View source for 1.6

{{DISPLAYTITLE:Algebraic and Analytic Methods - 1.6 Vectors and Vector-Valued Functions}}

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! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6#Ex1 1.6#Ex1] || <math qid="Q171">\mathbf{a} = (a_{1},a_{2},a_{3})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{a} = (a_{1},a_{2},a_{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = (a[1], a[2], a[3])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == (Subscript[a, 1], Subscript[a, 2], Subscript[a, 3])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6#Ex2 1.6#Ex2] || <math qid="Q172">\mathbf{b} = (b_{1},b_{2},b_{3})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{b} = (b_{1},b_{2},b_{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b = (b[1], b[2], b[3])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b == (Subscript[b, 1], Subscript[b, 2], Subscript[b, 3])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6.E2 1.6.E2] || <math qid="Q173">\mathbf{a}\cdot\mathbf{b} = a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{a}\cdot\mathbf{b} = a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a * b = a[1]*b[1]+ a[2]*b[2]+ a[3]*b[3]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a * b == Subscript[a, 1]*Subscript[b, 1]+ Subscript[a, 2]*Subscript[b, 2]+ Subscript[a, 3]*Subscript[b, 3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6.E3 1.6.E3] || <math qid="Q174">\|\mathbf{a}\| = \sqrt{\mathbf{a}\cdot\mathbf{a}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\|\mathbf{a}\| = \sqrt{\mathbf{a}\cdot\mathbf{a}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Error</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Norm[a] == Sqrt[a * a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- 
| [https://dlmf.nist.gov/1.6.E4 1.6.E4] || <math qid="Q175">\cos@@{\theta} = \frac{\mathbf{a}\cdot\mathbf{b}}{\|\mathbf{a}\|\;\|\mathbf{b}\|}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{\theta} = \frac{\mathbf{a}\cdot\mathbf{b}}{\|\mathbf{a}\|\;\|\mathbf{b}\|}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[\[Theta]] == Divide[a * b,Norm[a]*Norm[b]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2694569811-.3969495503*I
Test Values: {a = -1.5, b = -1.5, theta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .227765517+.4690753764*I
Test Values: {a = -1.5, b = -1.5, theta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .227765517+.4690753764*I
Test Values: {a = -1.5, b = -1.5, theta = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2694569811-.3969495503*I
Test Values: {a = -1.5, b = -1.5, theta = -1/2*3^(1/2)-1/2*I}</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[-0.2694569809427748, -0.3969495502290325]
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.2277655168641104, 0.46907537626850365]
Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6.E6 1.6.E6] || <math qid="Q179">\mathbf{a} = a_{1}\mathbf{i}+a_{2}\mathbf{j}+a_{3}\mathbf{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{a} = a_{1}\mathbf{i}+a_{2}\mathbf{j}+a_{3}\mathbf{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = a[1]*i + a[2]*j + a[3]*((0 , 0 , 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == Subscript[a, 1]*i + Subscript[a, 2]*j + Subscript[a, 3]*((0 , 0 , 1))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6#Ex6 1.6#Ex6] || <math qid="Q180">\mathbf{i}\times\mathbf{j} = \mathbf{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{i}\times\mathbf{j} = \mathbf{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">i * j = ((0 , 0 , 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">i * j == ((0 , 0 , 1))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6#Ex7 1.6#Ex7] || <math qid="Q181">\mathbf{j}\times\mathbf{k} = \mathbf{i}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{j}\times\mathbf{k} = \mathbf{i}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">j *((0 , 0 , 1)) = i</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">j *((0 , 0 , 1)) == i</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6#Ex8 1.6#Ex8] || <math qid="Q182">\mathbf{k}\times\mathbf{i} = \mathbf{j}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{k}\times\mathbf{i} = \mathbf{j}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((0 , 0 , 1)) * i = j</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((0 , 0 , 1)) * i == j</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6#Ex9 1.6#Ex9] || <math qid="Q183">\mathbf{j}\times\mathbf{i} = -\mathbf{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{j}\times\mathbf{i} = -\mathbf{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">j * i = -((0 , 0 , 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">j * i == -((0 , 0 , 1))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6#Ex10 1.6#Ex10] || <math qid="Q184">\mathbf{k}\times\mathbf{j} = -\mathbf{i}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{k}\times\mathbf{j} = -\mathbf{i}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((0 , 0 , 1)) * j = - i</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((0 , 0 , 1)) * j == - i</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6#Ex11 1.6#Ex11] || <math qid="Q185">\mathbf{i}\times\mathbf{k} = -\mathbf{j}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{i}\times\mathbf{k} = -\mathbf{j}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">i *((0 , 0 , 1)) = - j</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">i *((0 , 0 , 1)) == - j</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6.E12 1.6.E12] || <math qid="Q189">a_{j}b_{j} = \sum_{j=1}^{3}a_{j}b_{j}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{j}b_{j} = \sum_{j=1}^{3}a_{j}b_{j}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[j]*b[j] = sum(a[j]*b[j], j = 1..3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, j]*Subscript[b, j] == Sum[Subscript[a, j]*Subscript[b, j], {j, 1, 3}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- 
| [https://dlmf.nist.gov/1.6#Ex15 1.6#Ex15] || <math qid="Q194">\LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LeviCivita[1, 2, 3] = LeviCivita[3, 1, 2]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Part[LeviCivitaTensor[3,List], 1, 2, 3] == Part[LeviCivitaTensor[3,List], 3, 1, 2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|- 
| [https://dlmf.nist.gov/1.6#Ex15 1.6#Ex15] || <math qid="Q194">\LeviCivitasym{3}{1}{2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LeviCivitasym{3}{1}{2} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LeviCivita[3, 1, 2] = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Part[LeviCivitaTensor[3,List], 3, 1, 2] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|- 
| [https://dlmf.nist.gov/1.6#Ex16 1.6#Ex16] || <math qid="Q195">\LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LeviCivita[2, 1, 3] = LeviCivita[3, 2, 1]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Part[LeviCivitaTensor[3,List], 2, 1, 3] == Part[LeviCivitaTensor[3,List], 3, 2, 1]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|- 
| [https://dlmf.nist.gov/1.6#Ex16 1.6#Ex16] || <math qid="Q195">\LeviCivitasym{3}{2}{1} = -1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LeviCivitasym{3}{2}{1} = -1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LeviCivita[3, 2, 1] = - 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Part[LeviCivitaTensor[3,List], 3, 2, 1] == - 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|- 
| [https://dlmf.nist.gov/1.6#Ex17 1.6#Ex17] || <math qid="Q196">\LeviCivitasym{2}{2}{1} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LeviCivitasym{2}{2}{1} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LeviCivita[2, 2, 1] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Part[LeviCivitaTensor[3,List], 2, 2, 1] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|- 
| [https://dlmf.nist.gov/1.6.E16 1.6.E16] || <math qid="Q197">\LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>LeviCivita[j, k, ell]*LeviCivita[ell, m, n] = KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Part[LeviCivitaTensor[3,List], \[ScriptL], m, n] == KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m]</syntaxhighlight> || Failure || Failure || Error || Error
|- 
| [https://dlmf.nist.gov/1.6.E17 1.6.E17] || <math qid="Q198">\mathbf{e}_{j}\times\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}\mathbf{e}_{\ell}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathbf{e}_{j}\times\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}\mathbf{e}_{\ell}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>e[j] * e[k] = LeviCivita[j, k, ell]*e[ell]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[e, j] * Subscript[e, k] == Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Subscript[e, \[ScriptL]]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- 
| [https://dlmf.nist.gov/1.6.E18 1.6.E18] || <math qid="Q199">a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>a[j]*e[j] * b[k]*e[k] = LeviCivita[j, k, ell]*a[j]*b[k]*e[ell]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, j]*Subscript[e, j] * Subscript[b, k]*Subscript[e, k] == Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Subscript[a, j]*Subscript[b, k]*Subscript[e, \[ScriptL]]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.6.E43 1.6.E43] || <math qid="Q224">\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F(x , y) = F[1](x , y)* i + F[2](x , y)* j</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[x , y] == Subscript[F, 1][x , y]* i + Subscript[F, 2][x , y]* j</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- 
| [https://dlmf.nist.gov/1.6.E46 1.6.E46] || <math qid="Q227">\mathbf{T}_{u} = \pderiv{x}{u}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{u}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{u}(u_{0},v_{0})\mathbf{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathbf{T}_{u} = \pderiv{x}{u}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{u}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{u}(u_{0},v_{0})\mathbf{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>T[u] = diff(x, u)*(u[0], v[0])*i + diff(y, u)*(u[0], v[0])*j + diff(x + y*I, u)*(u[0], v[0])*((0 , 0 , 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[T, u] == D[x, u]*(Subscript[u, 0], Subscript[v, 0])*i + D[y, u]*(Subscript[u, 0], Subscript[v, 0])*j + D[x + y*I, u]*(Subscript[u, 0], Subscript[v, 0])*((0 , 0 , 1))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 2, k = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || -
|- 
| [https://dlmf.nist.gov/1.6.E47 1.6.E47] || <math qid="Q228">\mathbf{T}_{v} = \pderiv{x}{v}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{v}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{v}(u_{0},v_{0})\mathbf{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathbf{T}_{v} = \pderiv{x}{v}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{v}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{v}(u_{0},v_{0})\mathbf{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>T[v] = diff(x, v)*(u[0], v[0])*i + diff(y, v)*(u[0], v[0])*j + diff(x + y*I, v)*(u[0], v[0])*((0 , 0 , 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[T, v] == D[x, v]*(Subscript[u, 0], Subscript[v, 0])*i + D[y, v]*(Subscript[u, 0], Subscript[v, 0])*j + D[x + y*I, v]*(Subscript[u, 0], Subscript[v, 0])*((0 , 0 , 1))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 2, k = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
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| [https://dlmf.nist.gov/1.6.E49 1.6.E49] || <math qid="Q230">\|\mathbf{T}_{u}\times\mathbf{T}_{v}\| = \sqrt{\left(\pderiv{(x,y)}{(u,v)}\right)^{2}+\left(\pderiv{(y,z)}{(u,v)}\right)^{2}+\left(\pderiv{(x,z)}{(u,v)}\right)^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\|\mathbf{T}_{u}\times\mathbf{T}_{v}\| = \sqrt{\left(\pderiv{(x,y)}{(u,v)}\right)^{2}+\left(\pderiv{(y,z)}{(u,v)}\right)^{2}+\left(\pderiv{(x,z)}{(u,v)}\right)^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Norm[Subscript[T, u] * Subscript[T, v]] == Sqrt[(((D[(x , y), {temp, 1}]/.temp-> (u , v))))^(2)+(((D[(y ,(x + y*I)), {temp, 1}]/.temp-> (u , v))))^(2)+(((D[(x ,(x + y*I)), {temp, 1}]/.temp-> (u , v))))^(2)]</syntaxhighlight> || Translation Error || Translation Error || - || -
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| [https://dlmf.nist.gov/1.6.E50 1.6.E50] || <math qid="Q231">\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Norm[Subscript[T, \[Theta]] * Subscript[T, \[Phi]]] == \[Rho]^(2)* Abs[Sin[\[Theta]]]</syntaxhighlight> || Translation Error || Translation Error || - || -
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