Results of Numerical Methods
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 3.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{A}\mathbf{x} = \mathbf{b}} | A*x = b |
A*x == b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{A} = \mathbf{L}\mathbf{U}} | A = L*U |
A == L*U |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y_{j} = f_{j}-\ell_{j}y_{j-1}} | y[j] = f[j]- ell[j]*y[j - 1] |
Subscript[y, j] == Subscript[f, j]- Subscript[\[ScriptL], j]*Subscript[y, j - 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{j} = (y_{j}-u_{j}x_{j+1})/d_{j}} | x[j] = (y[j]- u[j]*x[j + 1])/ d[j] |
Subscript[x, j] == (Subscript[y, j]- Subscript[u, j]*Subscript[x, j + 1])/ Subscript[d, j] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\mathbf{x}\|_{p} = \left(\sum_{j=1}^{n}\abs{x_{j}}^{p}\right)^{1/p}} | abs(x)[p] = (sum((abs(x[j]))^(p), j = 1..n))^(1/ p) |
Subscript[Abs[x], p] == ((Sum[(Abs[Subscript[x, j]])^(p), {j, 1, n}, GenerateConditions->None]))^(1/ p) |
Failure | Failure | Error | Failed [300 / 300]
{Plus[-1.0, Subscript[1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {Rule[n, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-1.7142646344505674, 0.6191072997114272], Subscript[1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {Rule[n, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\|\mathbf{x}^{*}-\mathbf{x}\|_{p}}{\|\mathbf{x}\|_{p}} \leq \kappa(\mathbf{A})\frac{\|\mathbf{r}\|_{p}}{\|\mathbf{b}\|_{p}}} | (abs((x)^(*)- x)[p])/(abs(x)[p]) <= kappa*(A)*(abs(r)[p])/(abs(b)[p]) |
Divide[Subscript[Abs[(x)^(*)- x], p],Subscript[Abs[x], p]] <= \[Kappa]*(A)*Divide[Subscript[Abs[r], p],Subscript[Abs[b], p]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{A}\mathbf{x} = \lambda\mathbf{x}} | A*x = lambda*x |
A*x == \[Lambda]*x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P_{n}(z) = \sum_{k=0}^{n}\ell_{k}(z)f_{k}} | P[n]*(z) = sum(ell[k]*(z)* f[k], k = 0..n) |
Subscript[P, n]*(z) == Sum[Subscript[\[ScriptL], k]*(z)* Subscript[f, k], {k, 0, n}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n_{0} = -\tfrac{1}{2}(n-\sigma)} | n[0] = -(1)/(2)*(n - sigma) |
Subscript[n, 0] == -Divide[1,2]*(n - \[Sigma]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n_{1} = \tfrac{1}{2}(n+\sigma)} | n[1] = (1)/(2)*(n + sigma) |
Subscript[n, 1] == Divide[1,2]*(n + \[Sigma]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma = \tfrac{1}{2}(1-(-1)^{n})} | sigma = (1)/(2)*(1 -(- 1)^(n)) |
\[Sigma] == Divide[1,2]*(1 -(- 1)^(n)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = (1-t)f_{0}+tf_{1}+R_{1,t}} | f[t] = (1 - t)* f[0]+ t*f[1]+ R[1 , t] |
Subscript[f, t] == (1 - t)* Subscript[f, 0]+ t*Subscript[f, 1]+ Subscript[R, 1 , t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{1} = \tfrac{1}{8}} | c[1] = (1)/(8) |
Subscript[c, 1] == Divide[1,8] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-1}^{1}A_{k}^{2}f_{k}+R_{2,t}} | f[t] sum(A(A[k])^(2)*f[k], k = - 1..1)+ R[2 , t] |
Subscript[f, t] Sum[A(Subscript[A, k])^(2)*Subscript[f, k], {k, - 1, 1}, GenerateConditions->None]+ Subscript[R, 2 , t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{2} = \tfrac{1}{2}t(t-1)} | (A[- 1])^(2) = (1)/(2)*t*(t - 1) |
(Subscript[A, - 1])^(2) == Divide[1,2]*t*(t - 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{2} = 1-t^{2}} | (A[0])^(2) = 1 - (t)^(2) |
(Subscript[A, 0])^(2) == 1 - (t)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{2} = \tfrac{1}{2}t(t+1)} | (A[1])^(2) = (1)/(2)*t*(t + 1) |
(Subscript[A, 1])^(2) == Divide[1,2]*t*(t + 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{2} = 1/(9\sqrt{3})} | c[2] = 1/(9*sqrt(3)) |
Subscript[c, 2] == 1/(9*Sqrt[3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-1}^{2}A_{k}^{3}f_{k}+R_{3,t}} | f[t] sum(A(A[k])^(3)*f[k], k = - 1..2)+ R[3 , t] |
Subscript[f, t] Sum[A(Subscript[A, k])^(3)*Subscript[f, k], {k, - 1, 2}, GenerateConditions->None]+ Subscript[R, 3 , t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{3} = -\tfrac{1}{6}t(t-1)(t-2)} | (A[- 1])^(3) = -(1)/(6)*t*(t - 1)*(t - 2) |
(Subscript[A, - 1])^(3) == -Divide[1,6]*t*(t - 1)*(t - 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{3} = \tfrac{1}{2}(t^{2}-1)(t-2)} | (A[0])^(3) = (1)/(2)*((t)^(2)- 1)*(t - 2) |
(Subscript[A, 0])^(3) == Divide[1,2]*((t)^(2)- 1)*(t - 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{3} = -\tfrac{1}{2}t(t+1)(t-2)} | (A[1])^(3) = -(1)/(2)*t*(t + 1)*(t - 2) |
(Subscript[A, 1])^(3) == -Divide[1,2]*t*(t + 1)*(t - 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{3} = \tfrac{1}{6}t(t^{2}-1)} | (A[2])^(3) = (1)/(6)*t*((t)^(2)- 1) |
(Subscript[A, 2])^(3) == Divide[1,6]*t*((t)^(2)- 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-2}^{2}A_{k}^{4}f_{k}+R_{4,t}} | f[t] sum(A(A[k])^(4)*f[k], k = - 2..2)+ R[4 , t] |
Subscript[f, t] Sum[A(Subscript[A, k])^(4)*Subscript[f, k], {k, - 2, 2}, GenerateConditions->None]+ Subscript[R, 4 , t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t-2)} | (A[- 2])^(4) = (1)/(24)*t*((t)^(2)- 1)*(t - 2) |
(Subscript[A, - 2])^(4) == Divide[1,24]*t*((t)^(2)- 1)*(t - 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{4} = -\tfrac{1}{6}t(t-1)(t^{2}-4)} | (A[- 1])^(4) = -(1)/(6)*t*(t - 1)*((t)^(2)- 4) |
(Subscript[A, - 1])^(4) == -Divide[1,6]*t*(t - 1)*((t)^(2)- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{4} = \tfrac{1}{4}(t^{2}-1)(t^{2}-4)} | (A[0])^(4) = (1)/(4)*((t)^(2)- 1)*((t)^(2)- 4) |
(Subscript[A, 0])^(4) == Divide[1,4]*((t)^(2)- 1)*((t)^(2)- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{4} = -\tfrac{1}{6}t(t+1)(t^{2}-4)} | (A[1])^(4) = -(1)/(6)*t*(t + 1)*((t)^(2)- 4) |
(Subscript[A, 1])^(4) == -Divide[1,6]*t*(t + 1)*((t)^(2)- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t+2)} | (A[2])^(4) = (1)/(24)*t*((t)^(2)- 1)*(t + 2) |
(Subscript[A, 2])^(4) == Divide[1,24]*t*((t)^(2)- 1)*(t + 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-2}^{3}A_{k}^{5}f_{k}+R_{5,t}} | f[t] sum(A(A[k])^(5)*f[k], k = - 2..3)+ R[5 , t] |
Subscript[f, t] Sum[A(Subscript[A, k])^(5)*Subscript[f, k], {k, - 2, 3}, GenerateConditions->None]+ Subscript[R, 5 , t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-2}^{5} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t-3)} | (A[- 2])^(5) = -(1)/(120)*t*((t)^(2)- 1)*(t - 2)*(t - 3) |
(Subscript[A, - 2])^(5) == -Divide[1,120]*t*((t)^(2)- 1)*(t - 2)*(t - 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{5} = \tfrac{1}{24}t(t-1)(t^{2}-4)(t-3)} | (A[- 1])^(5) = (1)/(24)*t*(t - 1)*((t)^(2)- 4)*(t - 3) |
(Subscript[A, - 1])^(5) == Divide[1,24]*t*(t - 1)*((t)^(2)- 4)*(t - 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{5} = -\tfrac{1}{12}(t^{2}-1)(t^{2}-4)(t-3)} | (A[0])^(5) = -(1)/(12)*((t)^(2)- 1)*((t)^(2)- 4)*(t - 3) |
(Subscript[A, 0])^(5) == -Divide[1,12]*((t)^(2)- 1)*((t)^(2)- 4)*(t - 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{5} = \tfrac{1}{12}t(t+1)(t^{2}-4)(t-3)} | (A[1])^(5) = (1)/(12)*t*(t + 1)*((t)^(2)- 4)*(t - 3) |
(Subscript[A, 1])^(5) == Divide[1,12]*t*(t + 1)*((t)^(2)- 4)*(t - 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{5} = -\tfrac{1}{24}t(t^{2}-1)(t+2)(t-3)} | (A[2])^(5) = -(1)/(24)*t*((t)^(2)- 1)*(t + 2)*(t - 3) |
(Subscript[A, 2])^(5) == -Divide[1,24]*t*((t)^(2)- 1)*(t + 2)*(t - 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{3}^{5} = \tfrac{1}{120}t(t^{2}-1)(t^{2}-4)} | (A[3])^(5) = (1)/(120)*t*((t)^(2)- 1)*((t)^(2)- 4) |
(Subscript[A, 3])^(5) == Divide[1,120]*t*((t)^(2)- 1)*((t)^(2)- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-3}^{3}A_{k}^{6}f_{k}+R_{6,t}} | f[t] sum(A(A[k])^(6)*f[k], k = - 3..3)+ R[6 , t] |
Subscript[f, t] Sum[A(Subscript[A, k])^(6)*Subscript[f, k], {k, - 3, 3}, GenerateConditions->None]+ Subscript[R, 6 , t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t-3)(t^{2}-4)} | (A[- 3])^(6) = (1)/(720)*t*((t)^(2)- 1)*(t - 3)*((t)^(2)- 4) |
(Subscript[A, - 3])^(6) == Divide[1,720]*t*((t)^(2)- 1)*(t - 3)*((t)^(2)- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t^{2}-9)} | (A[- 2])^(6) = -(1)/(120)*t*((t)^(2)- 1)*(t - 2)*((t)^(2)- 9) |
(Subscript[A, - 2])^(6) == -Divide[1,120]*t*((t)^(2)- 1)*(t - 2)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{6} = \tfrac{1}{48}t(t-1)(t^{2}-4)(t^{2}-9)} | (A[- 1])^(6) = (1)/(48)*t*(t - 1)*((t)^(2)- 4)*((t)^(2)- 9) |
(Subscript[A, - 1])^(6) == Divide[1,48]*t*(t - 1)*((t)^(2)- 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{6} = -\tfrac{1}{36}(t^{2}-1)(t^{2}-4)(t^{2}-9)} | (A[0])^(6) = -(1)/(36)*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9) |
(Subscript[A, 0])^(6) == -Divide[1,36]*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{6} = \tfrac{1}{48}t(t+1)(t^{2}-4)(t^{2}-9)} | (A[1])^(6) = (1)/(48)*t*(t + 1)*((t)^(2)- 4)*((t)^(2)- 9) |
(Subscript[A, 1])^(6) == Divide[1,48]*t*(t + 1)*((t)^(2)- 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t+2)(t^{2}-9)} | (A[2])^(6) = -(1)/(120)*t*((t)^(2)- 1)*(t + 2)*((t)^(2)- 9) |
(Subscript[A, 2])^(6) == -Divide[1,120]*t*((t)^(2)- 1)*(t + 2)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t+3)(t^{2}-4)} | (A[3])^(6) = (1)/(720)*t*((t)^(2)- 1)*(t + 3)*((t)^(2)- 4) |
(Subscript[A, 3])^(6) == Divide[1,720]*t*((t)^(2)- 1)*(t + 3)*((t)^(2)- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-3}^{4}A_{k}^{7}f_{k}+R_{7,t}} | f[t] sum(A(A[k])^(7)*f[k], k = - 3..4)+ R[7 , t] |
Subscript[f, t] Sum[A(Subscript[A, k])^(7)*Subscript[f, k], {k, - 3, 4}, GenerateConditions->None]+ Subscript[R, 7 , t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-3}^{7} = -\tfrac{1}{5040}t(t^{2}-1)(t-3)(t-4)(t^{2}-4)} | (A[- 3])^(7) = -(1)/(5040)*t*((t)^(2)- 1)*(t - 3)*(t - 4)*((t)^(2)- 4) |
(Subscript[A, - 3])^(7) == -Divide[1,5040]*t*((t)^(2)- 1)*(t - 3)*(t - 4)*((t)^(2)- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-2}^{7} = \tfrac{1}{720}t(t^{2}-1)(t-2)(t-4)(t^{2}-9)} | (A[- 2])^(7) = (1)/(720)*t*((t)^(2)- 1)*(t - 2)*(t - 4)*((t)^(2)- 9) |
(Subscript[A, - 2])^(7) == Divide[1,720]*t*((t)^(2)- 1)*(t - 2)*(t - 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{7} = -\tfrac{1}{240}t(t-1)(t-4)(t^{2}-4)(t^{2}-9)} | (A[- 1])^(7) = -(1)/(240)*t*(t - 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9) |
(Subscript[A, - 1])^(7) == -Divide[1,240]*t*(t - 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{7} = \tfrac{1}{144}(t^{2}-1)(t-4)(t^{2}-4)(t^{2}-9)} | (A[0])^(7) = (1)/(144)*((t)^(2)- 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9) |
(Subscript[A, 0])^(7) == Divide[1,144]*((t)^(2)- 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{7} = -\tfrac{1}{144}t(t+1)(t-4)(t^{2}-4)(t^{2}-9)} | (A[1])^(7) = -(1)/(144)*t*(t + 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9) |
(Subscript[A, 1])^(7) == -Divide[1,144]*t*(t + 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{7} = \tfrac{1}{240}t(t^{2}-1)(t+2)(t-4)(t^{2}-9)} | (A[2])^(7) = (1)/(240)*t*((t)^(2)- 1)*(t + 2)*(t - 4)*((t)^(2)- 9) |
(Subscript[A, 2])^(7) == Divide[1,240]*t*((t)^(2)- 1)*(t + 2)*(t - 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{3}^{7} = -\tfrac{1}{720}t(t^{2}-1)(t+3)(t-4)(t^{2}-4)} | (A[3])^(7) = -(1)/(720)*t*((t)^(2)- 1)*(t + 3)*(t - 4)*((t)^(2)- 4) |
(Subscript[A, 3])^(7) == -Divide[1,720]*t*((t)^(2)- 1)*(t + 3)*(t - 4)*((t)^(2)- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{4}^{7} = \tfrac{1}{5040}t(t^{2}-1)(t^{2}-4)(t^{2}-9)} | (A[4])^(7) = (1)/(5040)*t*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9) |
(Subscript[A, 4])^(7) == Divide[1,5040]*t*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f = f_{0}} | f = f[0] |
f == Subscript[f, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f = ({[z_{1}]}f-{[z_{0}]}f)/(z_{1}-z_{0})} | f = ([z[1]]*f -[z[0]]*f)/(z[1]- z[0]) |
f == ([Subscript[z, 1]]*f -[Subscript[z, 0]]*f)/(Subscript[z, 1]- Subscript[z, 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3#Ex40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f = ({[z_{1},z_{2}]}f-{[z_{0},z_{1}]}f)/(z_{2}-z_{0})} | f = ([z[1], z[2]]*f -[z[0], z[1]]*f)/(z[2]- z[0]) |
f == ([Subscript[z, 1], Subscript[z, 2]]*f -[Subscript[z, 0], Subscript[z, 1]]*f)/(Subscript[z, 2]- Subscript[z, 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(f) = [f_{0}]x+(f-f_{0})[f_{0},f_{1}]x+(f-f_{0})(f-f_{1})[f_{0},f_{1},f_{2}]x} | x*(f) = [f[0]]* x +(f - f[0])[f[0], f[1]]* x +(f - f[0])*(f - f[1])[f[0], f[1], f[2]]* x |
x*(f) == [Subscript[f, 0]]* x +(f - Subscript[f, 0])[Subscript[f, 0], Subscript[f, 1]]* x +(f - Subscript[f, 0])*(f - Subscript[f, 1])[Subscript[f, 0], Subscript[f, 1], Subscript[f, 2]]* x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.3.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = -2.2+1.44011\;1973(f-0.09614\;53780)+0.08865\;85832\*(f-0.09614\;53780)(f-0.02670\;63331)} | x = - 2.2 + 1.440111973*(f - 0.0961453780)+ 0.0886585832 *(f - 0.0961453780)*(f - 0.0267063331) |
x == - 2.2 + 1.440111973*(f - 0.0961453780)+ 0.0886585832 *(f - 0.0961453780)*(f - 0.0267063331) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-1}^{3} = -\tfrac{1}{6}(2-6t+3t^{2})} | (B[- 1])^(3) = -(1)/(6)*(2 - 6*t + 3*(t)^(2)) |
(Subscript[B, - 1])^(3) == -Divide[1,6]*(2 - 6*t + 3*(t)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0}^{3} = -\tfrac{1}{2}(1+4t-3t^{2})} | (B[0])^(3) = -(1)/(2)*(1 + 4*t - 3*(t)^(2)) |
(Subscript[B, 0])^(3) == -Divide[1,2]*(1 + 4*t - 3*(t)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1}^{3} = \tfrac{1}{2}(2+2t-3t^{2})} | (B[1])^(3) = (1)/(2)*(2 + 2*t - 3*(t)^(2)) |
(Subscript[B, 1])^(3) == Divide[1,2]*(2 + 2*t - 3*(t)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2}^{3} = -\tfrac{1}{6}(1-3t^{2})} | (B[2])^(3) = -(1)/(6)*(1 - 3*(t)^(2)) |
(Subscript[B, 2])^(3) == -Divide[1,6]*(1 - 3*(t)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-2}^{4} = \tfrac{1}{12}(1-t-3t^{2}+2t^{3})} | (B[- 2])^(4) = (1)/(12)*(1 - t - 3*(t)^(2)+ 2*(t)^(3)) |
(Subscript[B, - 2])^(4) == Divide[1,12]*(1 - t - 3*(t)^(2)+ 2*(t)^(3)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-1}^{4} = -\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})} | (B[- 1])^(4) = -(1)/(6)*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3)) |
(Subscript[B, - 1])^(4) == -Divide[1,6]*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0}^{4} = -\tfrac{1}{2}t(5-2t^{2})} | (B[0])^(4) = -(1)/(2)*t*(5 - 2*(t)^(2)) |
(Subscript[B, 0])^(4) == -Divide[1,2]*t*(5 - 2*(t)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1}^{4} = \tfrac{1}{6}(4+8t-3t^{2}-4t^{3})} | (B[1])^(4) = (1)/(6)*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3)) |
(Subscript[B, 1])^(4) == Divide[1,6]*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2}^{4} = -\tfrac{1}{12}(1+t-3t^{2}-2t^{3})} | (B[2])^(4) = -(1)/(12)*(1 + t - 3*(t)^(2)- 2*(t)^(3)) |
(Subscript[B, 2])^(4) == -Divide[1,12]*(1 + t - 3*(t)^(2)- 2*(t)^(3)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-2}^{5} = \tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5t^{4})} | (B[- 2])^(5) = (1)/(120)*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4)) |
(Subscript[B, - 2])^(5) == Divide[1,120]*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-1}^{5} = -\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5t^{4})} | (B[- 1])^(5) = -(1)/(24)*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4)) |
(Subscript[B, - 1])^(5) == -Divide[1,24]*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0}^{5} = -\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t^{4})} | (B[0])^(5) = -(1)/(12)*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4)) |
(Subscript[B, 0])^(5) == -Divide[1,12]*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1}^{5} = \tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^{4})} | (B[1])^(5) = (1)/(12)*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4)) |
(Subscript[B, 1])^(5) == Divide[1,12]*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2}^{5} = -\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{4})} | (B[2])^(5) = -(1)/(24)*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4)) |
(Subscript[B, 2])^(5) == -Divide[1,24]*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{3}^{5} = \tfrac{1}{120}(4-15t^{2}+5t^{4})} | (B[3])^(5) = (1)/(120)*(4 - 15*(t)^(2)+ 5*(t)^(4)) |
(Subscript[B, 3])^(5) == Divide[1,120]*(4 - 15*(t)^(2)+ 5*(t)^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-3}^{6} = -\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+15t^{4}-6t^{5})} | (B[- 3])^(6) = -(1)/(720)*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5)) |
(Subscript[B, - 3])^(6) == -Divide[1,720]*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-2}^{6} = \tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5})} | (B[- 2])^(6) = (1)/(60)*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5)) |
(Subscript[B, - 2])^(6) == Divide[1,60]*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-1}^{6} = -\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+5t^{4}-6t^{5})} | (B[- 1])^(6) = -(1)/(48)*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5)) |
(Subscript[B, - 1])^(6) == -Divide[1,48]*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0}^{6} = -\tfrac{1}{18}t(49-28t^{2}+3t^{4})} | (B[0])^(6) = -(1)/(18)*t*(49 - 28*(t)^(2)+ 3*(t)^(4)) |
(Subscript[B, 0])^(6) == -Divide[1,18]*t*(49 - 28*(t)^(2)+ 3*(t)^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1}^{6} = \tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t^{4}+6t^{5})} | (B[1])^(6) = (1)/(48)*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5)) |
(Subscript[B, 1])^(6) == Divide[1,48]*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2}^{6} = -\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5})} | (B[2])^(6) = -(1)/(60)*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5)) |
(Subscript[B, 2])^(6) == -Divide[1,60]*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{3}^{6} = \tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15t^{4}+6t^{5})} | (B[3])^(6) = (1)/(720)*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5)) |
(Subscript[B, 3])^(6) == Divide[1,720]*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-3}^{7} = -\tfrac{1}{5040}(48-56t-168t^{2}+140t^{3}+35t^{4}-42t^{5}+7t^{6})} | (B[- 3])^(7) = -(1)/(5040)*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6)) |
(Subscript[B, - 3])^(7) == -Divide[1,5040]*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-2}^{7} = \tfrac{1}{720}(72-108t-213t^{2}+240t^{3}-10t^{4}-36t^{5}+7t^{6})} | (B[- 2])^(7) = (1)/(720)*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6)) |
(Subscript[B, - 2])^(7) == Divide[1,720]*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-1}^{7} = -\tfrac{1}{240}(144-360t-48t^{2}+260t^{3}-45t^{4}-30t^{5}+7t^{6})} | (B[- 1])^(7) = -(1)/(240)*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6)) |
(Subscript[B, - 1])^(7) == -Divide[1,240]*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0}^{7} = -\tfrac{1}{144}(36+392t-147t^{2}-224t^{3}+70t^{4}+24t^{5}-7t^{6})} | (B[0])^(7) = -(1)/(144)*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6)) |
(Subscript[B, 0])^(7) == -Divide[1,144]*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1}^{7} = \tfrac{1}{144}(144+216t-264t^{2}-156t^{3}+85t^{4}+18t^{5}-7t^{6})} | (B[1])^(7) = (1)/(144)*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6)) |
(Subscript[B, 1])^(7) == Divide[1,144]*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2}^{7} = -\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}+90t^{4}+12t^{5}-7t^{6})} | (B[2])^(7) = -(1)/(240)*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6)) |
(Subscript[B, 2])^(7) == -Divide[1,240]*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{3}^{7} = \tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+85t^{4}+6t^{5}-7t^{6})} | (B[3])^(7) = (1)/(720)*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6)) |
(Subscript[B, 3])^(7) == Divide[1,720]*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4#Ex30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{4}^{7} = -\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t^{6})} | (B[4])^(7) = -(1)/(5040)*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6)) |
(Subscript[B, 4])^(7) == -Divide[1,5040]*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.4.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}} | (1)/(factorial(k)) = (1)/(2*Pi*(r)^(k))*int(exp(r*cos(theta))*cos(r*sin(theta)- k*theta), theta = 0..2*Pi) |
Divide[1,(k)!] == Divide[1,2*Pi*(r)^(k)]*Integrate[Exp[r*Cos[\[Theta]]]*Cos[r*Sin[\[Theta]]- k*\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] |
Failure | Error | Failed [18 / 18] 18/18]: [[1. <- {r = -1.5, k = 1}.5000000000 <- {r = -1.5, k = 2}.1666666667 <- {r = -1.5, k = 3}1. <- {r = 1.5, k = 1}... skip entries to safe data |
Skipped - Because timed out |
| 3.5.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-pt}\BesselJ{0}@{t}\diff{t} = \frac{1}{\sqrt{p^{2}+1}}} | int(exp(- p*t)*BesselJ(0, t), t = 0..infinity) = (1)/(sqrt((p)^(2)+ 1)) |
Integrate[Exp[- p*t]*BesselJ[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,Sqrt[(p)^(2)+ 1]] |
Successful | Error | - | Failed [5 / 10]
{Complex[-1.732050807568877, -1.0] <- {Rule[p, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[-1.4678898250138706, 0.39331989319032856] <- {Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} |
| 3.5.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \frac{g_{k}}{n}\left(1-\sum_{j=1}^{\floor{n/2}}\frac{b_{j}}{4j^{2}-1}\cos@{2jk\cpi/n}\right)} | w[k] = (g[k])/(n)*(1 - sum((b[j])/(4*(j)^(2)- 1)*cos(2*j*k*Pi/ n), j = 1..floor(n/ 2))) |
Subscript[w, k] == Divide[Subscript[g, k],n]*(1 - Sum[Divide[Subscript[b, j],4*(j)^(2)- 1]*Cos[2*j*k*Pi/ n], {j, 1, Floor[n/ 2]}, GenerateConditions->None]) |
Failure | Failure | Failed [290 / 300] 290/300]: [[.3496793685+.1056624326*I <- {b[j] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}.5495724917+.2852208110*I <- {b[j] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}.5163460354+.3943375674*I <- {b[j] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 2}.5495724917+.2852208110*I <- {b[j] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 3}... skip entries to safe data |
Skipped - Because timed out |
| 3.5.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle E_{n}(f) = \gamma_{n}f^{(2n)}(\xi)/(2n)!} | E[n]*(f) = gamma[n]*(f)^(2*n)*(xi)/factorial(2*n) |
Subscript[E, n]*(f) == Subscript[\[Gamma], n]*(f)^(2*n)*(\[Xi])/(2*n)! |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle [a,b] = [-1,1]} | [a , b] = [- 1 , 1] |
[a , b] == [- 1 , 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = 1} | w*(x) = 1 |
w*(x) == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \frac{2^{2n+1}}{2n+1}\,\frac{(n!)^{4}}{((2n)!)^{2}}} | gamma[n] = ((2)^(2*n + 1))/(2*n + 1)*((factorial(n))^(4))/((factorial(2*n))^(2)) |
Subscript[\[Gamma], n] == Divide[(2)^(2*n + 1),2*n + 1]*Divide[((n)!)^(4),((2*n)!)^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle [a,b] = [-1,1]} | [a , b] = [- 1 , 1] |
[a , b] == [- 1 , 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = (1-x^{2})^{-1/2}} | w*(x) = (1 - (x)^(2))^(- 1/ 2) |
w*(x) == (1 - (x)^(2))^(- 1/ 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \frac{\cpi}{2^{2n-1}}} | gamma[n] = (Pi)/((2)^(2*n - 1)) |
Subscript[\[Gamma], n] == Divide[Pi,(2)^(2*n - 1)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.570796327 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}-.3926990818 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}-.9817477044e-1 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}-1.570796327 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [300 / 300]
{-1.5707963267948966 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}-0.39269908169872414 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{k} = \cos@{\frac{2k-1}{2n}\cpi}} | x[k] = cos((2*k - 1)/(2*n)*Pi) |
Subscript[x, k] == Cos[Divide[2*k - 1,2*n]*Pi] |
Failure | Failure | Failed [90 / 90] 90/90]: [[.8660254042+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}.1589186229+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}.2e-9+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}.8660254034+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}... skip entries to safe data |
Failed [90 / 90]
{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 1], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.15891862259789125, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 2], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \frac{\cpi}{n}} | w[k] = (Pi)/(n) |
Subscript[w, k] == Divide[Pi,n] |
Failure | Failure | Failed [30 / 30] 30/30]: [[-2.275567250+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}-.7047709230+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}-.1811721470+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}-3.641592654+.8660254040*I <- {w[k] = -1/2+1/2*I*3^(1/2), k = 1, n = 1}... skip entries to safe data |
Failed [90 / 90]
{Complex[-2.2755672498053543, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 1], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.7047709230104579, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 2], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{k} = \cos@{\frac{k}{n+1}\cpi}} | x[k] = cos((k)/(n + 1)*Pi) |
Subscript[x, k] == Cos[Divide[k,n + 1]*Pi] |
Failure | Failure | Failed [88 / 90] 88/90]: [[.8660254042+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}.3660254038+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}.1589186229+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}1.866025404+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}... skip entries to safe data |
Failed [88 / 90]
{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 1], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.3660254037844387, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 2], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \frac{\cpi}{n+1}\sin^{2}@{\frac{k}{n+1}\cpi}} | w[k] = (Pi)/(n + 1)*(sin((k)/(n + 1)*Pi))^(2) |
Subscript[w, k] == Divide[Pi,n + 1]*(Sin[Divide[k,n + 1]*Pi])^(2) |
Failure | Failure | Failed [90 / 90] 90/90]: [[-.7047709230+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}.806272408e-1+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}.4733263222+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}.8660254040+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}... skip entries to safe data |
Failed [90 / 90]
{Complex[-0.7047709230104579, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 1], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.08062724038699043, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 2], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \frac{\cpi}{2^{2n+1}}} | gamma[n] = (Pi)/((2)^(2*n + 1)) |
Subscript[\[Gamma], n] == Divide[Pi,(2)^(2*n + 1)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.3926990818 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}-.9817477044e-1 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}-.2454369261e-1 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}-.3926990818 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [300 / 300]
{-0.39269908169872414 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}-0.09817477042468103 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{k} = +\cos@{\frac{2k}{2n+1}\cpi}} | x[k] = + cos((2*k)/(2*n + 1)*Pi) |
Subscript[x, k] == + Cos[Divide[2*k,2*n + 1]*Pi] |
Failure | Failure | Failed [88 / 90] 88/90]: [[1.366025404+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}.5570084102+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}.2425356024+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}1.366025403+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}... skip entries to safe data |
Failed [88 / 90]
{Complex[1.3660254037844388, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 1], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5570084094094913, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 2], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{k} = -\cos@{\frac{2k}{2n+1}\cpi}} | x[k] = - cos((2*k)/(2*n + 1)*Pi) |
Subscript[x, k] == - Cos[Divide[2*k,2*n + 1]*Pi] |
Failure | Failure | Failed [88 / 90] 88/90]: [[.3660254043+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}1.175042398+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}1.489515206+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}.3660254051+.5000000000*I <- {x[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}... skip entries to safe data |
Failed [88 / 90]
{Complex[0.3660254037844387, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 1], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.1750423981593863, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 2], Rule[Subscript[x, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \frac{4\cpi}{2n+1}\sin^{2}@{\frac{k}{2n+1}\cpi}} | w[k] = (4*Pi)/(2*n + 1)*(sin((k)/(2*n + 1)*Pi))^(2) |
Subscript[w, k] == Divide[4*Pi,2*n + 1]*(Sin[Divide[k,2*n + 1]*Pi])^(2) |
Failure | Failure | Failed [90 / 90] 90/90]: [[-2.275567250+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 1}-.22894503e-2+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 2}.5280706399+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 1, n = 3}-2.275567248+.5000000000*I <- {w[k] = 1/2*3^(1/2)+1/2*I, k = 2, n = 1}... skip entries to safe data |
Failed [90 / 90]
{Complex[-2.2755672498053543, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 1], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.0022894499063851326, 0.49999999999999994] <- {Rule[k, 1], Rule[n, 2], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \frac{\cpi}{2^{2n}}} | gamma[n] = (Pi)/((2)^(2*n)) |
Subscript[\[Gamma], n] == Divide[Pi,(2)^(2*n)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.7853981635 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1, alpha = 1/2, beta = -1/2}-.1963495409 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2, alpha = 1/2, beta = -1/2}-.4908738522e-1 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3, alpha = 1/2, beta = -1/2}-.7853981635 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1, alpha = 1/2, beta = -1/2}... skip entries to safe data |
Failed [300 / 300]
{-0.7853981633974483 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, Rational[1, 2]], Rule[β, Rational[-1, 2]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}-0.19634954084936207 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, Rational[1, 2]], Rule[β, Rational[-1, 2]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle [a,b] = [-1,1]} | [a , b] = [- 1 , 1] |
[a , b] == [- 1 , 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = (1-x)^{\alpha}(1+x)^{\beta}} | w*(x) = (1 - x)^(alpha)*(1 + x)^(beta) |
w*(x) == (1 - x)^\[Alpha]*(1 + x)^\[Beta] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \dfrac{\EulerGamma@{n+\alpha+1}\EulerGamma@{n+\beta+1}\EulerGamma@{n+\alpha+\beta+1}}{(2n+\alpha+\beta+1)(\EulerGamma@{2n+\alpha+\beta+1})^{2}}2^{2n+\alpha+\beta+1}n!} | gamma[n] = (GAMMA(n + alpha + 1)*GAMMA(n + beta + 1)*GAMMA(n + alpha + beta + 1))/((2*n + alpha + beta + 1)*(GAMMA(2*n + alpha + beta + 1))^(2))*(2)^(2*n + alpha + beta + 1)* factorial(n) |
Subscript[\[Gamma], n] == Divide[Gamma[n + \[Alpha]+ 1]*Gamma[n + \[Beta]+ 1]*Gamma[n + \[Alpha]+ \[Beta]+ 1],(2*n + \[Alpha]+ \[Beta]+ 1)*(Gamma[2*n + \[Alpha]+ \[Beta]+ 1])^(2)]*(2)^(2*n + \[Alpha]+ \[Beta]+ 1)* (n)! |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.1963495408 <- {a = -1.5, alpha = 1.5, b = -1.5, beta = 1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}-.4090615438e-1 <- {a = -1.5, alpha = 1.5, b = -1.5, beta = 1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}-.9203884728e-2 <- {a = -1.5, alpha = 1.5, b = -1.5, beta = 1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}-.1963495408 <- {a = -1.5, alpha = 1.5, b = -1.5, beta = 1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Skipped - Because timed out |
| 3.5#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = x^{\alpha}e^{-x}} | w*(x) = (x)^(alpha)* exp(- x) |
w*(x) == (x)^\[Alpha]* Exp[- x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = n!\,\EulerGamma@{n+\alpha+1}} | gamma[n] = factorial(n)*GAMMA(n + alpha + 1) |
Subscript[\[Gamma], n] == (n)!*Gamma[n + \[Alpha]+ 1] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-3.323350970 <- {a = -1.5, alpha = 1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}-23.26345680 <- {a = -1.5, alpha = 1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}-314.0566667 <- {a = -1.5, alpha = 1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}-3.323350970 <- {a = -1.5, alpha = 1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [300 / 300]
{-3.3233509704478426 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}-23.2634567931349 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a,b) = (-\infty,\infty)} | (a , b) = (- infinity , infinity) |
(a , b) == (- Infinity , Infinity) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = e^{-x^{2}}} | w*(x) = exp(- (x)^(2)) |
w*(x) == Exp[- (x)^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \sqrt{\cpi}\,\frac{n!}{2^{n}}} | gamma[n] = sqrt(Pi)*(factorial(n))/((2)^(n)) |
Subscript[\[Gamma], n] == Sqrt[Pi]*Divide[(n)!,(2)^(n)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.8862269255 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 1}-.8862269255 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 2}-1.329340388 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, n = 3}-.8862269255 <- {a = -1.5, b = -1.5, w = 1/2*3^(1/2)+1/2*I, p[n] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [300 / 300]
{-0.8862269254527579 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}-0.8862269254527579 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle [a,b] = [0,1]} | [a , b] = [0 , 1] |
[a , b] == [0 , 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = \ln@{1/x}} | w*(x) = ln(1/ x) |
w*(x) == Log[1/ x] |
Failure | Failure | Failed [30 / 30] 30/30]: [[1.704503214+.7500000000*I <- {w = 1/2*3^(1/2)+1/2*I, x = 1.5}-.2601344786+.2500000000*I <- {w = 1/2*3^(1/2)+1/2*I, x = .5}2.425197989+1.*I <- {w = 1/2*3^(1/2)+1/2*I, x = 2}-.3445348919+1.299038106*I <- {w = -1/2+1/2*I*3^(1/2), x = 1.5}... skip entries to safe data |
Failed [30 / 30]
{Complex[1.7045032137848224, 0.7499999999999999] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}Complex[-0.26013447866772593, 0.24999999999999997] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]} |
| 3.5.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{k+1}(x) = (x-\alpha_{k})p_{k}(x)-\beta_{k}p_{k-1}(x)} | p[k + 1]*(x) = (x - alpha[k])* p[k]*(x)- beta[k]*p[k - 1]*(x) |
Subscript[p, k + 1]*(x) == (x - Subscript[\[Alpha], k])* Subscript[p, k]*(x)- Subscript[\[Beta], k]*Subscript[p, k - 1]*(x) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k} = \beta_{0}v_{k,1}^{2}} | w[k] = beta[0]*(v[k , 1])^(2) |
Subscript[w, k] == Subscript[\[Beta], 0]*(Subscript[v, k , 1])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.5.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{c-\iunit\infty}^{c+\iunit\infty}e^{\zeta}\zeta^{-s}p_{k}(1/\zeta)p_{\ell}(1/\zeta)\diff{\zeta} = 0} | int(exp(zeta)*(zeta)^(- s)* p[k]*(1/ zeta)* p[ell]*(1/ zeta), zeta = c - I*infinity..c + I*infinity) = 0 |
Integrate[Exp[\[Zeta]]*\[Zeta]^(- s)* Subscript[p, k]*(1/ \[Zeta])* Subscript[p, \[ScriptL]]*(1/ \[Zeta]), {\[Zeta], c - I*Infinity, c + I*Infinity}, GenerateConditions->None] == 0 |
Successful | Error | - | Failed [300 / 300]
{Complex[-3.0699801238394655, 1.7724538509055168] <- {Rule[c, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[Subscript[p, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-3.0699801238394655, 1.7724538509055168] <- {Rule[c, -1.5], Rule[k, 2], Rule[s, -1.5], Rule[Subscript[p, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.5.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{\lambda} = \frac{1}{2\cpi\iunit}\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\zeta-2\lambda\sqrt{\zeta}}\frac{\diff{\zeta}}{\zeta}} | erfc(lambda) = (1)/(2*Pi*I)*int(exp(zeta - 2*lambda*sqrt(zeta))*(1)/(zeta), zeta = c - I*infinity..c + I*infinity) |
Erfc[\[Lambda]] == Divide[1,2*Pi*I]*Integrate[Exp[\[Zeta]- 2*\[Lambda]*Sqrt[\[Zeta]]]*Divide[1,\[Zeta]], {\[Zeta], c - I*Infinity, c + I*Infinity}, GenerateConditions->None] |
Failure | Error | Failed [30 / 30] 30/30]: [[.9788588170e-1-.2531649186*I <- {c = 1.5, lambda = 1/2*3^(1/2)+1/2*I}1.977726380-.8570608782*I <- {c = 1.5, lambda = -1/2+1/2*I*3^(1/2)}.2227361984e-1+.8570608782*I <- {c = 1.5, lambda = 1/2-1/2*I*3^(1/2)}1.902114118+.2531649186*I <- {c = 1.5, lambda = -1/2*3^(1/2)-1/2*I}... skip entries to safe data |
Skipped - Because timed out |
| 3.5.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{\lambda} = \frac{1}{2\cpi\iunit}\int_{c-\iunit\infty}^{c+\iunit\infty}e^{\lambda^{2}(t-2\sqrt{t})}\frac{\diff{t}}{t}} | erfc(lambda) = (1)/(2*Pi*I)*int(exp((lambda)^(2)*(t - 2*sqrt(t)))*(1)/(t), t = c - I*infinity..c + I*infinity) |
Erfc[\[Lambda]] == Divide[1,2*Pi*I]*Integrate[Exp[\[Lambda]^(2)*(t - 2*Sqrt[t])]*Divide[1,t], {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None] |
Failure | Error | Failed [30 / 30] 30/30]: [[.9788588170e-1-.2531649186*I <- {c = 1.5, lambda = 1/2*3^(1/2)+1/2*I}1.977726380-.8570608782*I <- {c = 1.5, lambda = -1/2+1/2*I*3^(1/2)}.2227361984e-1+.8570608782*I <- {c = 1.5, lambda = 1/2-1/2*I*3^(1/2)}1.902114118+.2531649186*I <- {c = 1.5, lambda = -1/2*3^(1/2)-1/2*I}... skip entries to safe data |
Skipped - Because timed out |
| 3.5.E45 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{\lambda} = \frac{e^{-\lambda^{2}}}{2\cpi}\int_{-\cpi}^{\cpi}e^{-\lambda^{2}\tan^{2}@{\frac{1}{2}\theta}}\diff{\theta}} | erfc(lambda) = (exp(- (lambda)^(2)))/(2*Pi)*int(exp(- (lambda)^(2)* (tan((1)/(2)*theta))^(2)), theta = - Pi..Pi) |
Erfc[\[Lambda]] == Divide[Exp[- \[Lambda]^(2)],2*Pi]*Integrate[Exp[- \[Lambda]^(2)* (Tan[Divide[1,2]*\[Theta]])^(2)], {\[Theta], - Pi, Pi}, GenerateConditions->None] |
Failure | Failure | Failed [6 / 10] 6/10]: [[Float(infinity)+Float(infinity)*I <- {lambda = -1/2+1/2*I*3^(1/2)}Float(infinity)+Float(infinity)*I <- {lambda = 1/2-1/2*I*3^(1/2)}1.804228236+.5063298371*I <- {lambda = -1/2*3^(1/2)-1/2*I}1.932210292 <- {lambda = -1.5}... skip entries to safe data |
Failed [5 / 10]
{Complex[1.9554527597185267, -1.7141217559576072] <- {Rule[λ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[1.80422823640912, 0.5063298374329107] <- {Rule[λ, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} |
| 3.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n}w_{n+1}-b_{n}w_{n}+c_{n}w_{n-1} = 0} | a[n]*w[n + 1]- b[n]*w[n]+ c[n]*w[n - 1] = 0 |
Subscript[a, n]*Subscript[w, n + 1]- Subscript[b, n]*Subscript[w, n]+ Subscript[c, n]*Subscript[w, n - 1] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\lambda_{n}w_{n} = 1} | sum(lambda[n]*w[n], n = 0..infinity) = 1 |
Sum[Subscript[\[Lambda], n]*Subscript[w, n], {n, 0, Infinity}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.6.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{n+1}w_{n} = p_{n}w_{n+1}+e_{n}} | p[n + 1]*w[n] = p[n]*w[n + 1]+ exp(1)[n] |
Subscript[p, n + 1]*Subscript[w, n] == Subscript[p, n]*Subscript[w, n + 1]+ Subscript[E, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.6.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{n+1}-2nw_{n}+w_{n-1} = 0} | w[n + 1]- 2*n*w[n]+ w[n - 1] = 0 |
Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.6.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{n+1}-2nw_{n}+w_{n-1} = -(2/\cpi)(1-(-1)^{n})} | w[n + 1]- 2*n*w[n]+ w[n - 1] = -(2/ Pi)*(1 -(- 1)^(n)) |
Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1] == -(2/ Pi)*(1 -(- 1)^(n)) |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.273239544+0.*I <- {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 1}-1.732050808-1.000000000*I <- {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 2}-2.190862072-2.000000000*I <- {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 3}-.927858596e-1+.3660254040*I <- {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [300 / 300]
{1.2732395447351628 <- {Rule[n, 1], Rule[Subscript[w, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.7320508075688774, -0.9999999999999999] <- {Rule[n, 2], Rule[Subscript[w, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n}w_{n+1}-b_{n}w_{n} = d_{n}} | a[n]*w[n + 1]- b[n]*w[n] = d[n] |
Subscript[a, n]*Subscript[w, n + 1]- Subscript[b, n]*Subscript[w, n] == Subscript[d, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{11}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}f_{s}(z)} | A[11]*(tau , z) = sum(((tau)^(s))/(factorial(s))*f[s]*(z), s = 0..infinity) |
Subscript[A, 11]*(\[Tau], z) == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[f, s]*(z), {s, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{12}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}g_{s}(z)} | A[12]*(tau , z) = sum(((tau)^(s))/(factorial(s))*g[s]*(z), s = 0..infinity) |
Subscript[A, 12]*(\[Tau], z) == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[g, s]*(z), {s, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{21}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}f_{s+1}(z)} | A[21]*(tau , z) = sum(((tau)^(s))/(factorial(s))*f[s + 1]*(z), s = 0..infinity) |
Subscript[A, 21]*(\[Tau], z) == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[f, s + 1]*(z), {s, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{22}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}g_{s+1}(z)} | A[22]*(tau , z) = sum(((tau)^(s))/(factorial(s))*g[s + 1]*(z), s = 0..infinity) |
Subscript[A, 22]*(\[Tau], z) == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[g, s + 1]*(z), {s, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}h_{s}(z)} | b[1]*(tau , z) = sum(((tau)^(s))/(factorial(s))*h[s]*(z), s = 0..infinity) |
Subscript[b, 1]*(\[Tau], z) == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[h, s]*(z), {s, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{2}(\tau,z) = \sum_{s=0}^{\infty}\frac{\tau^{s}}{s!}h_{s+1}(z)} | b[2]*(tau , z) = sum(((tau)^(s))/(factorial(s))*h[s + 1]*(z), s = 0..infinity) |
Subscript[b, 2]*(\[Tau], z) == Sum[Divide[\[Tau]^(s),(s)!]*Subscript[h, s + 1]*(z), {s, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{A}\mathbf{w} = \mathbf{b}} | A*w = b |
A*w == b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w_{k}}{x}+(\lambda_{k}-q(x))w_{k} = 0} | diff(w[k], [x$(2)])+(lambda[k]- q*(x))* w[k] = 0 |
D[Subscript[w, k], {x, 2}]+(Subscript[\[Lambda], k]- q*(x))* Subscript[w, k] == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.2500000002-.4330127020*I <- {lambda = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, x = 1.5, lambda[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 1}-.2500000002-.4330127020*I <- {lambda = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, x = 1.5, lambda[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 2}-.2500000002-.4330127020*I <- {lambda = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, x = 1.5, lambda[k] = 1/2*3^(1/2)+1/2*I, w[k] = 1/2*3^(1/2)+1/2*I, k = 3}.4330127020-.2500000002*I <- {lambda = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, x = 1.5, lambda[k] = 1/2*3^(1/2)+1/2*I, w[k] = -1/2+1/2*I*3^(1/2), k = 1}... skip entries to safe data |
Failed [300 / 300]
{Complex[-0.25000000000000006, -0.43301270189221924] <- {Rule[k, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.25000000000000006, -0.43301270189221924] <- {Rule[k, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.7.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{k}(a) = w_{k}(b)} | w[k]*(a) = w[k]*(b) |
Subscript[w, k]*(a) == Subscript[w, k]*(b) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.7.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda_{1} < \lambda_{2}} | lambda[1] < lambda[2] |
Subscript[\[Lambda], 1] < Subscript[\[Lambda], 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \phi(z)} | z = phi*(z) |
z == \[Phi]*(z) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}} | abs(z[n + 1]- zeta) < A*(abs(z[n]- zeta))^(p) |
Abs[Subscript[z, n + 1]- \[Zeta]] < A*(Abs[Subscript[z, n]- \[Zeta]])^(p) |
Failure | Failure | Failed [30 / 300] 30/300]: [[0. < 0. <- {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = 1/2*3^(1/2)+1/2*I, n = 1}0. < 0. <- {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = 1/2*3^(1/2)+1/2*I, n = 2}0. < 0. <- {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = 1/2*3^(1/2)+1/2*I, n = 3}1.414213562 < 0. <- {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [300 / 300]
{False <- {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}False <- {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.8#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{n+1} = \phi(x_{n})} | x[n + 1] = phi*(x[n]) |
Subscript[x, n + 1] == \[Phi]*(Subscript[x, n]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}} | phi*(x) = x + x*(cot(x))^(2)- cot(x) |
\[Phi]*(x) == x + x*(Cot[x])^(2)- Cot[x] |
Failure | Failure | Failed [30 / 30] 30/30]: [[-.137590423+.7500000000*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 1.5}.881577740e-1+.2500000000*I <- {phi = 1/2*3^(1/2)+1/2*I, x = .5}-1.144507621+1.*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 2}-2.186628529+1.299038106*I <- {phi = -1/2+1/2*I*3^(1/2), x = 1.5}... skip entries to safe data |
Failed [30 / 30]
{Complex[-0.1375904227343937, 0.7499999999999999] <- {Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.186628528411051, 1.299038105676658] <- {Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 3.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}} | x[2] = x[1]-(x[1]- x[0])/(f[1]- f[0])*f[1] |
Subscript[x, 2] == Subscript[x, 1]-Divide[Subscript[x, 1]- Subscript[x, 0],Subscript[f, 1]- Subscript[f, 0]]*Subscript[f, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}} | z[n + 1] = z[n]-((phi*(z[n])- z[n])^(2))/(phi*(phi*(z[n]))- 2*phi*(z[n])+ z[n]) |
Subscript[z, n + 1] == Subscript[z, n]-Divide[(\[Phi]*(Subscript[z, n])- Subscript[z, n])^(2),\[Phi]*(\[Phi]*(Subscript[z, n]))- 2*\[Phi]*(Subscript[z, n])+ Subscript[z, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{n+1} = \phi(z_{n})} | z[n + 1] = phi*(z[n]) |
Subscript[z, n + 1] == \[Phi]*(Subscript[z, n]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = \frac{3z^{4}+1}{4z^{3}}} | phi*(z) = (3*(z)^(4)+ 1)/(4*(z)^(3)) |
\[Phi]*(z) == Divide[3*(z)^(4)+ 1,4*(z)^(3)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}} | Delta*s (r[3]*q[0]- r[2]*q[1])/(r(r[2])^(2)- ell*r[3]) |
\[CapitalDelta]*s Divide[Subscript[r, 3]*Subscript[q, 0]- Subscript[r, 2]*Subscript[q, 1],r(Subscript[r, 2])^(2)- \[ScriptL]*Subscript[r, 3]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}} | Delta*t (ell*q[1]- r[2]*q[0])/(r(r[2])^(2)- ell*r[3]) |
\[CapitalDelta]*t Divide[\[ScriptL]*Subscript[q, 1]- Subscript[r, 2]*Subscript[q, 0],r(Subscript[r, 2])^(2)- \[ScriptL]*Subscript[r, 3]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell = sr_{2}+tr_{3}} | ell = s*r[2]+ t*r[3] |
\[ScriptL] == s*Subscript[r, 2]+ t*Subscript[r, 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.8.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}} | diff(z, alpha) = -(diff(f, alpha))/(diff(f, z)) |
D[z, \[Alpha]] == -Divide[D[f, \[Alpha]],D[f, z]] |
Error | Failure | - | Failed [210 / 210]
{Indeterminate <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Indeterminate <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 3.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{x}{a_{19}} = -\frac{20^{19}}{19!}} | subs( temp=a[19], diff( x, temp$(1) ) ) = -((20)^(19))/(factorial(19)) |
(D[x, {temp, 1}]/.temp-> Subscript[a, 19]) == -Divide[(20)^(19),(19)!] |
Failure | Failure | Skip - No test values generated | Failed [30 / 30]
{4.309980412182177*^7 <- {Rule[x, 1.5], Rule[Subscript[a, 19], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}4.309980412182177*^7 <- {Rule[x, 1.5], Rule[Subscript[a, 19], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 3.8.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{n+1} = \phi(z_{n})} | z[n + 1] = phi*(z[n]) |
Subscript[z, n + 1] == \[Phi]*(Subscript[z, n]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\frac{t_{n}-\sigma}{s_{n}-\sigma} = 0} | limit((t[n]- sigma)/(s[n]- sigma), n = infinity) = 0 |
Limit[Divide[Subscript[t, n]- \[Sigma],Subscript[s, n]- \[Sigma]], n -> Infinity, GenerateConditions->None] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{n} = s_{n}-\frac{(\Delta s_{n})^{2}}{\Delta^{2}s_{n}}} | t[n] = s[n]-((Delta*s[n])^(2))/((Delta)^(2)* s[n]) |
Subscript[t, n] == Subscript[s, n]-Divide[(\[CapitalDelta]*Subscript[s, n])^(2),\[CapitalDelta]^(2)* Subscript[s, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\frac{s_{n+1}-\sigma}{s_{n}-\sigma} = \rho} | limit((s[n + 1]- sigma)/(s[n]- sigma), n = infinity) = rho |
Limit[Divide[Subscript[s, n + 1]- \[Sigma],Subscript[s, n]- \[Sigma]], n -> Infinity, GenerateConditions->None] == \[Rho] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{n,2k} = \frac{H_{k+1}(s_{n})}{H_{k}(\Delta^{2}s_{n})}} | t[n , 2*k] = (H[k + 1]*(s[n]))/(H[k]*((Delta)^(2)* s[n])) |
Subscript[t, n , 2*k] == Divide[Subscript[H, k + 1]*(Subscript[s, n]),Subscript[H, k]*(\[CapitalDelta]^(2)* Subscript[s, n])] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{-1}^{(n)} = 0} | (varepsilon[- 1])^(n) = 0 |
(Subscript[\[CurlyEpsilon], - 1])^(n) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{0}^{(n)} = s_{n}} | (varepsilon[0])^(n) = s[n] |
(Subscript[\[CurlyEpsilon], 0])^(n) == Subscript[s, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{m+1}^{(n)} = \varepsilon_{m-1}^{(n+1)}+\frac{1}{\varepsilon_{m}^{(n+1)}-\varepsilon_{m}^{(n)}}} | (varepsilon[m + 1])^(n) = (1)/(varepsilon(varepsilon[m])^(n + 1)- varepsilon(varepsilon[m])^(n)) |
(Subscript[\[CurlyEpsilon], m + 1])^(n) == Divide[1,\[CurlyEpsilon](Subscript[\[CurlyEpsilon], m])^(n + 1)- \[CurlyEpsilon](Subscript[\[CurlyEpsilon], m])^(n)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{n} = \sum_{j=1}^{n}\frac{(-1)^{j+1}}{j^{2}}} | s[n] = sum(((- 1)^(j + 1))/((j)^(2)), j = 1..n) |
Subscript[s, n] == Sum[Divide[(- 1)^(j + 1),(j)^(2)], {j, 1, n}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\cal L}_{k}^{(n)}(s) = \frac{\sum_{j=0}^{k}(-1)^{j}\binom{k}{j}c_{j,k,n}\ifrac{s_{n+j}}{a_{n+j+1}}}{\sum_{j=0}^{k}(-1)^{j}\binom{k}{j}c_{j,k,n}/a_{n+j+1}}} | (L[k])^(n)*(s) = (sum((- 1)^(j)*binomial(k,j)*c[j , k , n]*(s[n + j])/(a[n + j + 1]), j = 0..k))/(sum((- 1)^(j)*binomial(k,j)*c[j , k , n]/ a[n + j + 1], j = 0..k)) |
(Subscript[L, k])^(n)*(s) == Divide[Sum[(- 1)^(j)*Binomial[k,j]*Subscript[c, j , k , n]*Divide[Subscript[s, n + j],Subscript[a, n + j + 1]], {j, 0, k}, GenerateConditions->None],Sum[(- 1)^(j)*Binomial[k,j]*Subscript[c, j , k , n]/ Subscript[a, n + j + 1], {j, 0, k}, GenerateConditions->None]] |
Failure | Failure | Error | Skipped - Because timed out |
| 3.9.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\frac{s_{n+1}-\sigma}{s_{n}-\sigma} = 1} | limit((s[n + 1]- sigma)/(s[n]- sigma), n = infinity) = 1 |
Limit[Divide[Subscript[s, n + 1]- \[Sigma],Subscript[s, n]- \[Sigma]], n -> Infinity, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{j,k,n} = \frac{\Pochhammersym{\beta+n+j}{k-1}}{\Pochhammersym{\beta+n+k}{k-1}}} | c[j , k , n] = (pochhammer(beta + n + j, k - 1))/(pochhammer(beta + n + k, k - 1)) |
Subscript[c, j , k , n] == Divide[Pochhammer[\[Beta]+ n + j, k - 1],Pochhammer[\[Beta]+ n + k, k - 1]] |
Failure | Failure | Failed [36 / 81] 36/81]: [[-.277777778e-1 <- {beta = 1.5, j = 1, k = 2, n = 1}-.181818182e-1 <- {beta = 1.5, j = 1, k = 2, n = 2}-.128205129e-1 <- {beta = 1.5, j = 1, k = 2, n = 3}-.805594406e-1 <- {beta = 1.5, j = 1, k = 3, n = 1}... skip entries to safe data |
Failed [36 / 81]
{-0.02777777777777768 <- {Rule[j, 1], Rule[k, 2], Rule[n, 1], Rule[β, 1.5]}-0.018181818181818188 <- {Rule[j, 1], Rule[k, 2], Rule[n, 2], Rule[β, 1.5]} |
| 3.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{j,k,n} = \frac{\Pochhammersym{-\gamma-n-j}{k-1}}{\Pochhammersym{-\gamma-n-k}{k-1}}} | c[j , k , n] = (pochhammer(- gamma - n - j, k - 1))/(pochhammer(- gamma - n - k, k - 1)) |
Subscript[c, j , k , n] == Divide[Pochhammer[- \[Gamma]- n - j, k - 1],Pochhammer[- \[Gamma]- n - k, k - 1]] |
Failure | Failure | Failed [120 / 270] 120/270]: [[.295470259e-1 <- {gamma = 1/2*3^(1/2)+1/2*I, j = 1, k = 2, n = 1}.184734286e-1 <- {gamma = 1/2*3^(1/2)+1/2*I, j = 1, k = 2, n = 2}.126342713e-1 <- {gamma = 1/2*3^(1/2)+1/2*I, j = 1, k = 2, n = 3}.1117465202 <- {gamma = 1/2*3^(1/2)+1/2*I, j = 1, k = 3, n = 1}... skip entries to safe data |
Failed [120 / 270]
{Complex[0.004408174927732822, -0.03290306559789975] <- {Rule[j, 1], Rule[k, 2], Rule[n, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.003359414702213348, -0.020895843920590226] <- {Rule[j, 1], Rule[k, 2], Rule[n, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0} = u_{0}} | b[0] = u[0] |
Subscript[b, 0] == Subscript[u, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = 1} | b[1] = 1 |
Subscript[b, 1] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1} = u_{1}} | a[1] = u[1] |
Subscript[a, 1] == Subscript[u, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = 1+\frac{u_{n}}{u_{n-1}}} | b[n] = 1 +(u[n])/(u[n - 1]) |
Subscript[b, n] == 1 +Divide[Subscript[u, n],Subscript[u, n - 1]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = -\frac{u_{n}}{u_{n-1}}} | a[n] = -(u[n])/(u[n - 1]) |
Subscript[a, n] == -Divide[Subscript[u, n],Subscript[u, n - 1]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e_{0}^{n} = 0} | (exp(1)[0])^(n) = 0 |
(Subscript[E, 0])^(n) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{1}^{n} = c_{n+1}/c_{n}} | (q[1])^(n) = c[n + 1]/ c[n] |
(Subscript[q, 1])^(n) == Subscript[c, n + 1]/ Subscript[c, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}} | (exp(1)[j])^(k) = (exp(1)[j - 1])^(k + 1)+ (q[j])^(k + 1)- (q[j])^(k) |
(Subscript[E, j])^(k) == (Subscript[E, j - 1])^(k + 1)+ (Subscript[q, j])^(k + 1)- (Subscript[q, j])^(k) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}} | (q[j + 1])^(k) = (q[j])^(k + 1)*(exp(1)[j])^(k + 1)/ (exp(1)[j])^(k) |
(Subscript[q, j + 1])^(k) == (Subscript[q, j])^(k + 1)*(Subscript[E, j])^(k + 1)/ (Subscript[E, j])^(k) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{0} = c_{0}} | a[0] = c[0] |
Subscript[a, 0] == Subscript[c, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1} = q_{1}^{0}} | a[1] = (q[1])^(0) |
Subscript[a, 1] == (Subscript[q, 1])^(0) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{2} = e_{1}^{0}} | a[2] = (exp(1)[1])^(0) |
Subscript[a, 2] == (Subscript[E, 1])^(0) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{3} = q_{2}^{0}} | a[3] = (q[2])^(0) |
Subscript[a, 3] == (Subscript[q, 2])^(0) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{4} = e_{2}^{0}} | a[4] = (exp(1)[2])^(0) |
Subscript[a, 4] == (Subscript[E, 2])^(0) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{n} = b_{n}} | u[n] = b[n] |
Subscript[u, n] == Subscript[b, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}} | u[k] = b[k]+(a[k + 1])/(u[k + 1]) |
Subscript[u, k] == Subscript[b, k]+Divide[Subscript[a, k + 1],Subscript[u, k + 1]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C = \sum_{k=0}^{\infty}t_{k}} | C = sum(t[k], k = 0..infinity) |
C == Sum[Subscript[t, k], {k, 0, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{0} = a_{0}} | t[0] = a[0] |
Subscript[t, 0] == Subscript[a, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{k} = \rho_{k}t_{k-1}} | t[k] = rho[k]*t[k - 1] |
Subscript[t, k] == Subscript[\[Rho], k]*Subscript[t, k - 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho_{0} = 0} | rho[0] = 0 |
Subscript[\[Rho], 0] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}} | rho[k] = (a[k]*(1 + rho[k - 1]))/(1 - a[k]*(1 + rho[k - 1])) |
Subscript[\[Rho], k] == Divide[Subscript[a, k]*(1 + Subscript[\[Rho], k - 1]),1 - Subscript[a, k]*(1 + Subscript[\[Rho], k - 1])] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{0} = b_{0}} | C[0] = b[0] |
Subscript[C, 0] == Subscript[b, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{1} = 1/b_{1}} | D[1] = 1/ b[1] |
Subscript[D, 1] == 1/ Subscript[b, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.10#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}} | D[n] = (1)/(D[n - 1]*a[n]+ b[n]) |
Subscript[D, n] == Divide[1,Subscript[D, n - 1]*Subscript[a, n]+ Subscript[b, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{0} < x_{1}} | x[0] < x[1] |
Subscript[x, 0] < Subscript[x, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{n}x_{j}^{k}\delta a_{k} = (-1)^{j}(m_{j}-m)} | sum(x(x[j])^(k)*delta*a[k], k = 0..n) = (- 1)^(j)*(m[j]- m) |
Sum[x(Subscript[x, j])^(k)*\[Delta]*Subscript[a, k], {k, 0, n}, GenerateConditions->None] == (- 1)^(j)*(Subscript[m, j]- m) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{n}@{x} = \cos@{n\acos@@{x}}} | ChebyshevT(n, x) = cos(n*arccos(x)) |
ChebyshevT[n, x] == Cos[n*ArcCos[x]] |
Failure | Successful | Successful [Tested: 3] | Successful [Tested: 3] |
| 3.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{n+1}@{x}-2x\ChebyshevpolyT{n}@{x}+\ChebyshevpolyT{n-1}@{x} = 0} | ChebyshevT(n + 1, x)- 2*x*ChebyshevT(n, x)+ ChebyshevT(n - 1, x) = 0 |
ChebyshevT[n + 1, x]- 2*x*ChebyshevT[n, x]+ ChebyshevT[n - 1, x] == 0 |
Successful | Successful | - | Successful [Tested: 3] |
| 3.11.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon_{n}(x) = d_{n+1}\ChebyshevpolyT{n+1}@{\frac{2x-a-b}{b-a}}} | epsilon[n]*(x) = d[n + 1]*ChebyshevT(n + 1, (2*x - a - b)/(b - a)) |
Subscript[\[Epsilon], n]*(x) == Subscript[d, n + 1]*ChebyshevT[n + 1, Divide[2*x - a - b,b - a]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[Float(-infinity)-Float(infinity)*I <- {a = -1.5, b = -1.5, x = 1.5, d[n+1] = 1/2*3^(1/2)+1/2*I, epsilon[n] = 1/2*3^(1/2)+1/2*I, epsilon = 1, n = 1}Float(-infinity)-Float(infinity)*I <- {a = -1.5, b = -1.5, x = 1.5, d[n+1] = 1/2*3^(1/2)+1/2*I, epsilon[n] = 1/2*3^(1/2)+1/2*I, epsilon = 1, n = 2}Float(-infinity)-Float(infinity)*I <- {a = -1.5, b = -1.5, x = 1.5, d[n+1] = 1/2*3^(1/2)+1/2*I, epsilon[n] = 1/2*3^(1/2)+1/2*I, epsilon = 1, n = 3}Float(-infinity)-Float(infinity)*I <- {a = -1.5, b = -1.5, x = 1.5, d[n+1] = 1/2*3^(1/2)+1/2*I, epsilon[n] = 1/2*3^(1/2)+1/2*I, epsilon = 2, n = 1}... skip entries to safe data |
Failed [300 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[ϵ, 1], Rule[Subscript[d, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[ϵ, 2], Rule[Subscript[d, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.11.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{k} = 2xu_{k+1}-u_{k+2}+c_{k}} | u[k] = 2*x*u[k + 1]- u[k + 2]+ c[k] |
Subscript[u, k] == 2*x*Subscript[u, k + 1]- Subscript[u, k + 2]+ Subscript[c, k] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m_{j} = (-1)^{j}\epsilon_{k,\ell}(x_{j})} | m[j] = (- 1)^(j)* epsilon[k , ell]*(x[j]) |
Subscript[m, j] == (- 1)^(j)* Subscript[\[Epsilon], k , \[ScriptL]]*(Subscript[x, j]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{3,3}(x) = \frac{p_{0}+p_{1}x+p_{2}x^{2}+p_{3}x^{3}}{1+q_{1}x+q_{2}x^{2}+q_{3}x^{3}}} | R[3 , 3]*(x) = (p[0]+ p[1]*x + p[2]*(x)^(2)+ p[3]*(x)^(3))/(1 + q[1]*x + q[2]*(x)^(2)+ q[3]*(x)^(3)) |
Subscript[R, 3 , 3]*(x) == Divide[Subscript[p, 0]+ Subscript[p, 1]*x + Subscript[p, 2]*(x)^(2)+ Subscript[p, 3]*(x)^(3),1 + Subscript[q, 1]*x + Subscript[q, 2]*(x)^(2)+ Subscript[q, 3]*(x)^(3)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11#E23X | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle a_{0} = c_{0}b_{0}} | a[0] = c[0]*b[0] |
Subscript[a, 0] == Subscript[c, 0]*Subscript[b, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11#E23Xa | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle a_{1} = c_{1}b_{0}+c_{0}b_{1}} | a[1] = c[1]*b[0]+ c[0]*b[1] |
Subscript[a, 1] == Subscript[c, 1]*Subscript[b, 0]+ Subscript[c, 0]*Subscript[b, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (N-C)^{-1}+(S-C)^{-1} = (W-C)^{-1}+(E-C)^{-1}} | (N - C)^(- 1)+(S - C)^(- 1) = (W - C)^(- 1)+(E - C)^(- 1) |
(N - C)^(- 1)+(S - C)^(- 1) == (W - C)^(- 1)+(E - C)^(- 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle X_{k\ell} = \sum_{j=1}^{J}w(x_{j})\phi_{k}(x_{j})\phi_{\ell}(x_{j})} | X[k*ell] = sum(w*(x[j])* phi[k]*(x[j])* phi[ell]*(x[j]), j = 1..J) |
Subscript[X, k*\[ScriptL]] == Sum[w*(Subscript[x, j])* Subscript[\[Phi], k]*(Subscript[x, j])* Subscript[\[Phi], \[ScriptL]]*(Subscript[x, j]), {j, 1, J}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{j=0}^{n-1}\phi_{k}(x_{j})\conj{\phi_{\ell}(x_{j})} = n\Kroneckerdelta{k}{\ell}} | sum(phi[k]*(x[j])* conjugate(phi[ell]*(x[j])), j = 0..n - 1) = n*KroneckerDelta[k, ell] |
Sum[Subscript[\[Phi], k]*(Subscript[x, j])* Conjugate[Subscript[\[Phi], \[ScriptL]]*(Subscript[x, j])], {j, 0, n - 1}, GenerateConditions->None] == n*KroneckerDelta[k, \[ScriptL]] |
Error | Failure | - | Failed [300 / 300]
{Plus[1.0, Times[-1.0, KroneckerDelta[1.0, ℓ]]] <- {Rule[k, 1], Rule[n, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[2.0, Times[-2.0, KroneckerDelta[1.0, ℓ]]] <- {Rule[k, 1], Rule[n, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.11.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{j} = \sum_{k=0}^{n-1}a_{k}\phi_{k}(x_{j})} | f[j] = sum(a[k]*phi[k]*(x[j]), k = 0..n - 1) |
Subscript[f, j] == Sum[Subscript[a, k]*Subscript[\[Phi], k]*(Subscript[x, j]), {k, 0, n - 1}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{k} = \frac{1}{n}\sum_{j=0}^{n-1}f_{j}\conj{\phi_{k}(x_{j})}} | a[k] = (1)/(n)*sum(f[j]*conjugate(phi[k]*(x[j])), j = 0..n - 1) |
Subscript[a, k] == Divide[1,n]*Sum[Subscript[f, j]*Conjugate[Subscript[\[Phi], k]*(Subscript[x, j])], {j, 0, n - 1}, GenerateConditions->None] |
Error | Failure | - | Failed [300 / 300]
{Complex[0.0, 0.9999999999999999] <- {Rule[k, 1], Rule[n, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.0, 0.9999999999999999] <- {Rule[k, 1], Rule[n, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.11#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{j} = \sum_{k=0}^{n-1}a_{k}\omega_{n}^{jk}} | f[j] sum(a[k]*omega(omega[n])^(j*k), k = 0..n - 1) |
Subscript[f, j] Sum[Subscript[a, k]*\[Omega](Subscript[\[Omega], n])^(j*k), {k, 0, n - 1}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.11#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \omega_{n} = e^{2\cpi i/n}} | omega[n] = exp(2*Pi*I/ n) |
Subscript[\[Omega], n] == Exp[2*Pi*I/ n] |
Failure | Failure | Failed [290 / 300] 290/300]: [[-.1339745960+.4999999992*I <- {omega = 1/2*3^(1/2)+1/2*I, omega[n] = 1/2*3^(1/2)+1/2*I, n = 1}1.866025404+.5000000004*I <- {omega = 1/2*3^(1/2)+1/2*I, omega[n] = 1/2*3^(1/2)+1/2*I, n = 2}1.366025404-.3660254040*I <- {omega = 1/2*3^(1/2)+1/2*I, omega[n] = 1/2*3^(1/2)+1/2*I, n = 3}-1.500000000+.8660254032*I <- {omega = 1/2*3^(1/2)+1/2*I, omega[n] = -1/2+1/2*I*3^(1/2), n = 1}... skip entries to safe data |
Failed [290 / 300]
{Complex[-0.1339745962155613, 0.49999999999999994] <- {Rule[n, 1], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.8660254037844388, 0.49999999999999994] <- {Rule[n, 2], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 3.11.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \omega_{n}^{2(k-(n/2))} = \omega_{n/2}^{k}} | (omega[n])^(2*(k -(n/ 2))) = (omega[n/ 2])^(k) |
(Subscript[\[Omega], n])^(2*(k -(n/ 2))) == (Subscript[\[Omega], n/ 2])^(k) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi = 3.14159\;26535\;89793\;23846\;\ldots} | Pi = 3.14159265358979323846 |
Pi == 3.14159265358979323846 |
Successful | Successful | - | Successful [Tested: 1] |
| 3.12.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi = 4\int_{0}^{1}\frac{\diff{t}}{1+t^{2}}} | Pi = 4*int((1)/(1 + (t)^(2)), t = 0..1) |
Pi == 4*Integrate[Divide[1,1 + (t)^(2)], {t, 0, 1}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 1] |
| 3.12.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e = 2.71828\;18284\;59045\;23536\;\ldots} | exp(1) = 2.71828182845904523536 |
E == 2.71828182845904523536 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.12.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerConstant = 0.57721\;56649\;01532\;86060\;\ldots} | gamma = 0.57721566490153286060 |
EulerGamma == 0.57721566490153286060 |
Successful | Successful | - | Successful [Tested: 1] |