[2.595814528585838, -0.5954243253435487]
Test Values: {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[3.3416482752961656, 0.7036130644027555]
Test Values: {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5#Ex6 y = r ⁢ sin ⁡ ϕ 𝑦 𝑟 italic-ϕ {\displaystyle{\displaystyle y=r\sin\phi}}
y = r\sin@@{\phi}		 

y = r*sin(phi)

y == r*Sin[\[Phi]]
Failure Failure
Failed [300 / 300]
Result: -.211529498+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}


Result: 2.788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}


Result: .788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -.5}


Result: 1.788470502+.5063946946*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = .5}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-0.21152949854979308, 0.506394694834305]
Test Values: {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-2.506097038210817, 1.2879550752257174]
Test Values: {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5#Ex7 z = z 𝑧 𝑧 {\displaystyle{\displaystyle z=z}}
z = z		 

z = z
 
z == z
 Skipped - no semantic math Skipped - no semantic math - -
1.5.E15 ∂ 2 ⁡ f ∂ ⁡ x 2 + ∂ 2 ⁡ f ∂ ⁡ y 2 + ∂ 2 ⁡ f ∂ ⁡ z 2 = ∂ 2 ⁡ f ∂ ⁡ r 2 + 1 r ⁢ ∂ ⁡ f ∂ ⁡ r + 1 r 2 ⁢ ∂ 2 ⁡ f ∂ ⁡ ϕ 2 + ∂ 2 ⁡ f ∂ ⁡ z 2 partial-derivative 𝑓 𝑥 2 partial-derivative 𝑓 𝑦 2 partial-derivative 𝑓 𝑧 2 partial-derivative 𝑓 𝑟 2 1 𝑟 partial-derivative 𝑓 𝑟 1 superscript 𝑟 2 partial-derivative 𝑓 italic-ϕ 2 partial-derivative 𝑓 𝑧 2 {\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}+\frac{{\partial}^{2}f}{{\partial z}^{2}}=% \frac{{\partial}^{2}f}{{\partial r}^{2}}+\frac{1}{r}\frac{\partial f}{\partial r% }+\frac{1}{r^{2}}\frac{{\partial}^{2}f}{{\partial\phi}^{2}}+\frac{{\partial}^{% 2}f}{{\partial z}^{2}}}}
\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}+\pderiv[2]{f}{z}		 

diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) )

D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I))
Successful Successful - Successful [Tested: 300]
1.5#Ex8 x = ρ ⁢ sin ⁡ θ ⁢ cos ⁡ ϕ 𝑥 𝜌 𝜃 italic-ϕ {\displaystyle{\displaystyle x=\rho\sin\theta\cos\phi}}
x = \rho\sin@@{\theta}\cos@@{\phi}		 

x = rho*sin(theta)*cos(phi)

x == \[Rho]*Sin[\[Theta]]*Cos[\[Phi]]
Failure Failure
Failed [300 / 300]
Result: .7933233780-.2990618885*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = 1.5}


Result: -.2066766220-.2990618885*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = .5}


Result: 1.293323378-.2990618885*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = 2}


Result: 2.075937432-.6992275886*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = -1/2+1/2*I*3^(1/2), x = 1.5}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[0.7933233783531031, -0.29906188871772155]
Test Values: {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[1.1325168401075085, -1.15603698835011]
Test Values: {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5#Ex9 y = ρ ⁢ sin ⁡ θ ⁢ sin ⁡ ϕ 𝑦 𝜌 𝜃 italic-ϕ {\displaystyle{\displaystyle y=\rho\sin\theta\sin\phi}}
y = \rho\sin@@{\theta}\sin@@{\phi}		 

y = rho*sin(theta)*sin(phi)

y == \[Rho]*Sin[\[Theta]]*Sin[\[Phi]]
Failure Failure
Failed [300 / 300]
Result: -1.750303606-.8142131232*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = -1.5}


Result: 1.249696394-.8142131232*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = 1.5}


Result: -.7503036064-.8142131232*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = -.5}


Result: .2496963936-.8142131232*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = .5}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-1.750303605777159, -0.8142131229438421]
Test Values: {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-0.49444885508381575, -0.009630141394747549]
Test Values: {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5#Ex10 z = ρ ⁢ cos ⁡ θ 𝑧 𝜌 𝜃 {\displaystyle{\displaystyle z=\rho\cos\theta}}
z = \rho\cos@@{\theta}		 

z = rho*cos(theta)

z == \[Rho]*Cos[\[Theta]]
Failure Failure
Failed [300 / 300]
Result: .348818158e-1+.4784968852*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: -1.331143588+.8445222892*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}


Result: -.3311435882-.8875285188*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}


Result: -1.697168992-.5215031148*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[0.03488181560898618, 0.4784968849905366]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.8875285187939019, -0.3311435881754526]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
1.5.E17 ∂ 2 ⁡ f ∂ ⁡ x 2 + ∂ 2 ⁡ f ∂ ⁡ y 2 + ∂ 2 ⁡ f ∂ ⁡ z 2 = 1 ρ 2 ⁢ ∂ ∂ ⁡ ρ ⁡ ( ρ 2 ⁢ ∂ ⁡ f ∂ ⁡ ρ ) + 1 ρ 2 ⁢ sin 2 ⁡ θ ⁢ ∂ 2 ⁡ f ∂ ⁡ ϕ 2 + 1 ρ 2 ⁢ sin ⁡ θ ⁢ ∂ ∂ ⁡ θ ⁡ ( sin ⁡ θ ⁢ ∂ ⁡ f ∂ ⁡ θ ) partial-derivative 𝑓 𝑥 2 partial-derivative 𝑓 𝑦 2 partial-derivative 𝑓 𝑧 2 1 superscript 𝜌 2 partial-derivative 𝜌 superscript 𝜌 2 partial-derivative 𝑓 𝜌 1 superscript 𝜌 2 2 𝜃 partial-derivative 𝑓 italic-ϕ 2 1 superscript 𝜌 2 𝜃 partial-derivative 𝜃 𝜃 partial-derivative 𝑓 𝜃 {\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}+\frac{{\partial}^{2}f}{{\partial z}^{2}}={% \frac{1}{\rho^{2}}\frac{\partial}{\partial\rho}\left(\rho^{2}\frac{\partial f}% {\partial\rho}\right)+\frac{1}{\rho^{2}{\sin^{2}}\theta}\frac{{\partial}^{2}f}% {{\partial\phi}^{2}}}+\frac{1}{\rho^{2}\sin\theta}\frac{\partial}{\partial% \theta}\left(\sin\theta\frac{\partial f}{\partial\theta}\right)}}
\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)		 

diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = (1)/((rho)^(2))*diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))*diff(f, [phi$(2)]), rho)+(1)/((rho)^(2)* sin(theta))*diff(sin(theta)*diff(f, theta), theta)

D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == Divide[1,\[Rho]^(2)]*D[(\[Rho]^(2)* D[f, \[Rho]])+Divide[1,\[Rho]^(2)* (Sin[\[Theta]])^(2)]*D[f, {\[Phi], 2}], \[Rho]]+Divide[1,\[Rho]^(2)* Sin[\[Theta]]]*D[Sin[\[Theta]]*D[f, \[Theta]], \[Theta]]
Successful Successful - Successful [Tested: 300]
1.5.E19 ∂ ⁡ f ∂ ⁡ x = ∂ ⁡ f ∂ ⁡ y partial-derivative 𝑓 𝑥 partial-derivative 𝑓 𝑦 {\displaystyle{\displaystyle\frac{\partial f}{\partial x}=\frac{\partial f}{% \partial y}}}
\pderiv{f}{x} = \pderiv{f}{y}		 

diff(f, x) = diff(f, y)

D[f, x] == D[f, y]
Successful Successful - Successful [Tested: 180]
1.5.E23 | ∫ c 1 d ( ∂ ⁡ f / ∂ ⁡ x ) ⁢ d y | < ϵ superscript subscript subscript 𝑐 1 𝑑 partial-derivative 𝑓 𝑥 𝑦 italic-ϵ {\displaystyle{\displaystyle\left|\int_{c_{1}}^{d}(\ifrac{\partial f}{\partial x% })\mathrm{d}y\right|<\epsilon}}
\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon		 

abs(int(diff(f, x), y = c[1]..d)) < epsilon

Abs[Integrate[D[f, x], {y, Subscript[c, 1], d}, GenerateConditions->None]] < \[Epsilon]
Failure Failure Successful [Tested: 300] Successful [Tested: 300]
1.5.E25 a = x 0 𝑎 subscript 𝑥 0 {\displaystyle{\displaystyle a=x_{0}}}
a = x_{0}		 

a = x[0]
 
a == Subscript[x, 0]
 Skipped - no semantic math Skipped - no semantic math - -
1.5.E26 c = y 0 𝑐 subscript 𝑦 0 {\displaystyle{\displaystyle c=y_{0}}}
c = y_{0}		 

c = y[0]
 
c == Subscript[y, 0]
 Skipped - no semantic math Skipped - no semantic math - -
1.5#Ex11 a ≤ x 𝑎 𝑥 {\displaystyle{\displaystyle a\leq x}}
a \leq x		 

a <= x
 
a <= x
 Skipped - no semantic math Skipped - no semantic math - -
1.5#Ex12 ϕ 1 ⁢ ( x ) ≤ y subscript italic-ϕ 1 𝑥 𝑦 {\displaystyle{\displaystyle\phi_{1}(x)\leq y}}
\phi_{1}(x) \leq y		 

phi[1](x) <= y
 
Subscript[\[Phi], 1][x] <= y
 Skipped - no semantic math Skipped - no semantic math - -
1.5#Ex13 c ≤ y 𝑐 𝑦 {\displaystyle{\displaystyle c\leq y}}
c \leq y		 

c <= y
 
c <= y
 Skipped - no semantic math Skipped - no semantic math - -
1.5#Ex14 ψ 1 ⁢ ( y ) ≤ x subscript 𝜓 1 𝑦 𝑥 {\displaystyle{\displaystyle\psi_{1}(y)\leq x}}
\psi_{1}(y) \leq x		 

psi[1](y) <= x
 
Subscript[\[Psi], 1][y] <= x
 Skipped - no semantic math Skipped - no semantic math - -
1.5#Ex15 a ≤ x 𝑎 𝑥 {\displaystyle{\displaystyle a\leq x}}
a \leq x		 

a <= x
 
a <= x
 Skipped - no semantic math Skipped - no semantic math - -
1.5#Ex16 ϕ 1 ⁢ ( x ) ≤ y subscript italic-ϕ 1 𝑥 𝑦 {\displaystyle{\displaystyle\phi_{1}(x)\leq y}}
\phi_{1}(x) \leq y		 

phi[1](x) <= y
 
Subscript[\[Phi], 1][x] <= y
 Skipped - no semantic math Skipped - no semantic math - -
1.5#Ex17 ψ 1 ⁢ ( x , y ) ≤ z subscript 𝜓 1 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle\psi_{1}(x,y)\leq z}}
\psi_{1}(x,y) \leq z		 

psi[1](x , y) <= (x + y*I)
 
Subscript[\[Psi], 1][x , y] <= (x + y*I)
 Skipped - no semantic math Skipped - no semantic math - -
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