Results of Algebraic and Analytic Methods: Difference between revisions
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Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
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| [https://dlmf.nist.gov/1.2#Ex1 1.2#Ex1] || [[Item:Q54|<math>M(1) = A</math>]]<br><code>M(1) = A</code> || <math></math> || <code>M(1) = A</code> || <code>M[1] == A</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.2#Ex1 1.2#Ex1] || [[Item:Q54|<math>M(1) = A</math>]]<br><code>M(1) = A</code> || <math></math> || <code>M(1) = A</code> || <code>M[1] == A</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.2#Ex2 1.2#Ex2] || [[Item:Q55|<math>M(-1) = H</math>]]<br><code>M(-1) = H</code> || <math></math> || <code>M | | [https://dlmf.nist.gov/1.2#Ex2 1.2#Ex2] || [[Item:Q55|<math>M(-1) = H</math>]]<br><code>M(-1) = H</code> || <math></math> || <code>M(- 1) = H</code> || <code>M[- 1] == H</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.2.E26 1.2.E26] || [[Item:Q56|<math>\lim_{r\to 0}M(r) = G</math>]]<br><code>\lim_{r\to 0}M(r) = G</code> || <math></math> || <code>limit(M(r), r = 0) = G</code> || <code>Limit[M[r], r -> 0, GenerateConditions->None] == G</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.2.E26 1.2.E26] || [[Item:Q56|<math>\lim_{r\to 0}M(r) = G</math>]]<br><code>\lim_{r\to 0}M(r) = G</code> || <math></math> || <code>limit(M(r), r = 0) = G</code> || <code>Limit[M[r], r -> 0, GenerateConditions->None] == G</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
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| [https://dlmf.nist.gov/1.5#Ex16 1.5#Ex16] || [[Item:Q163|<math>\phi_{1}(x) \leq y</math>]]<br><code>\phi_{1}(x) \leq y</code> || <math></math> || <code>phi[1](x) <= y</code> || <code>Subscript[\[Phi], 1][x] <= y</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.5#Ex16 1.5#Ex16] || [[Item:Q163|<math>\phi_{1}(x) \leq y</math>]]<br><code>\phi_{1}(x) \leq y</code> || <math></math> || <code>phi[1](x) <= y</code> || <code>Subscript[\[Phi], 1][x] <= y</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.5#Ex17 1.5#Ex17] || [[Item:Q164|<math>\psi_{1}(x,y) \leq z</math>]]<br><code>\psi_{1}(x,y) \leq z</code> || <math></math> || <code>psi[1] | | [https://dlmf.nist.gov/1.5#Ex17 1.5#Ex17] || [[Item:Q164|<math>\psi_{1}(x,y) \leq z</math>]]<br><code>\psi_{1}(x,y) \leq z</code> || <math></math> || <code>psi[1](x , y) <= (x + y*I)</code> || <code>Subscript[\[Psi], 1][x , y] <= (x + y*I)</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.6#Ex1 1.6#Ex1] || [[Item:Q171|<math>\mathbf{a} = (a_{1},a_{2},a_{3})</math>]]<br><code>\mathbf{a} = (a_{1},a_{2},a_{3})</code> || <math></math> || <code>a = (a[1], a[2], a[3])</code> || <code>a == (Subscript[a, 1], Subscript[a, 2], Subscript[a, 3])</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.6#Ex1 1.6#Ex1] || [[Item:Q171|<math>\mathbf{a} = (a_{1},a_{2},a_{3})</math>]]<br><code>\mathbf{a} = (a_{1},a_{2},a_{3})</code> || <math></math> || <code>a = (a[1], a[2], a[3])</code> || <code>a == (Subscript[a, 1], Subscript[a, 2], Subscript[a, 3])</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
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| [https://dlmf.nist.gov/1.6.E18 1.6.E18] || [[Item:Q199|<math>a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}</math>]]<br><code>a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}</code> || <math></math> || <code>a[j]*exp(1)[j] * b[k]*exp(1)[k] = LeviCivita[j, k, ell]*a[j]*b[k]*exp(1)[ell]</code> || <code>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]]</code> || Translation Error || Translation Error || - || - | | [https://dlmf.nist.gov/1.6.E18 1.6.E18] || [[Item:Q199|<math>a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}</math>]]<br><code>a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}</code> || <math></math> || <code>a[j]*exp(1)[j] * b[k]*exp(1)[k] = LeviCivita[j, k, ell]*a[j]*b[k]*exp(1)[ell]</code> || <code>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]]</code> || Translation Error || Translation Error || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.6.E43 1.6.E43] || [[Item:Q224|<math>\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}</math>]]<br><code>\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}</code> || <math></math> || <code>F | | [https://dlmf.nist.gov/1.6.E43 1.6.E43] || [[Item:Q224|<math>\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}</math>]]<br><code>\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}</code> || <math></math> || <code>F(x , y) = F[1](x , y)* I + F[2](x , y)* j</code> || <code>F[x , y] == Subscript[F, 1][x , y]* I + Subscript[F, 2][x , y]* j</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.6.E46 1.6.E46] || [[Item:Q227|<math>\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><code>\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}</code> || <math></math> || <code>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])*k</code> || <code>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])*k</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.8660254040+.5000000000*I <- {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}</code><br><code>.8660254040+.5000000000*I <- {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}</code><br><code>.8660254040+.5000000000*I <- {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}</code><br><code>.8660254040+.5000000000*I <- {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}</code><br>... skip entries to safe data<br></div></div> || - | | [https://dlmf.nist.gov/1.6.E46 1.6.E46] || [[Item:Q227|<math>\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><code>\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}</code> || <math></math> || <code>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])*k</code> || <code>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])*k</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.8660254040+.5000000000*I <- {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}</code><br><code>.8660254040+.5000000000*I <- {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}</code><br><code>.8660254040+.5000000000*I <- {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}</code><br><code>.8660254040+.5000000000*I <- {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}</code><br>... skip entries to safe data<br></div></div> || - | ||
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| [https://dlmf.nist.gov/1.6.E50 1.6.E50] || [[Item:Q231|<math>\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}</math>]]<br><code>\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}</code> || <math></math> || <code>Error</code> || <code>Norm[Subscript[T, \[Theta]] * Subscript[T, \[Phi]]] == \[Rho]^(2)* Abs[Sin[\[Theta]]]</code> || Translation Error || Translation Error || - || - | | [https://dlmf.nist.gov/1.6.E50 1.6.E50] || [[Item:Q231|<math>\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}</math>]]<br><code>\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}</code> || <math></math> || <code>Error</code> || <code>Norm[Subscript[T, \[Theta]] * Subscript[T, \[Phi]]] == \[Rho]^(2)* Abs[Sin[\[Theta]]]</code> || Translation Error || Translation Error || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.7.E1 1.7.E1] || [[Item:Q242|<math>\left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)</math>]]<br><code>\left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)</code> || <math></math> || <code>(sum(a[j]*b[j], j = 1..n))^(2) (sum( | | [https://dlmf.nist.gov/1.7.E1 1.7.E1] || [[Item:Q242|<math>\left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)</math>]]<br><code>\left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)</code> || <math></math> || <code>(sum(a[j]*b[j], j = 1..n))^(2) <= (sum((a[j])^(2), j = 1..n))*(sum((b[j])^(2), j = 1..n))</code> || <code>((Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None]))^(2) <= (Sum[(Subscript[a, j])^(2), {j, 1, n}, GenerateConditions->None])*(Sum[(Subscript[b, j])^(2), {j, 1, n}, GenerateConditions->None])</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.7.E2 1.7.E2] || [[Item:Q243|<math>\sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}</math>]]<br><code>\sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}</code> || <math></math> || <code>sum(a[j]*b[j], j = 1..n) (sum( | | [https://dlmf.nist.gov/1.7.E2 1.7.E2] || [[Item:Q243|<math>\sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}</math>]]<br><code>\sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}</code> || <math></math> || <code>sum(a[j]*b[j], j = 1..n) <= (sum((a[j])^(p), j = 1..n))^(1/p)*(sum((b[j])^(q), j = 1..n))^(1/q)</code> || <code>Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None] <= ((Sum[(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)*((Sum[(Subscript[b, j])^(q), {j, 1, n}, GenerateConditions->None]))^(1/q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.7.E3 1.7.E3] || [[Item:Q244|<math>\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}</math>]]<br><code>\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}</code> || <math></math> || <code>(sum((a[j]+ b[j])^(p), j = 1..n))^(1/p) (sum( | | [https://dlmf.nist.gov/1.7.E3 1.7.E3] || [[Item:Q244|<math>\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}</math>]]<br><code>\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}</code> || <math></math> || <code>(sum((a[j]+ b[j])^(p), j = 1..n))^(1/p) <= (sum((a[j])^(p), j = 1..n))^(1/p)+(sum((b[j])^(p), j = 1..n))^(1/p)</code> || <code>((Sum[(Subscript[a, j]+ Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p) <= ((Sum[(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)+((Sum[(Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.7.E7 1.7.E7] || [[Item:Q248|<math>H \leq G</math>]]<br><code>H \leq G</code> || <math></math> || <code>H <= G</code> || <code>H <= G</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.7.E7 1.7.E7] || [[Item:Q248|<math>H \leq G</math>]]<br><code>H \leq G</code> || <math></math> || <code>H <= G</code> || <code>H <= G</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
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| [https://dlmf.nist.gov/1.9.E16 1.9.E16] || [[Item:Q290|<math>\frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}</math>]]<br><code>\frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}</code> || <math></math> || <code>(z[1])/(z[2]) = (z[1]*conjugate(z)[2])/((abs(z[2]))^(2))</code> || <code>Divide[Subscript[z, 1],Subscript[z, 2]] == Divide[Subscript[z, 1]*Subscript[Conjugate[z], 2],(Abs[Subscript[z, 2]])^(2)]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[1.0, Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, -1.0], Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div> | | [https://dlmf.nist.gov/1.9.E16 1.9.E16] || [[Item:Q290|<math>\frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}</math>]]<br><code>\frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}</code> || <math></math> || <code>(z[1])/(z[2]) = (z[1]*conjugate(z)[2])/((abs(z[2]))^(2))</code> || <code>Divide[Subscript[z, 1],Subscript[z, 2]] == Divide[Subscript[z, 1]*Subscript[Conjugate[z], 2],(Abs[Subscript[z, 2]])^(2)]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[1.0, Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, -1.0], Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9.E16 1.9.E16] || [[Item:Q290|<math>\frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}</math>]]<br><code>\frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}</code> || <math></math> || <code>(x[1]*x[2]+ y[1]*y[2]+ I*(x[2]*y[1]- x[1]*y[2]))/( | | [https://dlmf.nist.gov/1.9.E16 1.9.E16] || [[Item:Q290|<math>\frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}</math>]]<br><code>\frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}</code> || <math></math> || <code>(x + y*I[1]*conjugate(x + y*I)[2])/((abs(x + y*I[2]))^(2)) = (x[1]*x[2]+ y[1]*y[2]+ I*(x[2]*y[1]- x[1]*y[2]))/((x[2])^(2)+ (y[2])^(2))</code> || <code>Divide[Subscript[x + y*I, 1]*Subscript[Conjugate[x + y*I], 2],(Abs[Subscript[x + y*I, 2]])^(2)] == Divide[Subscript[x, 1]*Subscript[x, 2]+ Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 2]*Subscript[y, 1]- Subscript[x, 1]*Subscript[y, 2]),(Subscript[x, 2])^(2)+ (Subscript[y, 2])^(2)]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.6666666666666669, -0.6666666666666667], Times[Power[Abs[Subscript[Complex[1.5, -1.5], 2]], -2], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, 1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9.E17 1.9.E17] || [[Item:Q291|<math>|z_{1}z_{2}| = |z_{1}|\;|z_{2}|</math>]]<br><code>|z_{1}z_{2}| = |z_{1}|\;|z_{2}|</code> || <math></math> || <code>abs(z[1]*z[2]) = abs(z[1])*abs(z[2])</code> || <code>Abs[Subscript[z, 1]*Subscript[z, 2]] == Abs[Subscript[z, 1]]*Abs[Subscript[z, 2]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.9.E17 1.9.E17] || [[Item:Q291|<math>|z_{1}z_{2}| = |z_{1}|\;|z_{2}|</math>]]<br><code>|z_{1}z_{2}| = |z_{1}|\;|z_{2}|</code> || <math></math> || <code>abs(z[1]*z[2]) = abs(z[1])*abs(z[2])</code> || <code>Abs[Subscript[z, 1]*Subscript[z, 2]] == Abs[Subscript[z, 1]]*Abs[Subscript[z, 2]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
| Line 239: | Line 239: | ||
| [https://dlmf.nist.gov/1.9#Ex14 1.9#Ex14] || [[Item:Q332|<math>b_{1} = -a_{1}/a_{0}^{2}</math>]]<br><code>b_{1} = -a_{1}/a_{0}^{2}</code> || <math></math> || <code>b[1] = - a[1]/(a[0])^(2)</code> || <code>Subscript[b, 1] == - Subscript[a, 1]/(Subscript[a, 0])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.9#Ex14 1.9#Ex14] || [[Item:Q332|<math>b_{1} = -a_{1}/a_{0}^{2}</math>]]<br><code>b_{1} = -a_{1}/a_{0}^{2}</code> || <math></math> || <code>b[1] = - a[1]/(a[0])^(2)</code> || <code>Subscript[b, 1] == - Subscript[a, 1]/(Subscript[a, 0])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9#Ex15 1.9#Ex15] || [[Item:Q333|<math>b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3}</math>]]<br><code>b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3}</code> || <math></math> || <code>b[2] ( | | [https://dlmf.nist.gov/1.9#Ex15 1.9#Ex15] || [[Item:Q333|<math>b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3}</math>]]<br><code>b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3}</code> || <math></math> || <code>b[2] = ((a[1])^(2)- a[0]*a[2])/(a[0])^(3)</code> || <code>Subscript[b, 2] == ((Subscript[a, 1])^(2)- Subscript[a, 0]*Subscript[a, 2])/(Subscript[a, 0])^(3)</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9#Ex16 1.9#Ex16] || [[Item:Q336|<math>q_{1} = a_{1}</math>]]<br><code>q_{1} = a_{1}</code> || <math></math> || <code>q[1] = a[1]</code> || <code>Subscript[q, 1] == Subscript[a, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.9#Ex16 1.9#Ex16] || [[Item:Q336|<math>q_{1} = a_{1}</math>]]<br><code>q_{1} = a_{1}</code> || <math></math> || <code>q[1] = a[1]</code> || <code>Subscript[q, 1] == Subscript[a, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9#Ex17 1.9#Ex17] || [[Item:Q337|<math>q_{2} = (2a_{2}-a_{1}^{2})/2</math>]]<br><code>q_{2} = (2a_{2}-a_{1}^{2})/2</code> || <math></math> || <code>q[2] (2*a[2]- | | [https://dlmf.nist.gov/1.9#Ex17 1.9#Ex17] || [[Item:Q337|<math>q_{2} = (2a_{2}-a_{1}^{2})/2</math>]]<br><code>q_{2} = (2a_{2}-a_{1}^{2})/2</code> || <math></math> || <code>q[2] = (2*a[2]- (a[1])^(2))/2</code> || <code>Subscript[q, 2] == (2*Subscript[a, 2]- (Subscript[a, 1])^(2))/2</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9#Ex18 1.9#Ex18] || [[Item:Q338|<math>q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3</math>]]<br><code>q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3</code> || <math></math> || <code>q[3] (3*a[3]- 3*a[1]*a[2]+ | | [https://dlmf.nist.gov/1.9#Ex18 1.9#Ex18] || [[Item:Q338|<math>q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3</math>]]<br><code>q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3</code> || <math></math> || <code>q[3] = (3*a[3]- 3*a[1]*a[2]+ (a[1])^(3))/3</code> || <code>Subscript[q, 3] == (3*Subscript[a, 3]- 3*Subscript[a, 1]*Subscript[a, 2]+ (Subscript[a, 1])^(3))/3</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9#Ex19 1.9#Ex19] || [[Item:Q341|<math>p_{0} = 1</math>]]<br><code>p_{0} = 1</code> || <math></math> || <code>p[0] = 1</code> || <code>Subscript[p, 0] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.9#Ex19 1.9#Ex19] || [[Item:Q341|<math>p_{0} = 1</math>]]<br><code>p_{0} = 1</code> || <math></math> || <code>p[0] = 1</code> || <code>Subscript[p, 0] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
| Line 251: | Line 251: | ||
| [https://dlmf.nist.gov/1.9#Ex20 1.9#Ex20] || [[Item:Q342|<math>p_{1} = \nu a_{1}</math>]]<br><code>p_{1} = \nu a_{1}</code> || <math></math> || <code>p[1] = nu*a[1]</code> || <code>Subscript[p, 1] == \[Nu]*Subscript[a, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.9#Ex20 1.9#Ex20] || [[Item:Q342|<math>p_{1} = \nu a_{1}</math>]]<br><code>p_{1} = \nu a_{1}</code> || <math></math> || <code>p[1] = nu*a[1]</code> || <code>Subscript[p, 1] == \[Nu]*Subscript[a, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9#Ex21 1.9#Ex21] || [[Item:Q343|<math>p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2</math>]]<br><code>p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2</code> || <math></math> || <code>p[2] = ((nu - 1)* | | [https://dlmf.nist.gov/1.9#Ex21 1.9#Ex21] || [[Item:Q343|<math>p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2</math>]]<br><code>p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2</code> || <math></math> || <code>p[2] = nu*((nu - 1)*(a[1])^(2)+ 2*a[2])/2</code> || <code>Subscript[p, 2] == \[Nu]*((\[Nu]- 1)*(Subscript[a, 1])^(2)+ 2*Subscript[a, 2])/2</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.9.E63 1.9.E63] || [[Item:Q345|<math>f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}</math>]]<br><code>f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}</code> || <math>\abs{z-z_{0}} < R</math> || <code>(f(z))^(m) = sum(pochhammer(n + 1, m)*a[n + m]*(z - z[0])^(n), n = 0..infinity)</code> || <code>(f[z])^(m) == Sum[Pochhammer[n + 1, m]*Subscript[a, n + m]*(z - Subscript[z, 0])^(n), {n, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out | | [https://dlmf.nist.gov/1.9.E63 1.9.E63] || [[Item:Q345|<math>f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}</math>]]<br><code>f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}</code> || <math>\abs{z-z_{0}} < R</math> || <code>(f(z))^(m) = sum(pochhammer(n + 1, m)*a[n + m]*(z - z[0])^(n), n = 0..infinity)</code> || <code>(f[z])^(m) == Sum[Pochhammer[n + 1, m]*Subscript[a, n + m]*(z - Subscript[z, 0])^(n), {n, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out | ||
| Line 267: | Line 267: | ||
| [https://dlmf.nist.gov/1.10.E20 1.10.E20] || [[Item:Q375|<math>|\ln@{1+a_{n}(z)}| \leq M_{n}</math>]]<br><code>|\ln@{1+a_{n}(z)}| \leq M_{n}</code> || <math>n \geq N</math> || <code>abs(ln(1 + a[n](z))) <= M[n]</code> || <code>Abs[Log[1 + Subscript[a, n][z]]] <= Subscript[M, n]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [126 / 300]<div class="mw-collapsible-content"><code>126/300]: [[.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>1.465287519 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><code>{LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div> | | [https://dlmf.nist.gov/1.10.E20 1.10.E20] || [[Item:Q375|<math>|\ln@{1+a_{n}(z)}| \leq M_{n}</math>]]<br><code>|\ln@{1+a_{n}(z)}| \leq M_{n}</code> || <math>n \geq N</math> || <code>abs(ln(1 + a[n](z))) <= M[n]</code> || <code>Abs[Log[1 + Subscript[a, n][z]]] <= Subscript[M, n]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [126 / 300]<div class="mw-collapsible-content"><code>126/300]: [[.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>1.465287519 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><code>{LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.10.E21 1.10.E21] || [[Item:Q376|<math>\sum^{\infty}_{n=1}M_{n} < \infty</math>]]<br><code>\sum^{\infty}_{n=1}M_{n} < \infty</code> || <math></math> || <code>sum(M[n] , n = 1..infinity) | | [https://dlmf.nist.gov/1.10.E21 1.10.E21] || [[Item:Q376|<math>\sum^{\infty}_{n=1}M_{n} < \infty</math>]]<br><code>\sum^{\infty}_{n=1}M_{n} < \infty</code> || <math></math> || <code>sum(M[n](<)*infinity, n = 1..infinity)</code> || <code>Sum[Subscript[M, n][<]*Infinity, {n, 1, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.10.E22 1.10.E22] || [[Item:Q377|<math>P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}</math>]]<br><code>P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}</code> || <math></math> || <code>P(z) = product((1 -(z)/(z[n]))*exp(z/z[n]), n = 1..infinity)</code> || <code>P[z] == Product[(1 -Divide[z,Subscript[z, n]])*Exp[z/Subscript[z, n]], {n, 1, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.10.E22 1.10.E22] || [[Item:Q377|<math>P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}</math>]]<br><code>P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}</code> || <math></math> || <code>P(z) = product((1 -(z)/(z[n]))*exp(z/z[n]), n = 1..infinity)</code> || <code>P[z] == Product[(1 -Divide[z,Subscript[z, n]])*Exp[z/Subscript[z, n]], {n, 1, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
| Line 375: | Line 375: | ||
| [https://dlmf.nist.gov/1.15.E10 1.15.E10] || [[Item:Q552|<math>\sum^{\infty}_{n=0}a_{n} = s</math>]]<br><code>\sum^{\infty}_{n=0}a_{n} = s</code> || <math></math> || <code>sum(a[n], n = 0..infinity) = s</code> || <code>Sum[Subscript[a, n], {n, 0, Infinity}, GenerateConditions->None] == s</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.15.E10 1.15.E10] || [[Item:Q552|<math>\sum^{\infty}_{n=0}a_{n} = s</math>]]<br><code>\sum^{\infty}_{n=0}a_{n} = s</code> || <math></math> || <code>sum(a[n], n = 0..infinity) = s</code> || <code>Sum[Subscript[a, n], {n, 0, Infinity}, GenerateConditions->None] == s</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.15.E13 1.15.E13] || [[Item:Q555|<math>\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(P | | [https://dlmf.nist.gov/1.15.E13 1.15.E13] || [[Item:Q555|<math>\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(P(r , theta), theta = 0..2*Pi) = 1</code> || <code>Divide[1,2*Pi]*Integrate[P[r , \[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1</code> || Successful || Aborted || - || Successful [Tested: 1] | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.15.E16 1.15.E16] || [[Item:Q558|<math>\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(K[n](theta), theta = 0..2*Pi) = 1</code> || <code>Divide[1,2*Pi]*Integrate[Subscript[K, n][\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1</code> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | | [https://dlmf.nist.gov/1.15.E16 1.15.E16] || [[Item:Q558|<math>\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(K[n](theta), theta = 0..2*Pi) = 1</code> || <code>Divide[1,2*Pi]*Integrate[Subscript[K, n][\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1</code> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.15.E34 1.15.E34] || [[Item:Q576|<math>\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(P | | [https://dlmf.nist.gov/1.15.E34 1.15.E34] || [[Item:Q576|<math>\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(P(x , y), x = - infinity..infinity) = 1</code> || <code>Divide[1,2*Pi]*Integrate[P[x , y], {x, - Infinity, Infinity}, GenerateConditions->None] == 1</code> || Successful || Successful || - || Successful [Tested: 3] | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.15.E39 1.15.E39] || [[Item:Q581|<math>\Phi(z) = \Phi(x+iy)</math>]]<br><code>\Phi(z) = \Phi(x+iy)</code> || <math></math> || <code>Phi*((x + y*I)) = Phi*(x + I*y)</code> || <code>\[CapitalPhi]*((x + y*I)) == \[CapitalPhi]*(x + I*y)</code> || Successful || Successful || - || Successful [Tested: 180] | | [https://dlmf.nist.gov/1.15.E39 1.15.E39] || [[Item:Q581|<math>\Phi(z) = \Phi(x+iy)</math>]]<br><code>\Phi(z) = \Phi(x+iy)</code> || <math></math> || <code>Phi*((x + y*I)) = Phi*(x + I*y)</code> || <code>\[CapitalPhi]*((x + y*I)) == \[CapitalPhi]*(x + I*y)</code> || Successful || Successful || - || Successful [Tested: 180] | ||
| Line 413: | Line 413: | ||
| [https://dlmf.nist.gov/1.16.E23 1.16.E23] || [[Item:Q623|<math>(-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x</math>]]<br><code>(-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x</code> || <math></math> || <code>(- 1)^(n)* factorial(n)*(x[+])^(- 1 - n) = (D)^(n + 1)* [+]ln()*x</code> || <code>(- 1)^(n)* (n)!*(Subscript[x, +])^(- 1 - n) == Subscript[(D)^(n + 1)* , +]Log[]*x</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.16.E23 1.16.E23] || [[Item:Q623|<math>(-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x</math>]]<br><code>(-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x</code> || <math></math> || <code>(- 1)^(n)* factorial(n)*(x[+])^(- 1 - n) = (D)^(n + 1)* [+]ln()*x</code> || <code>(- 1)^(n)* (n)!*(Subscript[x, +])^(- 1 - n) == Subscript[(D)^(n + 1)* , +]Log[]*x</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.16.E24 1.16.E24] || [[Item:Q624|<math>|x^{N}\phi_{n}^{(k)}| \leq c_{k,N}</math>]]<br><code>|x^{N}\phi_{n}^{(k)}| \leq c_{k,N}</code> || <math></math> || <code>abs((x)^(N)* | | [https://dlmf.nist.gov/1.16.E24 1.16.E24] || [[Item:Q624|<math>|x^{N}\phi_{n}^{(k)}| \leq c_{k,N}</math>]]<br><code>|x^{N}\phi_{n}^{(k)}| \leq c_{k,N}</code> || <math></math> || <code>abs((x)^(N)* (phi[n])^(k)) <= c[k , N]</code> || <code>Abs[(x)^(N)* (Subscript[\[Phi], n])^(k)] <= Subscript[c, k , N]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.16.E28 1.16.E28] || [[Item:Q628|<math>|x^{m}\phi^{(k)}(x)| \leq c_{m,k}</math>]]<br><code>|x^{m}\phi^{(k)}(x)| \leq c_{m,k}</code> || <math></math> || <code>abs((x)^(m)* (phi(x)*)^(k)) <= c[m , k]</code> || <code>Abs[(x)^(m)* (\[Phi][x]*)^(k)] <= Subscript[c, m , k]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | | [https://dlmf.nist.gov/1.16.E28 1.16.E28] || [[Item:Q628|<math>|x^{m}\phi^{(k)}(x)| \leq c_{m,k}</math>]]<br><code>|x^{m}\phi^{(k)}(x)| \leq c_{m,k}</code> || <math></math> || <code>abs((x)^(m)* (phi(x)*)^(k)) <= c[m , k]</code> || <code>Abs[(x)^(m)* (\[Phi][x]*)^(k)] <= Subscript[c, m , k]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
Revision as of 12:19, 17 May 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}}
\binom{n}{k} = \frac{n!}{(n-k)!k!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k)) |
Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!] |
Successful | Successful | - | Successful [Tested: 9] |
| 1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{n!}{(n-k)!k!} = \binom{n}{n-k}}
\frac{n!}{(n-k)!k!} = \binom{n}{n-k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k) |
Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k] |
Successful | Successful | - | Successful [Tested: 9] |
| 1.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}}
\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | ((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k) |
Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k] |
Successful | Successful | - | Successful [Tested: 21] |
| 1.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}}
\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1) |
Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1] |
Successful | Successful | - | Successful [Tested: 21] |
| 1.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}}
\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m) |
Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m] |
Successful | Successful | - | Successful [Tested: 21] |
| 1.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)}
na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell) |
n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.2.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(r) = 0}
M(r) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | M(r) = 0 |
M[r] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(1) = A}
M(1) = A |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | M(1) = A |
M[1] == A |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(-1) = H}
M(-1) = H |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | M(- 1) = H |
M[- 1] == H |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.2.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{r\to 0}M(r) = G}
\lim_{r\to 0}M(r) = G |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit(M(r), r = 0) = G |
Limit[M[r], r -> 0, GenerateConditions->None] == G |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(2)}(x) = \deriv[2]{f}{x}}
f^{(2)}(x) = \deriv[2]{f}{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (f(x))^(2) = diff(f, [x$(2)]) |
(f[x])^(2) == D[f, {x, 2}] |
Failure | Failure | Failed [30 / 30] 30/30]: [[.7500000006+1.299038106*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5}.2500000002+.4330127020*I <- {f = 1/2*3^(1/2)+1/2*I, x = .5}1.000000001+1.732050808*I <- {f = 1/2*3^(1/2)+1/2*I, x = 2}-.7500000006-1.299038106*I <- {f = -1/2+1/2*I*3^(1/2), x = 1.5}... skip entries to safe data |
Failed [30 / 30]
{Complex[0.7500000000000002, 1.299038105676658] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}Complex[0.25000000000000006, 0.4330127018922193] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]} |
| 1.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)}
\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(f, [x$(2)]) = diff(diff(f, x), x) |
D[f, {x, 2}] == D[D[f, x], x] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 30] |
| 1.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)}
f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (f(x))^(n) = diff((f(x))^(n - 1), x) |
(f[x])^(n) == D[(f[x])^(n - 1), x] |
Failure | Failure | Failed [84 / 90] 84/90]: [[.299038106+.7500000000*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 1}-.1160254034+.7990381060*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 2}-.4999999999+.6339745980*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 3}-.5669872980+.2500000000*I <- {f = 1/2*3^(1/2)+1/2*I, x = .5, n = 1}... skip entries to safe data |
Failed [84 / 90]
{Complex[0.299038105676658, 0.7499999999999999] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}Complex[-0.11602540378443849, 0.799038105676658] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]} |
| 1.4.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}}
\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | int(f*g, x) = (int(f, x))*g - int((int(f, x))*diff(g, x), x) |
Integrate[f*g, x, GenerateConditions->None] == (Integrate[f, x, GenerateConditions->None])*g - Integrate[(Integrate[f, x, GenerateConditions->None])*D[g, x], x, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 100] |
| 1.4.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{n} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}}
R_{n} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a < c, c < x} | R[n] = ((f(c))^(n + 1))/(factorial(n + 1))*(x - a)^(n + 1) |
Subscript[R, n] == Divide[(f[c])^(n + 1),(n + 1)!]*(x - a)^(n + 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.4.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t}}
R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | R[n] = (1)/(factorial(n))*int((x - t)^(n)* (f(t))^(n + 1), t = a..x) |
Subscript[R, n] == Divide[1,(n)!]*Integrate[(x - t)^(n)* (f[t])^(n + 1), {t, a, x}, GenerateConditions->None] |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.991025404+2.448557159*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 1}.8660254040+3.875000000*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 2}-.6527245960+3.130552164*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 3}.6250000000+2.814582563*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [300 / 300]
{Complex[1.9910254037844388, 2.4485571585149866] <- {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.8660254037844387, 3.875] <- {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 1.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{y} = D_{y}f}
\pderiv{f}{y} = D_{y}f |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(f, y) = D[y]*f |
D[f, y] == Subscript[D, y]*f |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.5000000004-.8660254040*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I}.8660254040-.5000000004*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2+1/2*I*3^(1/2)}-.8660254040+.5000000004*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2-1/2*I*3^(1/2)}.5000000004+.8660254040*I <- {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]
{Complex[-0.5000000000000001, -0.8660254037844386] <- {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]]]}Complex[0.8660254037844387, -0.49999999999999994] <- {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]]]} |
| 1.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{y}f = f_{y}}
D_{y}f = f_{y} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | D[y]*f = f[y] |
Subscript[D, y]*f == Subscript[f, y] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.3660254036+.3660254040*I <- {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}1.000000000+0.*I <- {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)}.4e-9+1.732050808*I <- {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)}1.366025404+1.366025404*I <- {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]
{Complex[-0.3660254037844386, 0.36602540378443865] <- {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]]]}Complex[0.9999999999999999, -1.1102230246251565*^-16] <- {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]]]} |
| 1.5#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\phi}}
x = r\cos@@{\phi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x = r*cos(phi) |
x == r*Cos[\[Phi]] |
Failure | Failure | Failed [180 / 180] 180/180]: [[2.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}1.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}3.095814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 2}.404185472+.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = 1.5, x = 1.5}... skip entries to safe data |
Failed [180 / 180]
{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.5#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\phi}}
y = r\sin@@{\phi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | y = r*sin(phi) |
y == r*Sin[\[Phi]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.211529498+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}2.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -.5}1.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = .5}... skip entries to safe data |
Failed [300 / 300]
{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.5.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\phi}}
x = r\cos@@{\phi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x = r*cos(phi) |
x == r*Cos[\[Phi]] |
Failure | Failure | Failed [180 / 180] 180/180]: [[2.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}1.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}3.095814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 2}.404185472+.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = 1.5, x = 1.5}... skip entries to safe data |
Failed [180 / 180]
{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.5#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\phi}}
y = r\sin@@{\phi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | y = r*sin(phi) |
y == r*Sin[\[Phi]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.211529498+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}2.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -.5}1.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = .5}... skip entries to safe data |
Failed [300 / 300]
{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.5#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = z}
z = z |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z = z |
z == z |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \rho\sin@@{\theta}\cos@@{\phi}}
x = \rho\sin@@{\theta}\cos@@{\phi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x = rho*sin(theta)*cos(phi) |
x == \[Rho]*Sin[\[Theta]]*Cos[\[Phi]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.7933233780-.2990618885*I <- {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}-.2066766220-.2990618885*I <- {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}1.293323378-.2990618885*I <- {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}2.075937432-.6992275886*I <- {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]
{Complex[0.7933233783531031, -0.29906188871772155] <- {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]]]}Complex[1.1325168401075085, -1.15603698835011] <- {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]]]} |
| 1.5#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \rho\sin@@{\theta}\sin@@{\phi}}
y = \rho\sin@@{\theta}\sin@@{\phi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | y = rho*sin(theta)*sin(phi) |
y == \[Rho]*Sin[\[Theta]]*Sin[\[Phi]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.750303606-.8142131232*I <- {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}1.249696394-.8142131232*I <- {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}-.7503036064-.8142131232*I <- {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}.2496963936-.8142131232*I <- {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]
{Complex[-1.750303605777159, -0.8142131229438421] <- {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]]]}Complex[-0.49444885508381575, -0.009630141394747549] <- {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]]]} |
| 1.5#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \rho\cos@@{\theta}}
z = \rho\cos@@{\theta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z = rho*cos(theta) |
z == \[Rho]*Cos[\[Theta]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.348818158e-1+.4784968852*I <- {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}-1.331143588+.8445222892*I <- {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)}-.3311435882-.8875285188*I <- {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)}-1.697168992-.5215031148*I <- {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]
{Complex[0.03488181560898618, 0.4784968849905366] <- {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]]]}Complex[0.8875285187939019, -0.3311435881754526] <- {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]]]} |
| 1.5.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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)}
\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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{x} = \pderiv{f}{y}}
\pderiv{f}{x} = \pderiv{f}{y} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(f, x) = diff(f, y) |
D[f, x] == D[f, y] |
Successful | Successful | - | Successful [Tested: 180] |
| 1.5.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon}
\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = x_{0}}
a = x_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a = x[0] |
a == Subscript[x, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = y_{0}}
c = y_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | c = y[0] |
c == Subscript[y, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \leq x}
a \leq x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a <= x |
a <= x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi_{1}(x) \leq y}
\phi_{1}(x) \leq y |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | phi[1](x) <= y |
Subscript[\[Phi], 1][x] <= y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c \leq y}
c \leq y |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | c <= y |
c <= y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi_{1}(y) \leq x}
\psi_{1}(y) \leq x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | psi[1](y) <= x |
Subscript[\[Psi], 1][y] <= x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \leq x}
a \leq x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a <= x |
a <= x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi_{1}(x) \leq y}
\phi_{1}(x) \leq y |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | phi[1](x) <= y |
Subscript[\[Phi], 1][x] <= y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.5#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi_{1}(x,y) \leq z}
\psi_{1}(x,y) \leq z |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | psi[1](x , y) <= (x + y*I) |
Subscript[\[Psi], 1][x , y] <= (x + y*I) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{a} = (a_{1},a_{2},a_{3})}
\mathbf{a} = (a_{1},a_{2},a_{3}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a = (a[1], a[2], a[3]) |
a == (Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{b} = (b_{1},b_{2},b_{3})}
\mathbf{b} = (b_{1},b_{2},b_{3}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b = (b[1], b[2], b[3]) |
b == (Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{a}\cdot\mathbf{b} = a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}}
\mathbf{a}\cdot\mathbf{b} = a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a * b = a[1]*b[1]+ a[2]*b[2]+ a[3]*b[3] |
a * b == Subscript[a, 1]*Subscript[b, 1]+ Subscript[a, 2]*Subscript[b, 2]+ Subscript[a, 3]*Subscript[b, 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\mathbf{a}\| = \sqrt{\mathbf{a}\cdot\mathbf{a}}}
\|\mathbf{a}\| = \sqrt{\mathbf{a}\cdot\mathbf{a}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error |
Norm[a] == Sqrt[a * a] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\theta} = \frac{\mathbf{a}\cdot\mathbf{b}}{\|\mathbf{a}\|\;\|\mathbf{b}\|}}
\cos@@{\theta} = \frac{\mathbf{a}\cdot\mathbf{b}}{\|\mathbf{a}\|\;\|\mathbf{b}\|} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error |
Cos[\[Theta]] == Divide[a * b,Norm[a]*Norm[b]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.2694569811-.3969495503*I <- {a = -1.5, b = -1.5, theta = 1/2*3^(1/2)+1/2*I}.227765517+.4690753764*I <- {a = -1.5, b = -1.5, theta = -1/2+1/2*I*3^(1/2)}.227765517+.4690753764*I <- {a = -1.5, b = -1.5, theta = 1/2-1/2*I*3^(1/2)}-.2694569811-.3969495503*I <- {a = -1.5, b = -1.5, theta = -1/2*3^(1/2)-1/2*I}... skip entries to safe data |
Failed [300 / 300]
{Complex[-0.2694569809427748, -0.3969495502290325] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.2277655168641104, 0.46907537626850365] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{a} = a_{1}\mathbf{i}+a_{2}\mathbf{j}+a_{3}\mathbf{k}}
\mathbf{a} = a_{1}\mathbf{i}+a_{2}\mathbf{j}+a_{3}\mathbf{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a = a[1]*I + a[2]*j + a[3]*k |
a == Subscript[a, 1]*I + Subscript[a, 2]*j + Subscript[a, 3]*k |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{i}\times\mathbf{j} = \mathbf{k}}
\mathbf{i}\times\mathbf{j} = \mathbf{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | I * j = k |
I * j == k |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{j}\times\mathbf{k} = \mathbf{i}}
\mathbf{j}\times\mathbf{k} = \mathbf{i} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | j * k = I |
j * k == I |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{k}\times\mathbf{i} = \mathbf{j}}
\mathbf{k}\times\mathbf{i} = \mathbf{j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | k * I = j |
k * I == j |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{j}\times\mathbf{i} = -\mathbf{k}}
\mathbf{j}\times\mathbf{i} = -\mathbf{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | j * I = - k |
j * I == - k |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{k}\times\mathbf{j} = -\mathbf{i}}
\mathbf{k}\times\mathbf{j} = -\mathbf{i} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | k * j = - I |
k * j == - I |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{i}\times\mathbf{k} = -\mathbf{j}}
\mathbf{i}\times\mathbf{k} = -\mathbf{j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | I * k = - j |
I * k == - j |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{j}b_{j} = \sum_{j=1}^{3}a_{j}b_{j}}
a_{j}b_{j} = \sum_{j=1}^{3}a_{j}b_{j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[j]*b[j] = sum(a[j]*b[j], j = 1..3) |
Subscript[a, j]*Subscript[b, j] == Sum[Subscript[a, j]*Subscript[b, j], {j, 1, 3}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2}}
\LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | LeviCivita[1, 2, 3] = LeviCivita[3, 1, 2] |
Part[LeviCivitaTensor[3,List], 1, 2, 3] == Part[LeviCivitaTensor[3,List], 3, 1, 2] |
Successful | Successful | - | Successful [Tested: 1] |
| 1.6#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{3}{1}{2} = 1}
\LeviCivitasym{3}{1}{2} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | LeviCivita[3, 1, 2] = 1 |
Part[LeviCivitaTensor[3,List], 3, 1, 2] == 1 |
Successful | Successful | - | Successful [Tested: 1] |
| 1.6#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1}}
\LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | LeviCivita[2, 1, 3] = LeviCivita[3, 2, 1] |
Part[LeviCivitaTensor[3,List], 2, 1, 3] == Part[LeviCivitaTensor[3,List], 3, 2, 1] |
Successful | Successful | - | Successful [Tested: 1] |
| 1.6#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{3}{2}{1} = -1}
\LeviCivitasym{3}{2}{1} = -1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | LeviCivita[3, 2, 1] = - 1 |
Part[LeviCivitaTensor[3,List], 3, 2, 1] == - 1 |
Successful | Successful | - | Successful [Tested: 1] |
| 1.6#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{2}{2}{1} = 0}
\LeviCivitasym{2}{2}{1} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | LeviCivita[2, 2, 1] = 0 |
Part[LeviCivitaTensor[3,List], 2, 2, 1] == 0 |
Successful | Successful | - | Successful [Tested: 1] |
| 1.6.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m}}
\LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | LeviCivita[j, k, ell]*LeviCivita[ell, m, n] = KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m] |
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] |
Failure | Failure | Error | Error |
| 1.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{e}_{j}\times\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}\mathbf{e}_{\ell}}
\mathbf{e}_{j}\times\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}\mathbf{e}_{\ell} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | exp(1)[j] * exp(1)[k] = LeviCivita[j, k, ell]*exp(1)[ell] |
Subscript[E, j] * Subscript[E, k] == Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Subscript[E, \[ScriptL]] |
Translation Error | Translation Error | - | - |
| 1.6.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}}
a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[j]*exp(1)[j] * b[k]*exp(1)[k] = LeviCivita[j, k, ell]*a[j]*b[k]*exp(1)[ell] |
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]] |
Translation Error | Translation Error | - | - |
| 1.6.E43 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}}
\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | F(x , y) = F[1](x , y)* I + F[2](x , y)* j |
F[x , y] == Subscript[F, 1][x , y]* I + Subscript[F, 2][x , y]* j |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.6.E46 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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])*k |
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])*k |
Failure | Failure | Failed [300 / 300] 300/300]: [[.8660254040+.5000000000*I <- {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}.8660254040+.5000000000*I <- {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}.8660254040+.5000000000*I <- {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}.8660254040+.5000000000*I <- {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}... skip entries to safe data |
- |
| 1.6.E47 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}
\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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])*k |
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])*k |
Failure | Failure | Failed [300 / 300] 300/300]: [[.8660254040+.5000000000*I <- {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}.8660254040+.5000000000*I <- {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}.8660254040+.5000000000*I <- {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}.8660254040+.5000000000*I <- {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}... skip entries to safe data |
Error |
| 1.6.E49 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\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}}}
\|\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}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error |
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)] |
Translation Error | Translation Error | - | - |
| 1.6.E50 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}}
\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error |
Norm[Subscript[T, \[Theta]] * Subscript[T, \[Phi]]] == \[Rho]^(2)* Abs[Sin[\[Theta]]] |
Translation Error | Translation Error | - | - |
| 1.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)}
\left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (sum(a[j]*b[j], j = 1..n))^(2) <= (sum((a[j])^(2), j = 1..n))*(sum((b[j])^(2), j = 1..n)) |
((Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None]))^(2) <= (Sum[(Subscript[a, j])^(2), {j, 1, n}, GenerateConditions->None])*(Sum[(Subscript[b, j])^(2), {j, 1, n}, GenerateConditions->None]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}}
\sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(a[j]*b[j], j = 1..n) <= (sum((a[j])^(p), j = 1..n))^(1/p)*(sum((b[j])^(q), j = 1..n))^(1/q) |
Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None] <= ((Sum[(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)*((Sum[(Subscript[b, j])^(q), {j, 1, n}, GenerateConditions->None]))^(1/q) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}}
\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (sum((a[j]+ b[j])^(p), j = 1..n))^(1/p) <= (sum((a[j])^(p), j = 1..n))^(1/p)+(sum((b[j])^(p), j = 1..n))^(1/p) |
((Sum[(Subscript[a, j]+ Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p) <= ((Sum[(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)+((Sum[(Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle H \leq G}
H \leq G |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | H <= G |
H <= G |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.7.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(r) \leq M(s)}
M(r) \leq M(s) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r < s} | M(r) <= M(s) |
M[r] <= M[s] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}}
\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{\omega} > 0} | sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity) = sqrt((Pi)/(omega))*(1 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/omega)*cos(2*n*Pi*x), n = 1..infinity)) |
Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/\[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}, GenerateConditions->None]) |
Failure | Successful | Successful [Tested: 15] | Successful [Tested: 15] |
| 1.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x+iy}
z = x+iy |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (x + y*I) = x + I*y |
(x + y*I) == x + I*y |
Successful | Successful | - | Successful [Tested: 1] |
| 1.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{z} = x}
\realpart@@{z} = x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Re(x + y*I) = x |
Re[x + y*I] == x |
Failure | Failure | Successful [Tested: 18] | Successful [Tested: 18] |
| 1.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@{z} = y}
\imagpart@@{z} = y |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Im(x + y*I) = y |
Im[x + y*I] == y |
Failure | Failure | Successful [Tested: 18] | Successful [Tested: 18] |
| 1.9#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\theta}}
x = r\cos@@{\theta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x = r*cos(theta) |
x == r*Cos[\[Theta]] |
Failure | Failure | Failed [180 / 180] 180/180]: [[2.595814528-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = 1.5}1.595814528-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = .5}3.095814528-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = 2}3.341648276+.7036130646*I <- {r = -1.5, theta = -1/2+1/2*I*3^(1/2), x = 1.5}... skip entries to safe data |
Failed [180 / 180]
{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\theta}}
y = r\sin@@{\theta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | y = r*sin(theta) |
y == r*Sin[\[Theta]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.211529498+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = -1.5}2.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = 1.5}.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = -.5}1.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = .5}... skip entries to safe data |
Failed [300 / 300]
{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = (x^{2}+y^{2})^{1/2}}
r = (x^{2}+y^{2})^{1/2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | r = ((x)^(2)+ (y)^(2))^(1/2) |
r == ((x)^(2)+ (y)^(2))^(1/2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \omega = \atan@{|y/x|}\in\left[0,\tfrac{1}{2}\pi\right]}
\omega = \atan@{|y/x|}\in\left[0,\tfrac{1}{2}\pi\right] |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | omega 0 <= arctan(abs(y/x)) <= (1)/(2)*Pi |
\[Omega] 0 <= ArcTan[Abs[y/x]] <= Divide[1,2]*Pi |
Error | Failure | - | Failed [180 / 180]
{Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[-1.0, True]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.4999999999999998, 0.8660254037844387], Times[-1.0, True]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| = r}
|z| = r |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(z) = r |
Abs[z] == r |
Failure | Failure | Failed [39 / 42] 39/42]: [[2.5 <- {r = -1.5, z = 1/2*3^(1/2)+1/2*I}2.5 <- {r = -1.5, z = -1/2+1/2*I*3^(1/2)}2.5 <- {r = -1.5, z = 1/2-1/2*I*3^(1/2)}2.5 <- {r = -1.5, z = -1/2*3^(1/2)-1/2*I}... skip entries to safe data |
Failed [39 / 42]
{2.5 <- {Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}2.5 <- {Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{z} = \theta+2n\pi}
\phase@@{z} = \theta+2n\pi |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | argument(z) = theta + 2*n*Pi |
Arg[z] == \[Theta]+ 2*n*Pi |
Error | Failure | - | Failed [70 / 70]
{Complex[-19.191982549724898, -0.49999999999999994] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-17.82595714594046, -0.8660254037844387] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\realpart@@{z}| \leq |z|}
|\realpart@@{z}| \leq |z| |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(Re(z)) <= abs(z) |
Abs[Re[z]] <= Abs[z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 1.9#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\imagpart@@{z}| \leq |z|}
|\imagpart@@{z}| \leq |z| |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(Im(z)) <= abs(z) |
Abs[Im[z]] <= Abs[z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 1.9.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = re^{i\theta}}
z = re^{i\theta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z = r*exp(I*theta) |
z == r*Exp[I*\[Theta]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{i\theta} = \cos@@{\theta}+i\sin@@{\theta}}
e^{i\theta} = \cos@@{\theta}+i\sin@@{\theta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | exp(I*theta) = cos(theta)+ I*sin(theta) |
Exp[I*\[Theta]] == Cos[\[Theta]]+ I*Sin[\[Theta]] |
Successful | Successful | - | Successful [Tested: 10] |
| 1.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \conj{z} = x-iy}
\conj{z} = x-iy |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | conjugate(x + y*I) = x - I*y |
Conjugate[x + y*I] == x - I*y |
Failure | Failure | Successful [Tested: 18] | Successful [Tested: 18] |
| 1.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\conj{z}| = |z|}
|\conj{z}| = |z| |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(conjugate(z)) = abs(z) |
Abs[Conjugate[z]] == Abs[z] |
Successful | Successful | - | Successful [Tested: 7] |
| 1.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{\conj{z}} = -\phase@@{z}}
\phase@@{\conj{z}} = -\phase@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | argument(conjugate(z)) = - argument(z) |
Arg[Conjugate[z]] == - Arg[z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 1.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}+ z_{2} = x_{1}+ x_{2}+\iunit(y_{1}+ y_{2})}
z_{1}+ z_{2} = x_{1}+ x_{2}+\iunit(y_{1}+ y_{2}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x + y*I[1]+x + y*I[2] = x[1]+ x[2]+ I*(y[1]+ y[2]) |
Subscript[x + y*I, 1]+Subscript[x + y*I, 2] == Subscript[x, 1]+ Subscript[x, 2]+ I*(Subscript[y, 1]+ Subscript[y, 2]) |
Failure | Failure | Error | Failed [300 / 300]
{Plus[Complex[-0.7320508075688775, -2.732050807568877], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.3660254037844388, -1.3660254037844388], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}- z_{2} = x_{1}- x_{2}+\iunit(y_{1}- y_{2})}
z_{1}- z_{2} = x_{1}- x_{2}+\iunit(y_{1}- y_{2}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x + y*I[1]-x + y*I[2] = x[1]- x[2]+ I*(y[1]- y[2]) |
Subscript[x + y*I, 1]-Subscript[x + y*I, 2] == Subscript[x, 1]- Subscript[x, 2]+ I*(Subscript[y, 1]- Subscript[y, 2]) |
Failure | Failure | Error | Failed [300 / 300]
{Plus[Subscript[Complex[1.5, -1.5], 1], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.36602540378443876, -1.3660254037844384], Subscript[Complex[1.5, -1.5], 1], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}z_{2} = x_{1}x_{2}-y_{1}y_{2}+i(x_{1}y_{2}+x_{2}y_{1})}
z_{1}z_{2} = x_{1}x_{2}-y_{1}y_{2}+i(x_{1}y_{2}+x_{2}y_{1}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x + y*I[1]*x + y*I[2] = x[1]*x[2]- y[1]*y[2]+ I*(x[1]*y[2]+ x[2]*y[1]) |
Subscript[x + y*I, 1]*Subscript[x + y*I, 2] == Subscript[x, 1]*Subscript[x, 2]- Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 1]*Subscript[y, 2]+ Subscript[x, 2]*Subscript[y, 1]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}}
\frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (z[1])/(z[2]) = (z[1]*conjugate(z)[2])/((abs(z[2]))^(2)) |
Divide[Subscript[z, 1],Subscript[z, 2]] == Divide[Subscript[z, 1]*Subscript[Conjugate[z], 2],(Abs[Subscript[z, 2]])^(2)] |
Failure | Failure | Error | Failed [300 / 300]
{Plus[1.0, Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, -1.0], Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}}
\frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (x + y*I[1]*conjugate(x + y*I)[2])/((abs(x + y*I[2]))^(2)) = (x[1]*x[2]+ y[1]*y[2]+ I*(x[2]*y[1]- x[1]*y[2]))/((x[2])^(2)+ (y[2])^(2)) |
Divide[Subscript[x + y*I, 1]*Subscript[Conjugate[x + y*I], 2],(Abs[Subscript[x + y*I, 2]])^(2)] == Divide[Subscript[x, 1]*Subscript[x, 2]+ Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 2]*Subscript[y, 1]- Subscript[x, 1]*Subscript[y, 2]),(Subscript[x, 2])^(2)+ (Subscript[y, 2])^(2)] |
Failure | Failure | Error | Failed [300 / 300]
{DirectedInfinity[] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.6666666666666669, -0.6666666666666667], Times[Power[Abs[Subscript[Complex[1.5, -1.5], 2]], -2], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, 1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z_{1}z_{2}| = |z_{1}|\;|z_{2}|}
|z_{1}z_{2}| = |z_{1}|\;|z_{2}| |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(z[1]*z[2]) = abs(z[1])*abs(z[2]) |
Abs[Subscript[z, 1]*Subscript[z, 2]] == Abs[Subscript[z, 1]]*Abs[Subscript[z, 2]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@{z_{1}z_{2}} = \phase@@{z_{1}}+\phase@@{z_{2}}}
\phase@{z_{1}z_{2}} = \phase@@{z_{1}}+\phase@@{z_{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | argument(z[1]*z[2]) = argument(z[1])+ argument(z[2]) |
Arg[Subscript[z, 1]*Subscript[z, 2]] == Arg[Subscript[z, 1]]+ Arg[Subscript[z, 2]] |
Failure | Failure | Failed [25 / 100] 25/100]: [[-6.283185308 <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = -1.5}-6.283185308 <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = -.5}-6.283185308 <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = -2}-6.283185309 <- {z[1] = -1/2+1/2*I*3^(1/2), z[2] = -1/2+1/2*I*3^(1/2)}... skip entries to safe data |
Failed [25 / 100]
{-6.283185307179587 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], -1.5]}-6.283185307179587 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], -0.5]} |
| 1.9.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\frac{z_{1}}{z_{2}}} = \frac{|z_{1}|}{|z_{2}|}}
\abs{\frac{z_{1}}{z_{2}}} = \frac{|z_{1}|}{|z_{2}|} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs((z[1])/(z[2])) = (abs(z[1]))/(abs(z[2])) |
Abs[Divide[Subscript[z, 1],Subscript[z, 2]]] == Divide[Abs[Subscript[z, 1]],Abs[Subscript[z, 2]]] |
Successful | Successful | - | Successful [Tested: 100] |
| 1.9.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{\frac{z_{1}}{z_{2}}} = \phase@@{z_{1}}-\phase@@{z_{2}}}
\phase@@{\frac{z_{1}}{z_{2}}} = \phase@@{z_{1}}-\phase@@{z_{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | argument((z[1])/(z[2])) = argument(z[1])- argument(z[2]) |
Arg[Divide[Subscript[z, 1],Subscript[z, 2]]] == Arg[Subscript[z, 1]]- Arg[Subscript[z, 2]] |
Failure | Failure | Failed [25 / 100] 25/100]: [[-6.283185308 <- {z[1] = -1/2+1/2*I*3^(1/2), z[2] = -1/2*3^(1/2)-1/2*I}6.283185308 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -1/2+1/2*I*3^(1/2)}6.283185307 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -1.5}6.283185307 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -.5}... skip entries to safe data |
Failed [25 / 100]
{-6.283185307179586 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}6.283185307179586 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{n\theta}+i\sin@@{n\theta} = (\cos@@{\theta}+i\sin@@{\theta})^{n}}
\cos@@{n\theta}+i\sin@@{n\theta} = (\cos@@{\theta}+i\sin@@{\theta})^{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos(n*theta)+ I*sin(n*theta) = (cos(theta)+ I*sin(theta))^(n) |
Cos[n*\[Theta]]+ I*Sin[n*\[Theta]] == (Cos[\[Theta]]+ I*Sin[\[Theta]])^(n) |
Error | Successful | - | Successful [Tested: 10] |
| 1.9.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\abs{z_{1}}-\abs{z_{2}}} \leq \abs{z_{1}+z_{2}}}
\abs{\abs{z_{1}}-\abs{z_{2}}} \leq \abs{z_{1}+z_{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(abs(z[1])- abs(z[2])) <= abs(z[1]+ z[2]) |
Abs[Abs[Subscript[z, 1]]- Abs[Subscript[z, 2]]] <= Abs[Subscript[z, 1]+ Subscript[z, 2]] |
Failure | Failure | Successful [Tested: 100] | Successful [Tested: 100] |
| 1.9.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{z_{1}+z_{2}} \leq \abs{z_{1}}+\abs{z_{2}}}
\abs{z_{1}+z_{2}} \leq \abs{z_{1}}+\abs{z_{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(z[1]+ z[2]) <= abs(z[1])+ abs(z[2]) |
Abs[Subscript[z, 1]+ Subscript[z, 2]] <= Abs[Subscript[z, 1]]+ Abs[Subscript[z, 2]] |
Failure | Failure | Successful [Tested: 100] | Successful [Tested: 100] |
| 1.9#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{u}{x} = \pderiv{v}{y}}
\pderiv{u}{x} = \pderiv{v}{y} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(u, x) = diff(v, y) |
D[u, x] == D[v, y] |
Successful | Successful | - | Successful [Tested: 300] |
| 1.9#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{u}{y} = -\pderiv{v}{x}}
\pderiv{u}{y} = -\pderiv{v}{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(u, y) = - diff(v, x) |
D[u, y] == - D[v, x] |
Successful | Successful | - | Successful [Tested: 300] |
| 1.9.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{u}{x}+\pderiv[2]{u}{y} = \pderiv[2]{v}{x}+\pderiv[2]{v}{y}}
\pderiv[2]{u}{x}+\pderiv[2]{u}{y} = \pderiv[2]{v}{x}+\pderiv[2]{v}{y} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(u, [x$(2)])+ diff(u, [y$(2)]) = diff(v, [x$(2)])+ diff(v, [y$(2)]) |
D[u, {x, 2}]+ D[u, {y, 2}] == D[v, {x, 2}]+ D[v, {y, 2}] |
Successful | Successful | - | Successful [Tested: 300] |
| 1.9.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{v}{x}+\pderiv[2]{v}{y} = 0}
\pderiv[2]{v}{x}+\pderiv[2]{v}{y} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(v, [x$(2)])+ diff(v, [y$(2)]) = 0 |
D[v, {x, 2}]+ D[v, {y, 2}] == 0 |
Successful | Successful | - | Successful [Tested: 180] |
| 1.9.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{u}{r}+\frac{1}{r}\pderiv{u}{r}+\frac{1}{r^{2}}\pderiv[2]{u}{\theta} = 0}
\pderiv[2]{u}{r}+\frac{1}{r}\pderiv{u}{r}+\frac{1}{r^{2}}\pderiv[2]{u}{\theta} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(u, [r$(2)])+(1)/(r)*diff(u, r)+(1)/((r)^(2))*diff(u, [theta$(2)]) = 0 |
D[u, {r, 2}]+Divide[1,r]*D[u, r]+Divide[1,(r)^(2)]*D[u, {\[Theta], 2}] == 0 |
Successful | Successful | - | Successful [Tested: 300] |
| 1.9.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(z) = \frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})\diff{\phi}}
u(z) = \frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})\diff{\phi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | u(z) = (1)/(2*Pi)*int(u(z + r*exp(I*phi)), phi = 0..2*Pi) |
u[z] == Divide[1,2*Pi]*Integrate[u[z + r*Exp[I*\[Phi]]], {\[Phi], 0, 2*Pi}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 300] |
| 1.9.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(re^{i\theta}) = \frac{1}{2\pi}\int^{2\pi}_{0}\frac{(R^{2}-r^{2})h(Re^{i\phi})\diff{\phi}}{R^{2}-2Rr\cos@{\phi-\theta}+r^{2}}}
u(re^{i\theta}) = \frac{1}{2\pi}\int^{2\pi}_{0}\frac{(R^{2}-r^{2})h(Re^{i\phi})\diff{\phi}}{R^{2}-2Rr\cos@{\phi-\theta}+r^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | u(r*exp(I*theta)) = (1)/(2*Pi)*int((((R)^(2)- (r)^(2))*h(R*exp(I*phi)))/((R)^(2)- 2*R*r*cos(phi - theta)+ (r)^(2)), phi = 0..2*Pi) |
u[r*Exp[I*\[Theta]]] == Divide[1,2*Pi]*Integrate[Divide[((R)^(2)- (r)^(2))*h[R*Exp[I*\[Phi]]],(R)^(2)- 2*R*r*Cos[\[Phi]- \[Theta]]+ (r)^(2)], {\[Phi], 0, 2*Pi}, GenerateConditions->None] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[-0.1639294614698989, -0.894905511379796] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.6307543640677387, -0.014887794479775784] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.9.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \infty+ z = z+\infty}
\infty+ z = z+\infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | infinity + z = z + infinity |
Infinity + z == z + Infinity |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \infty\cdot z = z\cdot\infty}
\infty\cdot z = z\cdot\infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | infinity * z = z * infinity |
Infinity * z == z * Infinity |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z/\infty = 0}
z/\infty = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z/infinity = 0 |
z/Infinity == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z/0 = \infty}
z/0 = \infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z \neq 0} | z/0 = infinity |
z/0 == Infinity |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \frac{dw-b}{-cw+a}}
z = \frac{dw-b}{-cw+a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z = (d*w - b)/(- c*w + a) |
z == Divide[d*w - b,- c*w + a] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E48 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{f^{(n)}(z_{0})}{n!}}
a_{n} = \frac{f^{(n)}(z_{0})}{n!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[n] = ((f(z[0]))^(n))/(factorial(n)) |
Subscript[a, n] == Divide[(f[Subscript[z, 0]])^(n),(n)!] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E50 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=0}(a_{n}+ b_{n})z^{n} = \sum^{\infty}_{n=0}a_{n}z^{n}+\sum^{\infty}_{n=0}b_{n}z^{n}}
\sum^{\infty}_{n=0}(a_{n}+ b_{n})z^{n} = \sum^{\infty}_{n=0}a_{n}z^{n}+\sum^{\infty}_{n=0}b_{n}z^{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum((a[n]+ b[n])*(z)^(n), n = 0..infinity) = sum(a[n]*(z)^(n), n = 0..infinity)+ sum(b[n]*(z)^(n), n = 0..infinity) |
Sum[(Subscript[a, n]+ Subscript[b, n])*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] == Sum[Subscript[a, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None]+ Sum[Subscript[b, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E51 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sum^{\infty}_{n=0}a_{n}z^{n}\right)\left(\sum^{\infty}_{n=0}b_{n}z^{n}\right) = \sum^{\infty}_{n=0}c_{n}z^{n}}
\left(\sum^{\infty}_{n=0}a_{n}z^{n}\right)\left(\sum^{\infty}_{n=0}b_{n}z^{n}\right) = \sum^{\infty}_{n=0}c_{n}z^{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (sum(a[n]*(z)^(n), n = 0..infinity))*(sum(b[n]*(z)^(n), n = 0..infinity)) = sum(c[n]*(z)^(n), n = 0..infinity) |
(Sum[Subscript[a, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None])*(Sum[Subscript[b, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None]) == Sum[Subscript[c, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E52 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{n} = \sum^{n}_{k=0}a_{k}b_{n-k}}
c_{n} = \sum^{n}_{k=0}a_{k}b_{n-k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | c[n] = sum(a[k]*b[n - k], k = 0..n) |
Subscript[c, n] == Sum[Subscript[a, k]*Subscript[b, n - k], {k, 0, n}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0} = 1/a_{0}}
b_{0} = 1/a_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b[0] = 1/a[0] |
Subscript[b, 0] == 1/Subscript[a, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = -a_{1}/a_{0}^{2}}
b_{1} = -a_{1}/a_{0}^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b[1] = - a[1]/(a[0])^(2) |
Subscript[b, 1] == - Subscript[a, 1]/(Subscript[a, 0])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3}}
b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b[2] = ((a[1])^(2)- a[0]*a[2])/(a[0])^(3) |
Subscript[b, 2] == ((Subscript[a, 1])^(2)- Subscript[a, 0]*Subscript[a, 2])/(Subscript[a, 0])^(3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{1} = a_{1}}
q_{1} = a_{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | q[1] = a[1] |
Subscript[q, 1] == Subscript[a, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{2} = (2a_{2}-a_{1}^{2})/2}
q_{2} = (2a_{2}-a_{1}^{2})/2 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | q[2] = (2*a[2]- (a[1])^(2))/2 |
Subscript[q, 2] == (2*Subscript[a, 2]- (Subscript[a, 1])^(2))/2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3}
q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | q[3] = (3*a[3]- 3*a[1]*a[2]+ (a[1])^(3))/3 |
Subscript[q, 3] == (3*Subscript[a, 3]- 3*Subscript[a, 1]*Subscript[a, 2]+ (Subscript[a, 1])^(3))/3 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{0} = 1}
p_{0} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | p[0] = 1 |
Subscript[p, 0] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{1} = \nu a_{1}}
p_{1} = \nu a_{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | p[1] = nu*a[1] |
Subscript[p, 1] == \[Nu]*Subscript[a, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2}
p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | p[2] = nu*((nu - 1)*(a[1])^(2)+ 2*a[2])/2 |
Subscript[p, 2] == \[Nu]*((\[Nu]- 1)*(Subscript[a, 1])^(2)+ 2*Subscript[a, 2])/2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E63 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}}
f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{z-z_{0}} < R} | (f(z))^(m) = sum(pochhammer(n + 1, m)*a[n + m]*(z - z[0])^(n), n = 0..infinity) |
(f[z])^(m) == Sum[Pochhammer[n + 1, m]*Subscript[a, n + m]*(z - Subscript[z, 0])^(n), {n, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 1.9.E64 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z_{m,n}-z| < \epsilon}
|z_{m,n}-z| < \epsilon |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(z[m , n]- z) < epsilon |
Abs[Subscript[z, m , n]- z] < \[Epsilon] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E66 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{p,q} = \sum^{p}_{m=0}\sum^{q}_{n=0}\zeta_{m,n}}
z_{p,q} = \sum^{p}_{m=0}\sum^{q}_{n=0}\zeta_{m,n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z[p , q] = sum(sum(zeta[m , n], n = 0..q), m = 0..p) |
Subscript[z, p , q] == Sum[Sum[Subscript[\[Zeta], m , n], {n, 0, q}, GenerateConditions->None], {m, 0, p}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.9.E69 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{b}_{a}\sum^{\infty}_{n=0}|f_{n}(t)|\diff{t} < \infty}
\int^{b}_{a}\sum^{\infty}_{n=0}|f_{n}(t)|\diff{t} < \infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | int(sum(abs(f[n](t)), n = 0..infinity), t = a..b) < infinity |
Integrate[Sum[Abs[Subscript[f, n][t]], {n, 0, Infinity}, GenerateConditions->None], {t, a, b}, GenerateConditions->None] < Infinity |
Missing Macro Error | Missing Macro Error | - | - |
| 1.9.E70 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=0}\int^{b}_{a}|f_{n}(t)|\diff{t} < \infty}
\sum^{\infty}_{n=0}\int^{b}_{a}|f_{n}(t)|\diff{t} < \infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(int(abs(f[n](t)), t = a..b) , n = 0..infinity)< infinity |
Sum[Integrate[Abs[Subscript[f, n][t]], {t, a, b}, GenerateConditions->None] , {n, 0, Infinity}, GenerateConditions->None]< Infinity |
Missing Macro Error | Missing Macro Error | - | - |
| 1.9.E71 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\diff{t} = \sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\diff{t}}
\int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\diff{t} = \sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\diff{t} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | int(sum(f[n](t), n = 0..infinity), t = a..b) = sum(int(f[n](t), t = a..b), n = 0..infinity) |
Integrate[Sum[Subscript[f, n][t], {n, 0, Infinity}, GenerateConditions->None], {t, a, b}, GenerateConditions->None] == Sum[Integrate[Subscript[f, n][t], {t, a, b}, GenerateConditions->None], {n, 0, Infinity}, GenerateConditions->None] |
Successful | Aborted | - | Skipped - Because timed out |
| 1.10.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\ln@{1+a_{n}(z)}| \leq M_{n}}
|\ln@{1+a_{n}(z)}| \leq M_{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n \geq N} | abs(ln(1 + a[n](z))) <= M[n] |
Abs[Log[1 + Subscript[a, n][z]]] <= Subscript[M, n] |
Failure | Failure | Failed [126 / 300] 126/300]: [[.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 1}.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 2}.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 3}1.465287519 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [246 / 300]
{LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 1.10.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=1}M_{n} < \infty}
\sum^{\infty}_{n=1}M_{n} < \infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(M[n](<)*infinity, n = 1..infinity) |
Sum[Subscript[M, n][<]*Infinity, {n, 1, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.10.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}}
P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | P(z) = product((1 -(z)/(z[n]))*exp(z/z[n]), n = 1..infinity) |
P[z] == Product[(1 -Divide[z,Subscript[z, n]])*Exp[z/Subscript[z, n]], {n, 1, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{k} = \alpha b_{k+1}+a_{k}}
b_{k} = \alpha b_{k+1}+a_{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = n-1} | b[k] = alpha*b[k + 1]+ a[k] |
Subscript[b, k] == \[Alpha]*Subscript[b, k + 1]+ Subscript[a, k] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{k} = \alpha c_{k+1}+b_{k}}
c_{k} = \alpha c_{k+1}+b_{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = n-1} | c[k] = alpha*c[k + 1]+ b[k] |
Subscript[c, k] == \[Alpha]*Subscript[c, k + 1]+ Subscript[b, k] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#E10Xa | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sum_{1\leq j<k\leq n}z_{j}z_{k} = a_{n-2}/a_{n}}
\displaystyle\sum_{1\leq j<k\leq n}z_{j}z_{k} = a_{n-2}/a_{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(sum(z[j]*z[k], k = j + 1..n), j = 1..k - 1) = a[n - 2]/a[n] |
Sum[Sum[Subscript[z, j]*Subscript[z, k], {k, j + 1, n}, GenerateConditions->None], {j, 1, k - 1}, GenerateConditions->None] == Subscript[a, n - 2]/Subscript[a, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D = b^{2}-4ac}
D = b^{2}-4ac |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | D = (b)^(2)- 4*a*c |
D == (b)^(2)- 4*a*c |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3}}
\rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | rho = -(1)/(2)+(1)/(2)*sqrt(- 3) |
\[Rho] == -Divide[1,2]+Divide[1,2]*Sqrt[- 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho^{2} = e^{-2\pi i/3}}
\rho^{2} = e^{-2\pi i/3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (rho)^(2) = exp(- 2*Pi*I/3) |
\[Rho]^(2) == Exp[- 2*Pi*I/3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = (-3a^{2}+8b)/8}
p = (-3a^{2}+8b)/8 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | p = (- 3*(a)^(2)+ 8*b)/8 |
p == (- 3*(a)^(2)+ 8*b)/8 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = (a^{3}-4ab+8c)/8}
q = (a^{3}-4ab+8c)/8 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | q = ((a)^(3)- 4*a*b + 8*c)/8 |
q == ((a)^(3)- 4*a*b + 8*c)/8 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = (-3a^{4}+16a^{2}b-64ac+256d)/256}
r = (-3a^{4}+16a^{2}b-64ac+256d)/256 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | r = (- 3*(a)^(4)+ 16*(a)^(2)* b - 64*a*c + 256*d)/256 |
r == (- 3*(a)^(4)+ 16*(a)^(2)* b - 64*a*c + 256*d)/256 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0}
z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (z)^(3)- 2*p*(z)^(2)+((p)^(2)- 4*r)*z + (q)^(2) = 0 |
(z)^(3)- 2*p*(z)^(2)+((p)^(2)- 4*r)*z + (q)^(2) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q}
\sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sqrt(- theta[1])*sqrt(- theta[2])*sqrt(- theta[3]) = - q |
Sqrt[- Subscript[\[Theta], 1]]*Sqrt[- Subscript[\[Theta], 2]]*Sqrt[- Subscript[\[Theta], 3]] == - q |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{n} = a+ib}
z^{n} = a+ib |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (z)^(n) = a + I*b |
(z)^(n) == a + I*b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{1} = a_{1}}
D_{1} = a_{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | D[1] = a[1] |
Subscript[D, 1] == Subscript[a, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}}
A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A[k] = b[k]*A[k - 1]+ a[k]*A[k - 2] |
Subscript[A, k] == Subscript[b, k]*Subscript[A, k - 1]+ Subscript[a, k]*Subscript[A, k - 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}}
B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | B[k] = b[k]*B[k - 1]+ a[k]*B[k - 2] |
Subscript[B, k] == Subscript[b, k]*Subscript[B, k - 1]+ Subscript[a, k]*Subscript[B, k - 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1} = 1}
A_{-1} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A[- 1] = 1 |
Subscript[A, - 1] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0} = b_{0}}
A_{0} = b_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A[0] = b[0] |
Subscript[A, 0] == Subscript[b, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-1} = 0}
B_{-1} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | B[- 1] = 0 |
Subscript[B, - 1] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0} = 1}
B_{0} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | B[0] = 1 |
Subscript[B, 0] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}}
A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A[n]*B[n - 1]- B[n]*A[n - 1] = (- 1)^(n - 1)* product(a[k], k = 1..n) |
Subscript[A, n]*Subscript[B, n - 1]- Subscript[B, n]*Subscript[A, n - 1] == (- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}}
C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | C[n]- C[n - 1] = ((- 1)^(n - 1)* product(a[k], k = 1..n))/(B[n - 1]*B[n]) |
Subscript[C, n]- Subscript[C, n - 1] == Divide[(- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None],Subscript[B, n - 1]*Subscript[B, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}}
a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[n] = (A[n - 1]*B[n]- A[n]*B[n - 1])/(A[n - 1]*B[n - 2]- A[n - 2]*B[n - 1]) |
Subscript[a, n] == Divide[Subscript[A, n - 1]*Subscript[B, n]- Subscript[A, n]*Subscript[B, n - 1],Subscript[A, n - 1]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n - 1]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}}
a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[n] = (B[n])/(B[n - 2])*(C[n - 1]- C[n])/(C[n - 1]- C[n - 2]) |
Subscript[a, n] == Divide[Subscript[B, n],Subscript[B, n - 2]]*Divide[Subscript[C, n - 1]- Subscript[C, n],Subscript[C, n - 1]- Subscript[C, n - 2]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}}
b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b[n] = (A[n]*B[n - 2]- A[n - 2]*B[n])/(A[n - 1]*B[n - 2]- A[n - 2]*B[n - 1]) |
Subscript[b, n] == Divide[Subscript[A, n]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n],Subscript[A, n - 1]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n - 1]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}}
b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b[n] = (B[n])/(B[n - 1])*(C[n]- C[n - 2])/(C[n - 1]- C[n - 2]) |
Subscript[b, n] == Divide[Subscript[B, n],Subscript[B, n - 1]]*Divide[Subscript[C, n]- Subscript[C, n - 2],Subscript[C, n - 1]- Subscript[C, n - 2]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0} = A_{0}}
b_{0} = A_{0} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b[0] = A[0] |
Subscript[b, 0] == Subscript[A, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = B_{1}}
b_{1} = B_{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b[1] = B[1] |
Subscript[b, 1] == Subscript[B, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1} = A_{1}-A_{0}B_{1}}
a_{1} = A_{1}-A_{0}B_{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[1] = A[1]- A[0]*B[1] |
Subscript[a, 1] == Subscript[A, 1]- Subscript[A, 0]*Subscript[B, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}}
C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | C[n](w) = (A[n]+ A[n - 1]*w)/(B[n]+ B[n - 1]*w) |
Subscript[C, n][w] == Divide[Subscript[A, n]+ Subscript[A, n - 1]*w,Subscript[B, n]+ Subscript[B, n - 1]*w] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{0}\not = \infty}
C_{0}\not = \infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | C[0] <> infinity |
Subscript[C, 0] \[NotEqual]*Infinity |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}\not = C_{n-1}}
C_{n}\not = C_{n-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | C[n] <> C[n - 1] |
Subscript[C, n] \[NotEqual]*Subscript[C, n - 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |b_{n}| \geq |a_{n}|+1}
|b_{n}| \geq |a_{n}|+1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(b[n]) >= abs(a[n])+ 1 |
Abs[Subscript[b, n]] >= Abs[Subscript[a, n]]+ 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.12.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}}
-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | -(1)/(2)*Pi + delta < argument(b[n]) |
-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[b, n]] |
Failure | Failure | Failed [27 / 300] 27/300]: [[-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 1, n = 3}-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 2, n = 3}-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 3, n = 3}-.70796327e-1 < -2.617993878 <- {delta = 1.5, b[n] = -1/2*3^(1/2)-1/2*I, n = 1, n = 3}... skip entries to safe data |
Failed [49 / 100]
{Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.12.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta}
\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | argument(b[n]) < (1)/(2)*Pi - delta |
Arg[Subscript[b, n]] < Divide[1,2]*Pi - \[Delta] |
Failure | Failure | Failed [72 / 300] 72/300]: [[3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 1, n = 3}3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 2, n = 3}3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 3, n = 3}3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -.5, n = 1, n = 3}... skip entries to safe data |
Failed [64 / 100]
{Less[0.5235987755982988, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Less[2.0943951023931953, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.12.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}}
-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | -(1)/(2)*Pi + delta < argument(C[n]) |
-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[C, n]] |
Failure | Failure | Failed [27 / 300] 27/300]: [[-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 1, n = 3}-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 2, n = 3}-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 3, n = 3}-.70796327e-1 < -2.617993878 <- {delta = 1.5, C[n] = -1/2*3^(1/2)-1/2*I, n = 1, n = 3}... skip entries to safe data |
Failed [49 / 100]
{Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.12.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta}
\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | argument(C[n]) < (1)/(2)*Pi - delta |
Arg[Subscript[C, n]] < Divide[1,2]*Pi - \[Delta] |
Failure | Failure | Failed [72 / 300] 72/300]: [[3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 1, n = 3}3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 2, n = 3}3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 3, n = 3}3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -.5, n = 1, n = 3}... skip entries to safe data |
Failed [64 / 100]
{Less[0.5235987755982988, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Less[2.0943951023931953, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.12.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=1}|b_{n}| = \infty}
\sum^{\infty}_{n=1}|b_{n}| = \infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(abs(b[n]), n = 1..infinity) = infinity |
Sum[Abs[Subscript[b, n]], {n, 1, Infinity}, GenerateConditions->None] == Infinity |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.13.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = Aw_{1}(z)+Bw_{2}(z)}
w(z) = Aw_{1}(z)+Bw_{2}(z) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w(z) = Aw[1](z)+ Bw[2](z) |
w[z] == Subscript[Aw, 1][z]+ Subscript[Bw, 2][z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.13#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z_{0}) = 1}
w_{1}(z_{0}) = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w[1](z[0]) = 1 |
Subscript[w, 1][Subscript[z, 0]] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.13#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z_{0}) = 0}
w_{2}(z_{0}) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w[2](z[0]) = 0 |
Subscript[w, 2][Subscript[z, 0]] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.13.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Aw_{1}(z)+Bw_{2}(z) = 0}
Aw_{1}(z)+Bw_{2}(z) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Aw[1](z)+ Bw[2](z) = 0 |
Subscript[Aw, 1][z]+ Subscript[Bw, 2][z] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.13.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)}
w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w(z) = w[0](z)+ Aw[1](z)+ Bw[2](z) |
w[z] == Subscript[w, 0][z]+ Subscript[Aw, 1][z]+ Subscript[Bw, 2][z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.13.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}}
w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w[0](z) = w[2](z)* int((w[1](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)- w[1](z)* int((w[2](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z) |
Subscript[w, 0][z] == Subscript[w, 2][z]* Integrate[Divide[Subscript[w, 1][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]- Subscript[w, 1][z]* Integrate[Divide[Subscript[w, 2][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None] |
Translation Error | Translation Error | - | - |
| 1.13#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W(\xi) = w\left(\frac{1}{\xi}\right)}
W(\xi) = w\left(\frac{1}{\xi}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | W(xi) = w((1)/(xi)) |
W[\[Xi]] == w[Divide[1,\[Xi]]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.13.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{W}{z}-H(z)W = 0}
\deriv[2]{W}{z}-H(z)W = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(W, [z$(2)])- H(z)* W = 0 |
D[W, {z, 2}]- H[z]* W == 0 |
Translation Error | Translation Error | - | - |
| 1.13#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{U}{z}+IU = 0}
\deriv[2]{U}{z}+IU = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(U, [z$(2)])+ I*U = 0 |
D[U, {z, 2}]+ I*U == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}... skip entries to safe data |
Failed [210 / 210]
{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[Complex[0, 1], 1], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.7320508075688774, 0.9999999999999999] <- {Rule[Complex[0, 1], 2], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 1.13#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{V}{z}+JV = 0}
\deriv[2]{V}{z}+JV = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(V, [z$(2)])+ J*V = 0 |
D[V, {z, 2}]+ J*V == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 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]
{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{n} = \sum_{k=0}^{n}a_{k}}
s_{n} = \sum_{k=0}^{n}a_{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | s[n] = sum(a[k], k = 0..n) |
Subscript[s, n] == Sum[Subscript[a, k], {k, 0, n}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to 1-}\sum^{\infty}_{n=0}a_{n}x^{n} = s}
\lim_{x\to 1-}\sum^{\infty}_{n=0}a_{n}x^{n} = s |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit(sum(a[n]*(x)^(n), n = 0..infinity), x = 1, left) = s |
Limit[Sum[Subscript[a, n]*(x)^(n), {n, 0, Infinity}, GenerateConditions->None], x -> 1, Direction -> "FromBelow", GenerateConditions->None] == s |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\frac{n!}{(\alpha+1)_{n}}\sum^{n}_{k=0}\frac{(\alpha+1)_{k}}{k!}a_{n-k} = s}
\lim_{n\to\infty}\frac{n!}{(\alpha+1)_{n}}\sum^{n}_{k=0}\frac{(\alpha+1)_{k}}{k!}a_{n-k} = s |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit((factorial(n))/(alpha + 1[n])*sum((alpha + 1[k])/(factorial(k))*a[n - k], k = 0..n), n = infinity) = s |
Limit[Divide[(n)!,Subscript[\[Alpha]+ 1, n]]*Sum[Divide[Subscript[\[Alpha]+ 1, k],(k)!]*Subscript[a, n - k], {k, 0, n}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == s |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{t\to\infty}e^{-t}\sum^{\infty}_{n=0}\frac{s_{n}}{n!}t^{n} = s}
\lim_{t\to\infty}e^{-t}\sum^{\infty}_{n=0}\frac{s_{n}}{n!}t^{n} = s |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit(exp(- t)*sum((s[n])/(factorial(n))*(t)^(n), n = 0..infinity), t = infinity) = s |
Limit[Exp[- t]*Sum[Divide[Subscript[s, n],(n)!]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None], t -> Infinity, GenerateConditions->None] == s |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=0}a_{n} = s}
\sum^{\infty}_{n=0}a_{n} = s |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(a[n], n = 0..infinity) = s |
Sum[Subscript[a, n], {n, 0, Infinity}, GenerateConditions->None] == s |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1}
\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2*Pi)*int(P(r , theta), theta = 0..2*Pi) = 1 |
Divide[1,2*Pi]*Integrate[P[r , \[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1 |
Successful | Aborted | - | Successful [Tested: 1] |
| 1.15.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1}
\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2*Pi)*int(K[n](theta), theta = 0..2*Pi) = 1 |
Divide[1,2*Pi]*Integrate[Subscript[K, n][\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1 |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 1.15.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1}
\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2*Pi)*int(P(x , y), x = - infinity..infinity) = 1 |
Divide[1,2*Pi]*Integrate[P[x , y], {x, - Infinity, Infinity}, GenerateConditions->None] == 1 |
Successful | Successful | - | Successful [Tested: 3] |
| 1.15.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Phi(z) = \Phi(x+iy)}
\Phi(z) = \Phi(x+iy) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Phi*((x + y*I)) = Phi*(x + I*y) |
\[CapitalPhi]*((x + y*I)) == \[CapitalPhi]*(x + I*y) |
Successful | Successful | - | Successful [Tested: 180] |
| 1.15.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{\infty}_{-\infty}K_{R}(s)\diff{s} = 1}
\int^{\infty}_{-\infty}K_{R}(s)\diff{s} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | int(K[R](s), s = - infinity..infinity) = 1 |
Integrate[Subscript[K, R][s], {s, - Infinity, Infinity}, GenerateConditions->None] == 1 |
Failure | Aborted | Failed [7 / 10] 7/10]: [[-.1339745960+.5000000000*I <- {R = 1/2*3^(1/2)+1/2*I}-1.500000000+.8660254040*I <- {R = -1/2+1/2*I*3^(1/2)}-.5000000000-.8660254040*I <- {R = 1/2-1/2*I*3^(1/2)}-1.866025404-.5000000000*I <- {R = -1/2*3^(1/2)-1/2*I}... skip entries to safe data |
Skipped - Because timed out |
| 1.15.E48 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I^{\alpha}I^{\beta} = I^{\alpha+\beta}}
I^{\alpha}I^{\beta} = I^{\alpha+\beta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{\alpha} > 0, \realpart@@{\beta} > 0} | (I)^(alpha)* (I)^(beta) = (I)^(alpha + beta) |
(I)^\[Alpha]* (I)^\[Beta] == (I)^(\[Alpha]+ \[Beta]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E52 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D^{k}I^{\alpha} = D^{n}I^{\alpha+n-k}}
D^{k}I^{\alpha} = D^{n}I^{\alpha+n-k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = 1} | (D)^(k)* (I)^(alpha) = (D)^(n)* (I)^(alpha + n - k) |
(D)^(k)* (I)^\[Alpha] == (D)^(n)* (I)^(\[Alpha]+ n - k) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E53 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D^{\alpha}D^{\beta} = D^{\alpha+\beta}}
D^{\alpha}D^{\beta} = D^{\alpha+\beta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (D)^(alpha)* (D)^(beta) = (D)^(alpha + beta) |
(D)^\[Alpha]* (D)^\[Beta] == (D)^(\[Alpha]+ \[Beta]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} > -\frac{K}{n}}
a_{n} > -\frac{K}{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n > 0, K > 0} | a[n] > -(K)/(n) |
Subscript[a, n] > -Divide[K,n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E55 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=0}a_{n} = s}
\sum^{\infty}_{n=0}a_{n} = s |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(a[n], n = 0..infinity) = s |
Sum[Subscript[a, n], {n, 0, Infinity}, GenerateConditions->None] == s |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.15.E56 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to 1-}(1-x)\sum^{\infty}_{n=0}a_{n}x^{n} = s}
\lim_{x\to 1-}(1-x)\sum^{\infty}_{n=0}a_{n}x^{n} = s |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit((1 - x)*sum(a[n]*(x)^(n), n = 0..infinity), x = 1, left) = s |
Limit[(1 - x)*Sum[Subscript[a, n]*(x)^(n), {n, 0, Infinity}, GenerateConditions->None], x -> 1, Direction -> "FromBelow", GenerateConditions->None] == s |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Lambda(\alpha_{1}\phi_{1}+\alpha_{2}\phi_{2}) = \alpha_{1}\Lambda(\phi_{1})+\alpha_{2}\Lambda(\phi_{2})}
\Lambda(\alpha_{1}\phi_{1}+\alpha_{2}\phi_{2}) = \alpha_{1}\Lambda(\phi_{1})+\alpha_{2}\Lambda(\phi_{2}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Lambda(alpha[1]*phi[1]+ alpha[2]*phi[2]) = alpha[1]*Lambda(phi[1])+ alpha[2]*Lambda(phi[2]) |
\[CapitalLambda][Subscript[\[Alpha], 1]*Subscript[\[Phi], 1]+ Subscript[\[Alpha], 2]*Subscript[\[Phi], 2]] == Subscript[\[Alpha], 1]*\[CapitalLambda][Subscript[\[Phi], 1]]+ Subscript[\[Alpha], 2]*\[CapitalLambda][Subscript[\[Phi], 2]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\Lambda(\phi_{n}) = \Lambda(\phi)}
\lim_{n\to\infty}\Lambda(\phi_{n}) = \Lambda(\phi) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit(Lambda(phi[n]), n = infinity) = Lambda(phi) |
Limit[\[CapitalLambda][Subscript[\[Phi], n]], n -> Infinity, GenerateConditions->None] == \[CapitalLambda][\[Phi]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma_{n} = f^{(n)}(x_{0}+)-f^{(n)}(x_{0}-)}
\sigma_{n} = f^{(n)}(x_{0}+)-f^{(n)}(x_{0}-) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sigma[n] = (f)^(n)*(x[0]+)- (f)^(n)*(x[0]-) |
Subscript[\[Sigma], n] == (f)^(n)*(Subscript[x, 0]+)- (f)^(n)*(Subscript[x, 0]-) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{\alpha}_{+} = x^{\alpha}\HeavisideH@{x}}
x^{\alpha}_{+} = x^{\alpha}\HeavisideH@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (x[+])^(alpha) = (x)^(alpha)* Heaviside(x) |
(Subscript[x, +])^\[Alpha] == (x)^\[Alpha]* HeavisideTheta[x] |
Error | Failure | - | Error |
| 1.16.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Dx^{\alpha}_{+} = \alpha x_{+}^{\alpha-1}}
Dx^{\alpha}_{+} = \alpha x_{+}^{\alpha-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | D*(x[+])^(alpha) = alpha*(x[+])^(alpha - 1) |
D*(Subscript[x, +])^\[Alpha] == \[Alpha]*(Subscript[x, +])^(\[Alpha]- 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{\alpha}_{+} = \frac{1}{(\alpha+1)_{n}}D^{n}x_{+}^{\alpha+n}}
x^{\alpha}_{+} = \frac{1}{(\alpha+1)_{n}}D^{n}x_{+}^{\alpha+n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (x[+])^(alpha) = (1)/(alpha + 1[n])*(D)^(n)* (x[+])^(alpha + n) |
(Subscript[x, +])^\[Alpha] == Divide[1,Subscript[\[Alpha]+ 1, n]]*(D)^(n)* (Subscript[x, +])^(\[Alpha]+ n) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln_{+}x = \HeavisideH@{x}\ln@@{x}}
\ln_{+}x = \HeavisideH@{x}\ln@@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | $0[+]ln()*x = Heaviside(x)*ln(x) |
Subscript[$0, +]Log[]*x == HeavisideTheta[x]*Log[x] |
Translation Error | Translation Error | - | - |
| 1.16.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x}
(-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (- 1)^(n)* factorial(n)*(x[+])^(- 1 - n) = (D)^(n + 1)* [+]ln()*x |
(- 1)^(n)* (n)!*(Subscript[x, +])^(- 1 - n) == Subscript[(D)^(n + 1)* , +]Log[]*x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x^{N}\phi_{n}^{(k)}| \leq c_{k,N}}
|x^{N}\phi_{n}^{(k)}| \leq c_{k,N} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs((x)^(N)* (phi[n])^(k)) <= c[k , N] |
Abs[(x)^(N)* (Subscript[\[Phi], n])^(k)] <= Subscript[c, k , N] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x^{m}\phi^{(k)}(x)| \leq c_{m,k}}
|x^{m}\phi^{(k)}(x)| \leq c_{m,k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs((x)^(m)* (phi(x)*)^(k)) <= c[m , k] |
Abs[(x)^(m)* (\[Phi][x]*)^(k)] <= Subscript[c, m , k] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{\boldsymbol{{\alpha}}} = \iunit^{-|\boldsymbol{{\alpha}}|}D^{\boldsymbol{{\alpha}}}}
D_{\boldsymbolTemplate:\alpha} = \iunit^{-|\boldsymbolTemplate:\alpha|}D^{\boldsymbolTemplate:\alpha} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | D[alpha] = (I)^(-abs(alpha))* (D)^(alpha) |
Subscript[D, \[Alpha]] == (I)^(-Abs[\[Alpha]])* (D)^\[Alpha] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.8660254041+1.500000000*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = 1/2*3^(1/2)+1/2*I}-.4999999999+1.866025404*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = -1/2+1/2*I*3^(1/2)}.5000000001+.1339745960*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = 1/2-1/2*I*3^(1/2)}-.8660254039+.5000000000*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = -1/2*3^(1/2)-1/2*I}... skip entries to safe data |
Failed [300 / 300]
{Complex[0.8660254037844387, 1.5] <- {Rule[D, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[D, α], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.4999999999999998, 1.8660254037844388] <- {Rule[D, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[D, α], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 1.16.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(\mathbf{x}) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{x}^{\boldsymbol{{\alpha}}}}
P(\mathbf{x}) = \sum_{\boldsymbolTemplate:\alpha}c_{\boldsymbolTemplate:\alpha}\mathbf{x}^{\boldsymbolTemplate:\alpha} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | P(x) = sum(c[alpha]*(x)^(alpha), $0[alpha]*c[alpha]*(x)^(alpha) = - infinity..infinity) |
P[x] == Sum[Subscript[c, \[Alpha]]*(x)^\[Alpha], {Subscript[$0, \[Alpha]]*Subscript[c, \[Alpha]]*(x)^\[Alpha], - Infinity, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(\mathbf{D}) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{D}^{\alpha}}
P(\mathbf{D}) = \sum_{\boldsymbolTemplate:\alpha}c_{\boldsymbolTemplate:\alpha}\mathbf{D}^{\alpha} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | P(D) = sum(c[alpha]*(D)^(alpha), $0[alpha]*c[alpha]*(D)^(alpha) = - infinity..infinity) |
P[D] == Sum[Subscript[c, \[Alpha]]*(D)^\[Alpha], {Subscript[$0, \[Alpha]]*Subscript[c, \[Alpha]]*(D)^\[Alpha], - Infinity, Infinity}, GenerateConditions->None] |
Translation Error | Translation Error | - | - |
| 1.16#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(D) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}D_{\boldsymbol{{\alpha}}}}
P(D) = \sum_{\boldsymbolTemplate:\alpha}c_{\boldsymbolTemplate:\alpha}D_{\boldsymbolTemplate:\alpha} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | P(D) = sum(c[alpha]*D[alpha], $0[alpha]*c[alpha]*D[alpha] = - infinity..infinity) |
P[D] == Sum[Subscript[c, \[Alpha]]*Subscript[D, \[Alpha]], {Subscript[$0, \[Alpha]]*Subscript[c, \[Alpha]]*Subscript[D, \[Alpha]], - Infinity, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{F}(P(D)u) = P(-\mathbf{x})\mathcal{F}(u)}
\mathcal{F}(P(D)u) = P(-\mathbf{x})\mathcal{F}(u) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | F(P(D)* u) = P(- x)* F(u) |
F[P[D]* u] == P[- x]* F[u] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{F}(Pu) = P(D)\mathcal{F}(u)}
\mathcal{F}(Pu) = P(D)\mathcal{F}(u) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | F(P*u) = P(D)* F(u) |
F[P*u] == P[D]* F[u] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.16.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{\infty}_{-\infty}\Diracdelta@{t}\expe^{\iunit xt}\diff{t} = 1}
\int^{\infty}_{-\infty}\Diracdelta@{t}\expe^{\iunit xt}\diff{t} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | int(Dirac(t)*exp(I*x*t), t = - infinity..infinity) = 1 |
Integrate[DiracDelta[t]*Exp[I*x*t], {t, - Infinity, Infinity}, GenerateConditions->None] == 1 |
Successful | Successful | - | Successful [Tested: 3] |
| 1.16.E43 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\cpi}\int^{\infty}_{-\infty}\expe^{\iunit xt}\diff{t} = \Diracdelta@{x}}
\frac{1}{2\cpi}\int^{\infty}_{-\infty}\expe^{\iunit xt}\diff{t} = \Diracdelta@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2*Pi)*int(exp(I*x*t), t = - infinity..infinity) = Dirac(x) |
Divide[1,2*Pi]*Integrate[Exp[I*x*t], {t, - Infinity, Infinity}, GenerateConditions->None] == DiracDelta[x] |
Successful | Failure | - | Failed [3 / 3]
{Complex[-0.07099199156997928, 3.003857199159988*^-16] <- {Rule[x, 1.5]}Complex[0.07742603591272186, 0.30312240144001046] <- {Rule[x, 0.5]} |
| 1.16.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sign@{x} = 2\HeavisideH@{x}-1}
\sign@{x} = 2\HeavisideH@{x}-1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \neq 0} | signum(x) = 2*Heaviside(x)- 1 |
Sign[x] == 2*HeavisideTheta[x]- 1 |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 1.17.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x} = 0}
\Diracdelta@{x} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \neq 0} | Dirac(x) = 0 |
DiracDelta[x] == 0 |
Failure | Successful | Successful [Tested: 3] | Successful [Tested: 1] |
| 1.17.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\Diracdelta@{x-a}\phi(x)\diff{x} = \phi(a)}
\int_{-\infty}^{\infty}\Diracdelta@{x-a}\phi(x)\diff{x} = \phi(a) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | int(Dirac(x - a)*phi(x), x = - infinity..infinity) = phi(a) |
Integrate[DiracDelta[x - a]*\[Phi][x], {x, - Infinity, Infinity}, GenerateConditions->None] == \[Phi][a] |
Successful | Successful | - | Successful [Tested: 10] |
| 1.17.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \phi(a)}
\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \phi(a) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi(x), x = - infinity..infinity), n = infinity) = phi(a) |
Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi][x], {x, - Infinity, Infinity}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == \[Phi][a] |
Successful | Aborted | - | Successful [Tested: 60] |
| 1.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \tfrac{1}{2}\phi(a-)+\tfrac{1}{2}\phi(a+)}
\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \tfrac{1}{2}\phi(a-)+\tfrac{1}{2}\phi(a+) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi(x), x = - infinity..infinity), n = infinity) = (1)/(2)*phi(a -)+(1)/(2)*phi(a +) |
Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi][x], {x, - Infinity, Infinity}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == Divide[1,2]*\[Phi][a -]+Divide[1,2]*\[Phi][a +] |
Error | Failure | - | Error |
| 1.17.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left(\int_{-\infty}^{\infty}\phi(x)e^{itx}\diff{x}\right)\diff{t} = \phi(a)}
\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left(\int_{-\infty}^{\infty}\phi(x)e^{itx}\diff{x}\right)\diff{t} = \phi(a) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2*Pi)*int(exp(- I*a*t)*(int(phi(x)* exp(I*t*x), x = - infinity..infinity)), t = - infinity..infinity) = phi(a) |
Divide[1,2*Pi]*Integrate[Exp[- I*a*t]*(Integrate[\[Phi][x]* Exp[I*t*x], {x, - Infinity, Infinity}, GenerateConditions->None]), {t, - Infinity, Infinity}, GenerateConditions->None] == \[Phi][a] |
Failure | Aborted | Failed [60 / 60] 60/60]: [[Float(undefined)+.7500000000*I <- {a = -1.5, phi = 1/2*3^(1/2)+1/2*I}Float(undefined)+1.299038106*I <- {a = -1.5, phi = -1/2+1/2*I*3^(1/2)}Float(undefined)-1.299038106*I <- {a = -1.5, phi = 1/2-1/2*I*3^(1/2)}Float(undefined)-.7500000000*I <- {a = -1.5, phi = -1/2*3^(1/2)-1/2*I}... skip entries to safe data |
Skipped - Because timed out |
| 1.17.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}\right)\phi(x)\diff{x} = \phi(a)}
\int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}\right)\phi(x)\diff{x} = \phi(a) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | int(((1)/(2*Pi)*int(exp(I*(x - a)*t), t = - infinity..infinity))*phi(x), x = - infinity..infinity) = phi(a) |
Integrate[(Divide[1,2*Pi]*Integrate[Exp[I*(x - a)*t], {t, - Infinity, Infinity}, GenerateConditions->None])*\[Phi][x], {x, - Infinity, Infinity}, GenerateConditions->None] == \[Phi][a] |
Successful | Aborted | - | Skipped - Because timed out |
| 1.17.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\diff{t} = \sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}}
\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\diff{t} = \sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2*Pi)*int(exp(- (t)^(2)/(4*n))*exp(I*(x - a)*t), t = - infinity..infinity) = sqrt((n)/(Pi))*exp(- n*(x - a)^(2)) |
Divide[1,2*Pi]*Integrate[Exp[- (t)^(2)/(4*n)]*Exp[I*(x - a)*t], {t, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[n,Pi]]*Exp[- n*(x - a)^(2)] |
Failure | Successful | Successful [Tested: 54] | Successful [Tested: 54] |
| 1.17.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}}
\Diracdelta@{x-a} = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Dirac(x - a) = (1)/(2*Pi)*int(exp(I*(x - a)*t), t = - infinity..infinity) |
DiracDelta[x - a] == Divide[1,2*Pi]*Integrate[Exp[I*(x - a)*t], {t, - Infinity, Infinity}, GenerateConditions->None] |
Successful | Failure | - | Skipped - Because timed out |
| 1.17.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = x\int_{0}^{\infty}t\BesselJ{\nu}@{xt}\BesselJ{\nu}@{at}\diff{t}}
\Diracdelta@{x-a} = x\int_{0}^{\infty}t\BesselJ{\nu}@{xt}\BesselJ{\nu}@{at}\diff{t} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{\nu} > -1, x > 0, a > 0} | Dirac(x - a) = x*int(t*BesselJ(nu, x*t)*BesselJ(nu, a*t), t = 0..infinity) |
DiracDelta[x - a] == x*Integrate[t*BesselJ[\[Nu], x*t]*BesselJ[\[Nu], a*t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Aborted | Error | Skipped - Because timed out |
| 1.17.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{2xa}{\pi}\int_{0}^{\infty}t^{2}\sphBesselJ{\ell}@{xt}\sphBesselJ{\ell}@{at}\diff{t}}
\Diracdelta@{x-a} = \frac{2xa}{\pi}\int_{0}^{\infty}t^{2}\sphBesselJ{\ell}@{xt}\sphBesselJ{\ell}@{at}\diff{t} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, a > 0} | Error |
DiracDelta[x - a] == Divide[2*x*a,Pi]*Integrate[(t)^(2)* SphericalBesselJ[\[ScriptL], x*t]*SphericalBesselJ[\[ScriptL], a*t], {t, 0, Infinity}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 1.17.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \int_{-\infty}^{\infty}\AiryAi@{t-x}\AiryAi@{t-a}\diff{t}}
\Diracdelta@{x-a} = \int_{-\infty}^{\infty}\AiryAi@{t-x}\AiryAi@{t-a}\diff{t} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Dirac(x - a) = int(AiryAi(t - x)*AiryAi(t - a), t = - infinity..infinity) |
DiracDelta[x - a] == Integrate[AiryAi[t - x]*AiryAi[t - a], {t, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 1.17.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}\left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\diff{x}\right) = \phi(a)}
\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}\left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\diff{x}\right) = \phi(a) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2*Pi)*sum(exp(- I*k*a)*(int(phi(x)* exp(I*k*x), x = - Pi..Pi)), k = - infinity..infinity) = phi(a) |
Divide[1,2*Pi]*Sum[Exp[- I*k*a]*(Integrate[\[Phi][x]* Exp[I*k*x], {x, - Pi, Pi}, GenerateConditions->None]), {k, - Infinity, Infinity}, GenerateConditions->None] == \[Phi][a] |
Error | Failure | - | Successful [Tested: 60] |
| 1.17.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}\right)\diff{x} = \phi(a)}
\int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}\right)\diff{x} = \phi(a) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | int(phi(x)*((1)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity)), x = - Pi..Pi) = phi(a) |
Integrate[\[Phi][x]*(Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}, GenerateConditions->None]), {x, - Pi, Pi}, GenerateConditions->None] == \[Phi][a] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 1.17.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}}
\Diracdelta@{x-a} = \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Dirac(x - a) = (1)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity) |
DiracDelta[x - a] == Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [18 / 18]
{Times[-0.15915494309189535, NSum[Power[E, Times[Complex[0.0, 3.0], k]] <- {k, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}Times[-0.15915494309189535, NSum[Power[E, Times[Complex[0.0, 2.0], k]] <- {k, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]} |
| 1.17.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \sum_{k=0}^{\infty}(k+\tfrac{1}{2})\LegendrepolyP{k}@{x}\LegendrepolyP{k}@{a}}
\Diracdelta@{x-a} = \sum_{k=0}^{\infty}(k+\tfrac{1}{2})\LegendrepolyP{k}@{x}\LegendrepolyP{k}@{a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Dirac(x - a) = sum((k +(1)/(2))*LegendreP(k, x)*LegendreP(k, a), k = 0..infinity) |
DiracDelta[x - a] == Sum[(k +Divide[1,2])*LegendreP[k, x]*LegendreP[k, a], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Error | Failed [18 / 18]
{Times[-1.0, NSum[Times[Plus[Rational[1, 2], k], LegendreP[k, -1.5], LegendreP[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}Times[-1.0, NSum[Times[Plus[Rational[1, 2], k], LegendreP[k, -1.5], LegendreP[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]} |
| 1.17.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = e^{-(x+a)/2}\sum_{k=0}^{\infty}\LaguerrepolyL[]{k}@{x}\LaguerrepolyL[]{k}@{a}}
\Diracdelta@{x-a} = e^{-(x+a)/2}\sum_{k=0}^{\infty}\LaguerrepolyL[]{k}@{x}\LaguerrepolyL[]{k}@{a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Dirac(x - a) = exp(-(x + a)/2)*sum(LaguerreL(k, x)*LaguerreL(k, a), k = 0..infinity) |
DiracDelta[x - a] == Exp[-(x + a)/2]*Sum[LaguerreL[k, x]*LaguerreL[k, a], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Error | Failed [18 / 18]
{Times[-1.0, NSum[Times[LaguerreL[k, -1.5], LaguerreL[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}Times[-1.6487212707001282, NSum[Times[LaguerreL[k, -1.5], LaguerreL[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]} |
| 1.17.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{e^{-(x^{2}+a^{2})/2}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{\HermitepolyH{k}@{x}\HermitepolyH{k}@{a}}{2^{k}k!}}
\Diracdelta@{x-a} = \frac{e^{-(x^{2}+a^{2})/2}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{\HermitepolyH{k}@{x}\HermitepolyH{k}@{a}}{2^{k}k!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Dirac(x - a) = (exp(-((x)^(2)+ (a)^(2))/2))/(sqrt(Pi))*sum((HermiteH(k, x)*HermiteH(k, a))/((2)^(k)* factorial(k)), k = 0..infinity) |
DiracDelta[x - a] == Divide[Exp[-((x)^(2)+ (a)^(2))/2],Sqrt[Pi]]*Sum[Divide[HermiteH[k, x]*HermiteH[k, a],(2)^(k)* (k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [18 / 18]
{Times[-0.05946514461181468, NSum[Times[Power[2, Times[-1, k]], Power[Factorial[k], -1], HermiteH[k, -1.5], HermiteH[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}Times[-0.16164302202498515, NSum[Times[Power[2, Times[-1, k]], Power[Factorial[k], -1], HermiteH[k, -1.5], HermiteH[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]} |
| 1.17.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{\cos@@{\theta_{1}}-\cos@@{\theta_{2}}}\Diracdelta@{\phi_{1}-\phi_{2}} = \sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell}\sphharmonicY{\ell}{m}@{\theta_{1}}{\phi_{1}}\conj{\sphharmonicY{\ell}{m}@{\theta_{2}}{\phi_{2}}}}
\Diracdelta@{\cos@@{\theta_{1}}-\cos@@{\theta_{2}}}\Diracdelta@{\phi_{1}-\phi_{2}} = \sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell}\sphharmonicY{\ell}{m}@{\theta_{1}}{\phi_{1}}\conj{\sphharmonicY{\ell}{m}@{\theta_{2}}{\phi_{2}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Dirac(cos(theta[1])- cos(theta[2]))*Dirac(phi[1]- phi[2]) = sum(sum(SphericalY(ell, m, theta[1], phi[1])*conjugate(SphericalY(ell, m, theta[2], phi[2])), m = - ell..ell), ell = 0..infinity) |
DiracDelta[Cos[Subscript[\[Theta], 1]]- Cos[Subscript[\[Theta], 2]]]*DiracDelta[Subscript[\[Phi], 1]- Subscript[\[Phi], 2]] == Sum[Sum[SphericalHarmonicY[\[ScriptL], m, Subscript[\[Theta], 1], Subscript[\[Phi], 1]]*Conjugate[SphericalHarmonicY[\[ScriptL], m, Subscript[\[Theta], 2], Subscript[\[Phi], 2]]], {m, - \[ScriptL], \[ScriptL]}, GenerateConditions->None], {\[ScriptL], 0, Infinity}, GenerateConditions->None] |
Aborted | Failure | Skipped - Because timed out | Skipped - Because timed out |