Results of Algebraic and Analytic Methods

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
1.2.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}}	`binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))`	`Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]`	Successful	Successful	-	Successful [Tested: 9]
1.2.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{n!}{(n-k)!k!} = \binom{n}{n-k}}	`(factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)`	`Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]`	Successful	Successful	-	Successful [Tested: 9]
1.2.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}}	`((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)`	`Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]`	Successful	Successful	-	Successful [Tested: 21]
1.2.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}}	`binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)`	`Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]`	Successful	Successful	-	Successful [Tested: 21]
1.2.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}}	`sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)`	`Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]`	Successful	Successful	-	Successful [Tested: 21]
1.2.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)}	`na +(1)/(2)n(n - 1) d = (1)/(2)n(a + ell)`	`na +Divide[1,2]n(n - 1) d == Divide[1,2]n(a + \[ScriptL])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.2.E22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(r) = 0}	`M*(r) = 0`	`M*(r) == 0`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.2#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(1) = A}	`M*(1) = A`	`M*(1) == A`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.2#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(-1) = H}	`M*(- 1) = H`	`M*(- 1) == H`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.2.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{r\to 0}M(r) = G}	`limit(M*(r), r = 0) = G`	`Limit[M*(r), r -> 0, GenerateConditions->None] == G`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.4.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(2)}(x) = \deriv[2]{f}{x}}	`(f)^(2)*(x) = diff(f, [x$(2)])`	`(f)^(2)*(x) == D[f, {x, 2}]`	Failure	Failure	Failed [30 / 30] `30/30]: [[.7500000006+1.299038106I <- {f = 1/23^(1/2)+1/2I, x = 1.5}` `.2500000002+.4330127020I <- {f = 1/23^(1/2)+1/2I, x = .5}` `1.000000001+1.732050808I <- {f = 1/23^(1/2)+1/2I, x = 2}` `-.7500000006-1.299038106I <- {f = -1/2+1/2I3^(1/2), x = 1.5}` ... skip entries to safe data	Failed [30 / 30] `{Complex[0.7500000000000002, 1.299038105676658] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}` `Complex[0.25000000000000006, 0.4330127018922193] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]}`
1.4.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)}	`diff(f, [x$(2)]) = diff(diff(f, x), x)`	`D[f, {x, 2}] == D[D[f, x], x]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 30]
1.4.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(n)} = f^{(n)}(x)}	`(f)^(n) = (f)^(n)*(x)`	`(f)^(n) == (f)^(n)*(x)`	Failure	Failure	Failed [90 / 90] `90/90]: [[-.4330127020-.2500000000I <- {f = 1/23^(1/2)+1/2I, x = 1.5, n = 1}` `-.2500000002-.4330127020I <- {f = 1/23^(1/2)+1/2I, x = 1.5, n = 2}` `-.1616869430e-9-.5000000005I <- {f = 1/23^(1/2)+1/2I, x = 1.5, n = 3}` `.4330127020+.2500000000I <- {f = 1/23^(1/2)+1/2I, x = .5, n = 1}` ... skip entries to safe data	Failed [90 / 90] `{Complex[-0.4330127018922193, -0.24999999999999994] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}` `Complex[-0.2500000000000001, -0.4330127018922194] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]}`
1.4.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)}	`(f)^(n)(x) = diff((f)^(n - 1)(x), x)`	`(f)^(n)(x) == D[(f)^(n - 1)(x), x]`	Failure	Failure	Failed [84 / 90] `84/90]: [[.299038106+.7500000000I <- {f = 1/23^(1/2)+1/2I, x = 1.5, n = 1}` `-.1160254034+.7990381060I <- {f = 1/23^(1/2)+1/2I, x = 1.5, n = 2}` `-.4999999999+.6339745980I <- {f = 1/23^(1/2)+1/2I, x = 1.5, n = 3}` `-.5669872980+.2500000000I <- {f = 1/23^(1/2)+1/2I, x = .5, n = 1}` ... skip entries to safe data	Failed [84 / 90] `{Complex[0.299038105676658, 0.7499999999999999] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}` `Complex[-0.11602540378443849, 0.799038105676658] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]}`
1.4.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}}	`int(fg, x) = (int(f, x)) g - int((int(f, x))* diff(g, x), x)`	`Integrate[fg, x, GenerateConditions->None] == (Integrate[f, x, GenerateConditions->None]) g - Integrate[(Integrate[f, x, GenerateConditions->None])* D[g, x], x, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 100]
1.4.E36	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{n} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}}	`R[n] = ((f)^(n + 1)(c))/(factorial(n + 1))(x - a)^(n + 1)`	`Subscript[R, n] == Divide[(f)^(n + 1)(c),(n + 1)!](x - a)^(n + 1)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.4.E37	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t}}	`R[n] = (1)/(factorial(n))int((x - t)^(n) (f)^(n + 1)*(t), t = a..x)`	`Subscript[R, n] == Divide[1,(n)!]Integrate[(x - t)^(n) (f)^(n + 1)*(t), {t, a, x}, GenerateConditions->None]`	Failure	Failure	Failed [300 / 300] `300/300]: [[1.991025404+2.448557159I <- {a = -1.5, f = 1/23^(1/2)+1/2I, x = 1.5, R[n] = 1/23^(1/2)+1/2I, n = 1}` `.8660254040+3.875000000I <- {a = -1.5, f = 1/23^(1/2)+1/2I, x = 1.5, R[n] = 1/23^(1/2)+1/2I, n = 2}` `-.6527245960+3.130552164I <- {a = -1.5, f = 1/23^(1/2)+1/2I, x = 1.5, R[n] = 1/23^(1/2)+1/2I, n = 3}` `.6250000000+2.814582563I <- {a = -1.5, f = 1/23^(1/2)+1/2I, x = 1.5, R[n] = -1/2+1/2I3^(1/2), n = 1}` ... skip entries to safe data	Failed [300 / 300] `{Complex[1.9910254037844388, 2.4485571585149866] <- {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.8660254037844387, 3.875] <- {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
1.5.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{y} = D_{y}f}	`diff(f, y) = D[y]*f`	`D[f, y] == Subscript[D, y]*f`	Failure	Failure	Failed [300 / 300] `300/300]: [[-.5000000004-.8660254040I <- {f = 1/23^(1/2)+1/2I, y = -1.5, D[y] = 1/23^(1/2)+1/2I}` `.8660254040-.5000000004I <- {f = 1/23^(1/2)+1/2I, y = -1.5, D[y] = -1/2+1/2I3^(1/2)}` `-.8660254040+.5000000004I <- {f = 1/23^(1/2)+1/2I, y = -1.5, D[y] = 1/2-1/2I3^(1/2)}` `.5000000004+.8660254040I <- {f = 1/23^(1/2)+1/2I, y = -1.5, D[y] = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Failed [300 / 300] `{Complex[-0.5000000000000001, -0.8660254037844386] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.8660254037844387, -0.49999999999999994] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{y}f = f_{y}}	`D[y]*f = f[y]`	`Subscript[D, y]*f == Subscript[f, y]`	Failure	Failure	Failed [300 / 300] `300/300]: [[-.3660254036+.3660254040I <- {f = 1/23^(1/2)+1/2I, y = -1.5, D[y] = 1/23^(1/2)+1/2I, f[y] = 1/23^(1/2)+1/2I}` `1.000000000+0.I <- {f = 1/23^(1/2)+1/2I, y = -1.5, D[y] = 1/23^(1/2)+1/2I, f[y] = -1/2+1/2I3^(1/2)}` `.4e-9+1.732050808I <- {f = 1/23^(1/2)+1/2I, y = -1.5, D[y] = 1/23^(1/2)+1/2I, f[y] = 1/2-1/2I3^(1/2)}` `1.366025404+1.366025404I <- {f = 1/23^(1/2)+1/2I, y = -1.5, D[y] = 1/23^(1/2)+1/2I, f[y] = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Failed [300 / 300] `{Complex[-0.3660254037844386, 0.36602540378443865] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.9999999999999999, -1.1102230246251565*^-16] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\phi}}	`x = r*cos(phi)`	`x == r*Cos[\[Phi]]`	Failure	Failure	Failed [180 / 180] `180/180]: [[2.595814528-.5954243254I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, x = 1.5}` `1.595814528-.5954243254I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, x = .5}` `3.095814528-.5954243254I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, x = 2}` `.404185472+.5954243254I <- {phi = 1/23^(1/2)+1/2I, r = 1.5, x = 1.5}` ... skip entries to safe data	Failed [180 / 180] `{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\phi}}	`y = r*sin(phi)`	`y == r*Sin[\[Phi]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[-.211529498+.5063946946I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, y = -1.5}` `2.788470502+.5063946946I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, y = 1.5}` `.788470502+.5063946946I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, y = -.5}` `1.788470502+.5063946946I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, y = .5}` ... skip entries to safe data	Failed [300 / 300] `{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}}	`diff(f, [x$(2)])+ diff(f, [y$(2)]) = diff(f, [r$(2)])+(1)/(r)diff(f, r)+(1)/((r)^(2))diff(f, [phi$(2)])`	`D[f, {x, 2}]+ D[f, {y, 2}] == D[f, {r, 2}]+Divide[1,r]D[f, r]+Divide[1,(r)^(2)]D[f, {\[Phi], 2}]`	Successful	Successful	-	Successful [Tested: 300]
1.5#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\phi}}	`x = r*cos(phi)`	`x == r*Cos[\[Phi]]`	Failure	Failure	Failed [180 / 180] `180/180]: [[2.595814528-.5954243254I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, x = 1.5}` `1.595814528-.5954243254I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, x = .5}` `3.095814528-.5954243254I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, x = 2}` `.404185472+.5954243254I <- {phi = 1/23^(1/2)+1/2I, r = 1.5, x = 1.5}` ... skip entries to safe data	Failed [180 / 180] `{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\phi}}	`y = r*sin(phi)`	`y == r*Sin[\[Phi]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[-.211529498+.5063946946I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, y = -1.5}` `2.788470502+.5063946946I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, y = 1.5}` `.788470502+.5063946946I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, y = -.5}` `1.788470502+.5063946946I <- {phi = 1/23^(1/2)+1/2I, r = -1.5, y = .5}` ... skip entries to safe data	Failed [300 / 300] `{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = z}	`z = z`	`z == z`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}+\pderiv[2]{f}{z}}	`diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + yI), diff( f, temp$(2) ) ) = diff(f, [r$(2)])+(1)/(r)diff(f, r)+(1)/((r)^(2))diff(f, [phi$(2)])+ subs( temp=(x + yI), diff( f, temp$(2) ) )`	`D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + yI)) == D[f, {r, 2}]+Divide[1,r]D[f, r]+Divide[1,(r)^(2)]D[f, {\[Phi], 2}]+ (D[f, {temp, 2}]/.temp-> (x + yI))`	Successful	Successful	-	Successful [Tested: 300]
1.5#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \rho\sin@@{\theta}\cos@@{\phi}}	`x = rhosin(theta)cos(phi)`	`x == \[Rho]Sin[\[Theta]]Cos[\[Phi]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[.7933233780-.2990618885I <- {phi = 1/23^(1/2)+1/2I, rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, x = 1.5}` `-.2066766220-.2990618885I <- {phi = 1/23^(1/2)+1/2I, rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, x = .5}` `1.293323378-.2990618885I <- {phi = 1/23^(1/2)+1/2I, rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, x = 2}` `2.075937432-.6992275886I <- {phi = 1/23^(1/2)+1/2I, rho = 1/23^(1/2)+1/2I, theta = -1/2+1/2I3^(1/2), x = 1.5}` ... skip entries to safe data	Failed [300 / 300] `{Complex[0.7933233783531031, -0.29906188871772155] <- {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.1325168401075085, -1.15603698835011] <- {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \rho\sin@@{\theta}\sin@@{\phi}}	`y = rhosin(theta)sin(phi)`	`y == \[Rho]Sin[\[Theta]]Sin[\[Phi]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[-1.750303606-.8142131232I <- {phi = 1/23^(1/2)+1/2I, rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, y = -1.5}` `1.249696394-.8142131232I <- {phi = 1/23^(1/2)+1/2I, rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, y = 1.5}` `-.7503036064-.8142131232I <- {phi = 1/23^(1/2)+1/2I, rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, y = -.5}` `.2496963936-.8142131232I <- {phi = 1/23^(1/2)+1/2I, rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, y = .5}` ... skip entries to safe data	Failed [300 / 300] `{Complex[-1.750303605777159, -0.8142131229438421] <- {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.49444885508381575, -0.009630141394747549] <- {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \rho\cos@@{\theta}}	`z = rho*cos(theta)`	`z == \[Rho]*Cos[\[Theta]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[.348818158e-1+.4784968852I <- {rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `-1.331143588+.8445222892I <- {rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}` `-.3311435882-.8875285188I <- {rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)}` `-1.697168992-.5215031148I <- {rho = 1/23^(1/2)+1/2I, theta = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Failed [300 / 300] `{Complex[0.03488181560898618, 0.4784968849905366] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.8875285187939019, -0.3311435881754526] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.5.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)}	`diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + yI), diff( f, temp$(2) ) ) = (1)/((rho)^(2))diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))diff(f, [phi$(2)]), rho)+(1)/((rho)^(2) sin(theta))diff(sin(theta)diff(f, theta), theta)`	`D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + yI)) == Divide[1,\[Rho]^(2)]D[(\[Rho]^(2)* D[f, \[Rho]])+Divide[1,\[Rho]^(2)* (Sin[\[Theta]])^(2)]D[f, {\[Phi], 2}], \[Rho]]+Divide[1,\[Rho]^(2) Sin[\[Theta]]]D[Sin[\[Theta]]D[f, \[Theta]], \[Theta]]`	Successful	Successful	-	Successful [Tested: 300]
1.5.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{x} = \pderiv{f}{y}}	`diff(f, x) = diff(f, y)`	`D[f, x] == D[f, y]`	Successful	Successful	-	Successful [Tested: 180]
1.5.E23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon}	`abs(int(diff(f, x), y = c[1]..d)) < epsilon`	`Abs[Integrate[D[f, x], {y, Subscript[c, 1], d}, GenerateConditions->None]] < \[Epsilon]`	Failure	Failure	Successful [Tested: 300]	Successful [Tested: 300]
1.5.E25	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = x_{0}}	`a = x[0]`	`a == Subscript[x, 0]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = y_{0}}	`c = y[0]`	`c == Subscript[y, 0]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \leq x}	`a <= x`	`a <= x`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5#Ex12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi_{1}(x) \leq y}	`phi[1]*(x) <= y`	`Subscript[\[Phi], 1]*(x) <= y`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5#Ex13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c \leq y}	`c <= y`	`c <= y`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5#Ex14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi_{1}(y) \leq x}	`psi[1]*(y) <= x`	`Subscript[\[Psi], 1]*(y) <= x`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5#Ex15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \leq x}	`a <= x`	`a <= x`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5#Ex16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi_{1}(x) \leq y}	`phi[1]*(x) <= y`	`Subscript[\[Phi], 1]*(x) <= y`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.5#Ex17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi_{1}(x,y) \leq z}	`psi[1](x , y) <= (x + yI)`	`Subscript[\[Psi], 1](x , y) <= (x + yI)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.6#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{a} = (a_{1},a_{2},a_{3})}	`a = (a[1], a[2], a[3])`	`a == (Subscript[a, 1], Subscript[a, 2], Subscript[a, 3])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.6#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{b} = (b_{1},b_{2},b_{3})}	`b = (b[1], b[2], b[3])`	`b == (Subscript[b, 1], Subscript[b, 2], Subscript[b, 3])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.6.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{a}\cdot\mathbf{b} = a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}}	`a * b = a[1]b[1]+ a[2]b[2]+ a[3]*b[3]`	`a * b == Subscript[a, 1]Subscript[b, 1]+ Subscript[a, 2]Subscript[b, 2]+ Subscript[a, 3]*Subscript[b, 3]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.6.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \\|\mathbf{a}\\| = \sqrt{\mathbf{a}\cdot\mathbf{a}}}	`abs(a) = sqrt(a * a)`	`Abs[a] == Sqrt[a * a]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.6.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\theta} = \frac{\mathbf{a}\cdot\mathbf{b}}{\\|\mathbf{a}\\|\;\\|\mathbf{b}\\|}}	`cos(theta) = (a * b)/(abs(a)*abs(b))`	`Cos[\[Theta]] == Divide[a * b,Abs[a]*Abs[b]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[-.2694569811-.3969495503I <- {a = -1.5, b = -1.5, theta = 1/23^(1/2)+1/2I}` `.227765517+.4690753764I <- {a = -1.5, b = -1.5, theta = -1/2+1/2I3^(1/2)}` `.227765517+.4690753764I <- {a = -1.5, b = -1.5, theta = 1/2-1/2I3^(1/2)}` `-.2694569811-.3969495503I <- {a = -1.5, b = -1.5, theta = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Failed [300 / 300] `{Complex[-0.2694569809427748, -0.3969495502290325] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.2277655168641104, 0.46907537626850365] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.6.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{a} = a_{1}\mathbf{i}+a_{2}\mathbf{j}+a_{3}\mathbf{k}}	`a = a[1]I + a[2]j + a[3]*k`	`a == Subscript[a, 1]I + Subscript[a, 2]j + Subscript[a, 3]*k`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.6.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{j}b_{j} = \sum_{j=1}^{3}a_{j}b_{j}}	`a[j]b[j] = sum(a[j]b[j], j = 1..3)`	`Subscript[a, j]Subscript[b, j] == Sum[Subscript[a, j]Subscript[b, j], {j, 1, 3}, GenerateConditions->None]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.6#Ex15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2}}	`LeviCivita[1, 2, 3] = LeviCivita[3, 1, 2]`	`Part[LeviCivitaTensor[3,List], 1, 2, 3] == Part[LeviCivitaTensor[3,List], 3, 1, 2]`	Successful	Successful	-	Successful [Tested: 1]
1.6#Ex15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{3}{1}{2} = 1}	`LeviCivita[3, 1, 2] = 1`	`Part[LeviCivitaTensor[3,List], 3, 1, 2] == 1`	Successful	Successful	-	Successful [Tested: 1]
1.6#Ex16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1}}	`LeviCivita[2, 1, 3] = LeviCivita[3, 2, 1]`	`Part[LeviCivitaTensor[3,List], 2, 1, 3] == Part[LeviCivitaTensor[3,List], 3, 2, 1]`	Successful	Successful	-	Successful [Tested: 1]
1.6#Ex16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{3}{2}{1} = -1}	`LeviCivita[3, 2, 1] = - 1`	`Part[LeviCivitaTensor[3,List], 3, 2, 1] == - 1`	Successful	Successful	-	Successful [Tested: 1]
1.6#Ex17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{2}{2}{1} = 0}	`LeviCivita[2, 2, 1] = 0`	`Part[LeviCivitaTensor[3,List], 2, 2, 1] == 0`	Successful	Successful	-	Successful [Tested: 1]
1.6.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m}}	`LeviCivita[j, k, ell]LeviCivita[ell, m, n] = KroneckerDelta[j, m]KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m]`	`Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]Part[LeviCivitaTensor[3,List], \[ScriptL], m, n] == KroneckerDelta[j, m]KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m]`	Failure	Failure	Error	Failed [81 / 81] `{Times[Part[{{{0.0, 0.0, 0.0} <- {0.0, 0.0, 1.0}, {0.0, -1.0, 0.0}` `{0.0, 0.0, -1.0} <- {0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}` `{0.0, 1.0, 0.0} <- {-1.0, 0.0, 0.0}, {0.0, 0.0, 0.0}` `{0.0, 0.0, 0.0} <- {0.0, 0.0, 1.0}, {0.0, -1.0, 0.0}` ... skip entries to safe data
1.6.E43	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}}	`F(x , y) = F[1](x , y)* I + F[2](x , y) j`	`F(x , y) == Subscript[F, 1](x , y)* I + Subscript[F, 2](x , y) j`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.6.E46	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{T}_{u} = \pderiv{x}{u}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{u}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{u}(u_{0},v_{0})\mathbf{k}}	`T[u] = diff(x, u)(u[0], v[0]) I + diff(y, u)(u[0], v[0]) j + diff(x + yI, u)(u[0], v[0])* k`	`Subscript[T, u] == D[x, u](Subscript[u, 0], Subscript[v, 0]) I + D[y, u](Subscript[u, 0], Subscript[v, 0]) j + D[x + yI, u](Subscript[u, 0], Subscript[v, 0])* k`	Failure	Failure	Failed [300 / 300] `300/300]: [[.8660254040+.5000000000I <- {u = 1/23^(1/2)+1/2I, x = 1.5, y = -1.5, T[u] = 1/23^(1/2)+1/2I, u[0] = 1/23^(1/2)+1/2I, v[0] = 1/23^(1/2)+1/2I, j = 1, k = 1}` `.8660254040+.5000000000I <- {u = 1/23^(1/2)+1/2I, x = 1.5, y = -1.5, T[u] = 1/23^(1/2)+1/2I, u[0] = 1/23^(1/2)+1/2I, v[0] = 1/23^(1/2)+1/2I, j = 1, k = 2}` `.8660254040+.5000000000I <- {u = 1/23^(1/2)+1/2I, x = 1.5, y = -1.5, T[u] = 1/23^(1/2)+1/2I, u[0] = 1/23^(1/2)+1/2I, v[0] = 1/23^(1/2)+1/2I, j = 1, k = 3}` `.8660254040+.5000000000I <- {u = 1/23^(1/2)+1/2I, x = 1.5, y = -1.5, T[u] = 1/23^(1/2)+1/2I, u[0] = 1/23^(1/2)+1/2I, v[0] = 1/23^(1/2)+1/2I, j = 2, k = 1}` ... skip entries to safe data	Error
1.6.E47	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{T}_{v} = \pderiv{x}{v}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{v}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{v}(u_{0},v_{0})\mathbf{k}}	`T[v] = diff(x, v)(u[0], v[0]) I + diff(y, v)(u[0], v[0]) j + diff(x + yI, v)(u[0], v[0])* k`	`Subscript[T, v] == D[x, v](Subscript[u, 0], Subscript[v, 0]) I + D[y, v](Subscript[u, 0], Subscript[v, 0]) j + D[x + yI, v](Subscript[u, 0], Subscript[v, 0])* k`	Failure	Failure	Failed [300 / 300] `300/300]: [[.8660254040+.5000000000I <- {v = 1/23^(1/2)+1/2I, x = 1.5, y = -1.5, T[v] = 1/23^(1/2)+1/2I, u[0] = 1/23^(1/2)+1/2I, v[0] = 1/23^(1/2)+1/2I, j = 1, k = 1}` `.8660254040+.5000000000I <- {v = 1/23^(1/2)+1/2I, x = 1.5, y = -1.5, T[v] = 1/23^(1/2)+1/2I, u[0] = 1/23^(1/2)+1/2I, v[0] = 1/23^(1/2)+1/2I, j = 1, k = 2}` `.8660254040+.5000000000I <- {v = 1/23^(1/2)+1/2I, x = 1.5, y = -1.5, T[v] = 1/23^(1/2)+1/2I, u[0] = 1/23^(1/2)+1/2I, v[0] = 1/23^(1/2)+1/2I, j = 1, k = 3}` `.8660254040+.5000000000I <- {v = 1/23^(1/2)+1/2I, x = 1.5, y = -1.5, T[v] = 1/23^(1/2)+1/2I, u[0] = 1/23^(1/2)+1/2I, v[0] = 1/23^(1/2)+1/2I, j = 2, k = 1}` ... skip entries to safe data	Error
1.7.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)}	`(sum(a[j]*b[j], j = 1..n))^(2) (sum(b(b[j])^(2), j = 1..n))`	`((Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None]))^(2) (Sum[b(Subscript[b, j])^(2), {j, 1, n}, GenerateConditions->None])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.7.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}}	`sum(a[j]*b[j], j = 1..n) (sum(b(b[j])^(q), j = 1..n))^(1/ q)`	`Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None] ((Sum[b(Subscript[b, j])^(q), {j, 1, n}, GenerateConditions->None]))^(1/ q)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.7.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}}	`(sum((a[j]+ b[j])^(p), j = 1..n))^(1/ p) (sum(a(a[j])^(p), j = 1..n))^(1/ p)(sum(b(b[j])^(p), j = 1..n))^(1/ p)`	`((Sum[(Subscript[a, j]+ Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/ p) ((Sum[a(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/ p)((Sum[b(Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/ p)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.7.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle H \leq G}	`H <= G`	`H <= G`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.7.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(r) \leq M(s)}	`M(r) <= M(s)`	`M(r) <= M(s)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.8.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}}	`sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity) = sqrt((Pi)/(omega))(1 + 2sum(exp(- (n)^(2)* (Pi)^(2)/ omega)cos(2nPix), n = 1..infinity))`	`Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,\[Omega]]](1 + 2Sum[Exp[- (n)^(2)* (Pi)^(2)/ \[Omega]]Cos[2nPix], {n, 1, Infinity}, GenerateConditions->None])`	Failure	Successful	Successful [Tested: 15]	Successful [Tested: 15]
1.9.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x+iy}	`(x + yI) = x + Iy`	`(x + yI) == x + Iy`	Successful	Successful	-	Successful [Tested: 1]
1.9#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{z} = x}	`Re(x + y*I) = x`	`Re[x + y*I] == x`	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
1.9#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@{z} = y}	`Im(x + y*I) = y`	`Im[x + y*I] == y`	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
1.9#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\theta}}	`x = r*cos(theta)`	`x == r*Cos[\[Theta]]`	Failure	Failure	Failed [180 / 180] `180/180]: [[2.595814528-.5954243254I <- {r = -1.5, theta = 1/23^(1/2)+1/2I, x = 1.5}` `1.595814528-.5954243254I <- {r = -1.5, theta = 1/23^(1/2)+1/2I, x = .5}` `3.095814528-.5954243254I <- {r = -1.5, theta = 1/23^(1/2)+1/2I, x = 2}` `3.341648276+.7036130646I <- {r = -1.5, theta = -1/2+1/2I3^(1/2), x = 1.5}` ... skip entries to safe data	Failed [180 / 180] `{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\theta}}	`y = r*sin(theta)`	`y == r*Sin[\[Theta]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[-.211529498+.5063946946I <- {r = -1.5, theta = 1/23^(1/2)+1/2I, y = -1.5}` `2.788470502+.5063946946I <- {r = -1.5, theta = 1/23^(1/2)+1/2I, y = 1.5}` `.788470502+.5063946946I <- {r = -1.5, theta = 1/23^(1/2)+1/2I, y = -.5}` `1.788470502+.5063946946I <- {r = -1.5, theta = 1/23^(1/2)+1/2I, y = .5}` ... skip entries to safe data	Failed [300 / 300] `{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = (x^{2}+y^{2})^{1/2}}	`r = ((x)^(2)+ (y)^(2))^(1/ 2)`	`r == ((x)^(2)+ (y)^(2))^(1/ 2)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \omega = \atan@{\|y/x\|}\in\left[0,\tfrac{1}{2}\pi\right]}	`omega 0 <= arctan(abs(y/ x)) <= (1)/(2)*Pi`	`\[Omega] 0 <= ArcTan[Abs[y/ x]] <= Divide[1,2]*Pi`	Error	Failure	-	Failed [180 / 180] `{Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[-1.0, True]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.4999999999999998, 0.8660254037844387], Times[-1.0, True]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|z\| = r}	`abs(z) = r`	`Abs[z] == r`	Failure	Failure	Failed [39 / 42] `39/42]: [[2.5 <- {r = -1.5, z = 1/23^(1/2)+1/2I}` `2.5 <- {r = -1.5, z = -1/2+1/2I3^(1/2)}` `2.5 <- {r = -1.5, z = 1/2-1/2I3^(1/2)}` `2.5 <- {r = -1.5, z = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Failed [39 / 42] `{2.5 <- {Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `2.5 <- {Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{z} = \theta+2n\pi}	`argument(z) = theta + 2nPi`	`Arg[z] == \[Theta]+ 2nPi`	Error	Failure	-	Failed [70 / 70] `{Complex[-19.191982549724898, -0.49999999999999994] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-17.82595714594046, -0.8660254037844387] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\realpart@@{z}\| \leq \|z\|}	`abs(Re(z)) <= abs(z)`	`Abs[Re[z]] <= Abs[z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
1.9#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\imagpart@@{z}\| \leq \|z\|}	`abs(Im(z)) <= abs(z)`	`Abs[Im[z]] <= Abs[z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
1.9.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = re^{i\theta}}	`z = rexp(Itheta)`	`z == rExp[I\[Theta]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{i\theta} = \cos@@{\theta}+i\sin@@{\theta}}	`exp(Itheta) = cos(theta)+ Isin(theta)`	`Exp[I\[Theta]] == Cos[\[Theta]]+ ISin[\[Theta]]`	Successful	Successful	-	Successful [Tested: 10]
1.9.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \conj{z} = x-iy}	`conjugate(x + yI) = x - Iy`	`Conjugate[x + yI] == x - Iy`	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
1.9.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\conj{z}\| = \|z\|}	`abs(conjugate(z)) = abs(z)`	`Abs[Conjugate[z]] == Abs[z]`	Successful	Successful	-	Successful [Tested: 7]
1.9.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{\conj{z}} = -\phase@@{z}}	`argument(conjugate(z)) = - argument(z)`	`Arg[Conjugate[z]] == - Arg[z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
1.9.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}+ z_{2} = x_{1}+ x_{2}+\iunit(y_{1}+ y_{2})}	`x + yI[1]+x + yI[2] = x[1]+ x[2]+ I*(y[1]+ y[2])`	`Subscript[x + yI, 1]+Subscript[x + yI, 2] == Subscript[x, 1]+ Subscript[x, 2]+ I*(Subscript[y, 1]+ Subscript[y, 2])`	Failure	Failure	Error	Failed [300 / 300] `{Plus[Complex[-0.7320508075688775, -2.732050807568877], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.3660254037844388, -1.3660254037844388], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}- z_{2} = x_{1}- x_{2}+\iunit(y_{1}- y_{2})}	`x + yI[1]-x + yI[2] = x[1]- x[2]+ I*(y[1]- y[2])`	`Subscript[x + yI, 1]-Subscript[x + yI, 2] == Subscript[x, 1]- Subscript[x, 2]+ I*(Subscript[y, 1]- Subscript[y, 2])`	Failure	Failure	Error	Failed [300 / 300] `{Plus[Subscript[Complex[1.5, -1.5], 1], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.36602540378443876, -1.3660254037844384], Subscript[Complex[1.5, -1.5], 1], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}z_{2} = x_{1}x_{2}-y_{1}y_{2}+i(x_{1}y_{2}+x_{2}y_{1})}	`x + yI[1]x + yI[2] = x[1]x[2]- y[1]y[2]+ I(x[1]y[2]+ x[2]y[1])`	`Subscript[x + yI, 1]Subscript[x + yI, 2] == Subscript[x, 1]Subscript[x, 2]- Subscript[y, 1]Subscript[y, 2]+ I(Subscript[x, 1]Subscript[y, 2]+ Subscript[x, 2]Subscript[y, 1])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{\|z_{2}\|^{2}}}	`(z[1])/(z[2]) = (z[1]*conjugate(z)[2])/((abs(z[2]))^(2))`	`Divide[Subscript[z, 1],Subscript[z, 2]] == Divide[Subscript[z, 1]*Subscript[Conjugate[z], 2],(Abs[Subscript[z, 2]])^(2)]`	Failure	Failure	Error	Failed [300 / 300] `{Plus[1.0, Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[0.0, -1.0], Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{z_{1}\conj{z}_{2}}{\|z_{2}\|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}}	`(x[1]x[2]+ y[1]y[2]+ I(x[2]y[1]- x[1]*y[2]))/(x(x[2])^(2)+ y(y[2])^(2))`	`Divide[Subscript[x, 1]Subscript[x, 2]+ Subscript[y, 1]Subscript[y, 2]+ I(Subscript[x, 2]Subscript[y, 1]- Subscript[x, 1]*Subscript[y, 2]),x(Subscript[x, 2])^(2)+ y(Subscript[y, 2])^(2)]`	Failure	Failure	Error	Failed [300 / 300] `{DirectedInfinity[] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.6666666666666669, -0.6666666666666667], Times[Power[Abs[Subscript[Complex[1.5, -1.5], 2]], -2], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, 1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|z_{1}z_{2}\| = \|z_{1}\|\;\|z_{2}\|}	`abs(z[1]z[2]) = abs(z[1])abs(z[2])`	`Abs[Subscript[z, 1]Subscript[z, 2]] == Abs[Subscript[z, 1]]Abs[Subscript[z, 2]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@{z_{1}z_{2}} = \phase@@{z_{1}}+\phase@@{z_{2}}}	`argument(z[1]*z[2]) = argument(z[1])+ argument(z[2])`	`Arg[Subscript[z, 1]*Subscript[z, 2]] == Arg[Subscript[z, 1]]+ Arg[Subscript[z, 2]]`	Failure	Failure	Failed [25 / 100] `25/100]: [[-6.283185308 <- {z[1] = 1/23^(1/2)+1/2I, z[2] = -1.5}` `-6.283185308 <- {z[1] = 1/23^(1/2)+1/2I, z[2] = -.5}` `-6.283185308 <- {z[1] = 1/23^(1/2)+1/2I, z[2] = -2}` `-6.283185309 <- {z[1] = -1/2+1/2I3^(1/2), z[2] = -1/2+1/2I3^(1/2)}` ... skip entries to safe data	Failed [25 / 100] `{-6.283185307179587 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], -1.5]}` `-6.283185307179587 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], -0.5]}`
1.9.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\frac{z_{1}}{z_{2}}} = \frac{\|z_{1}\|}{\|z_{2}\|}}	`abs((z[1])/(z[2])) = (abs(z[1]))/(abs(z[2]))`	`Abs[Divide[Subscript[z, 1],Subscript[z, 2]]] == Divide[Abs[Subscript[z, 1]],Abs[Subscript[z, 2]]]`	Successful	Successful	-	Successful [Tested: 100]
1.9.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{\frac{z_{1}}{z_{2}}} = \phase@@{z_{1}}-\phase@@{z_{2}}}	`argument((z[1])/(z[2])) = argument(z[1])- argument(z[2])`	`Arg[Divide[Subscript[z, 1],Subscript[z, 2]]] == Arg[Subscript[z, 1]]- Arg[Subscript[z, 2]]`	Failure	Failure	Failed [25 / 100] `25/100]: [[-6.283185308 <- {z[1] = -1/2+1/2I3^(1/2), z[2] = -1/23^(1/2)-1/2I}` `6.283185308 <- {z[1] = 1/2-1/2I3^(1/2), z[2] = -1/2+1/2I3^(1/2)}` `6.283185307 <- {z[1] = 1/2-1/2I3^(1/2), z[2] = -1.5}` `6.283185307 <- {z[1] = 1/2-1/2I3^(1/2), z[2] = -.5}` ... skip entries to safe data	Failed [25 / 100] `{-6.283185307179586 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}` `6.283185307179586 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9.E22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{n\theta}+i\sin@@{n\theta} = (\cos@@{\theta}+i\sin@@{\theta})^{n}}	`cos(ntheta)+ Isin(ntheta) = (cos(theta)+ Isin(theta))^(n)`	`Cos[n\[Theta]]+ ISin[n\[Theta]] == (Cos[\[Theta]]+ ISin[\[Theta]])^(n)`	Error	Successful	-	Successful [Tested: 10]
1.9.E23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\abs{z_{1}}-\abs{z_{2}}} \leq \abs{z_{1}+z_{2}}}	`abs(abs(z[1])- abs(z[2])) <= abs(z[1]+ z[2])`	`Abs[Abs[Subscript[z, 1]]- Abs[Subscript[z, 2]]] <= Abs[Subscript[z, 1]+ Subscript[z, 2]]`	Failure	Failure	Successful [Tested: 100]	Successful [Tested: 100]
1.9.E23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{z_{1}+z_{2}} \leq \abs{z_{1}}+\abs{z_{2}}}	`abs(z[1]+ z[2]) <= abs(z[1])+ abs(z[2])`	`Abs[Subscript[z, 1]+ Subscript[z, 2]] <= Abs[Subscript[z, 1]]+ Abs[Subscript[z, 2]]`	Failure	Failure	Successful [Tested: 100]	Successful [Tested: 100]
1.9#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{u}{x} = \pderiv{v}{y}}	`diff(u, x) = diff(v, y)`	`D[u, x] == D[v, y]`	Successful	Successful	-	Successful [Tested: 300]
1.9#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{u}{y} = -\pderiv{v}{x}}	`diff(u, y) = - diff(v, x)`	`D[u, y] == - D[v, x]`	Successful	Successful	-	Successful [Tested: 300]
1.9.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{u}{x}+\pderiv[2]{u}{y} = \pderiv[2]{v}{x}+\pderiv[2]{v}{y}}	`diff(u, [x$(2)])+ diff(u, [y$(2)]) = diff(v, [x$(2)])+ diff(v, [y$(2)])`	`D[u, {x, 2}]+ D[u, {y, 2}] == D[v, {x, 2}]+ D[v, {y, 2}]`	Successful	Successful	-	Successful [Tested: 300]
1.9.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{v}{x}+\pderiv[2]{v}{y} = 0}	`diff(v, [x$(2)])+ diff(v, [y$(2)]) = 0`	`D[v, {x, 2}]+ D[v, {y, 2}] == 0`	Successful	Successful	-	Successful [Tested: 180]
1.9.E27	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{u}{r}+\frac{1}{r}\pderiv{u}{r}+\frac{1}{r^{2}}\pderiv[2]{u}{\theta} = 0}	`diff(u, [r$(2)])+(1)/(r)diff(u, r)+(1)/((r)^(2))diff(u, [theta$(2)]) = 0`	`D[u, {r, 2}]+Divide[1,r]D[u, r]+Divide[1,(r)^(2)]D[u, {\[Theta], 2}] == 0`	Successful	Successful	-	Successful [Tested: 300]
1.9.E33	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(z) = \frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})\diff{\phi}}	`u(z) = (1)/(2Pi)int(u(z + rexp(Iphi)), phi = 0..2*Pi)`	`u(z) == Divide[1,2Pi]Integrate[u(z + rExp[I\[Phi]]), {\[Phi], 0, 2*Pi}, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 300]
1.9.E34	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(re^{i\theta}) = \frac{1}{2\pi}\int^{2\pi}_{0}\frac{(R^{2}-r^{2})h(Re^{i\phi})\diff{\phi}}{R^{2}-2Rr\cos@{\phi-\theta}+r^{2}}}	`u(rexp(Itheta)) = (1)/(2Pi)int((((R)^(2)- (r)^(2)) h(Rexp(Iphi)))/((R)^(2)- 2Rrcos(phi - theta)+ (r)^(2)), phi = 0..2*Pi)`	`u(rExp[I\[Theta]]) == Divide[1,2Pi]Integrate[Divide[((R)^(2)- (r)^(2)) h(RExp[I\[Phi]]),(R)^(2)- 2RrCos[\[Phi]- \[Theta]]+ (r)^(2)], {\[Phi], 0, 2*Pi}, GenerateConditions->None]`	Error	Failure	Skipped - Because timed out	Failed [300 / 300] `{Complex[-0.1639294614698989, -0.894905511379796] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.6307543640677387, -0.014887794479775784] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.9.E36	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \infty+ z = z+\infty}	`infinity + z = z + infinity`	`Infinity + z == z + Infinity`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E37	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \infty\cdot z = z\cdot\infty}	`infinity * z = z * infinity`	`Infinity * z == z * Infinity`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E38	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z/\infty = 0}	`z/ infinity = 0`	`z/ Infinity == 0`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E39	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z/0 = \infty}	`z/ 0 = infinity`	`z/ 0 == Infinity`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E44	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \frac{dw-b}{-cw+a}}	`z = (dw - b)/(- cw + a)`	`z == Divide[dw - b,- cw + a]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E48	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{f^{(n)}(z_{0})}{n!}}	`a[n] = ((f)^(n)*(z[0]))/(factorial(n))`	`Subscript[a, n] == Divide[(f)^(n)*(Subscript[z, 0]),(n)!]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E50	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=0}(a_{n}+ b_{n})z^{n} = \sum^{\infty}_{n=0}a_{n}z^{n}+\sum^{\infty}_{n=0}b_{n}z^{n}}	`sum((a[n]+ b[n])* (z)^(n), n = 0..infinity) = sum(a[n](z)^(n), n = 0..infinity)+ sum(b[n](z)^(n), n = 0..infinity)`	`Sum[(Subscript[a, n]+ Subscript[b, n])* (z)^(n), {n, 0, Infinity}, GenerateConditions->None] == Sum[Subscript[a, n](z)^(n), {n, 0, Infinity}, GenerateConditions->None]+ Sum[Subscript[b, n](z)^(n), {n, 0, Infinity}, GenerateConditions->None]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E51	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sum^{\infty}_{n=0}a_{n}z^{n}\right)\left(\sum^{\infty}_{n=0}b_{n}z^{n}\right) = \sum^{\infty}_{n=0}c_{n}z^{n}}	`(sum(a[n](z)^(n), n = 0..infinity))(sum(b[n](z)^(n), n = 0..infinity)) = sum(c[n](z)^(n), n = 0..infinity)`	`(Sum[Subscript[a, n](z)^(n), {n, 0, Infinity}, GenerateConditions->None])(Sum[Subscript[b, n](z)^(n), {n, 0, Infinity}, GenerateConditions->None]) == Sum[Subscript[c, n](z)^(n), {n, 0, Infinity}, GenerateConditions->None]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E52	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{n} = \sum^{n}_{k=0}a_{k}b_{n-k}}	`c[n] = sum(a[k]*b[n - k], k = 0..n)`	`Subscript[c, n] == Sum[Subscript[a, k]*Subscript[b, n - k], {k, 0, n}, GenerateConditions->None]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0} = 1/a_{0}}	`b[0] = 1/ a[0]`	`Subscript[b, 0] == 1/ Subscript[a, 0]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = -a_{1}/a_{0}^{2}}	`b[1] = - a[1]/ (a[0])^(2)`	`Subscript[b, 1] == - Subscript[a, 1]/ (Subscript[a, 0])^(2)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3}}	`b[2] (a(a[1])^(2)- a[0]*a[2])/ (a[0])^(3)`	`Subscript[b, 2] (a(Subscript[a, 1])^(2)- Subscript[a, 0]*Subscript[a, 2])/ (Subscript[a, 0])^(3)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{1} = a_{1}}	`q[1] = a[1]`	`Subscript[q, 1] == Subscript[a, 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{2} = (2a_{2}-a_{1}^{2})/2}	`q[2] (2*a[2]- a(a[1])^(2))/ 2`	`Subscript[q, 2] (2*Subscript[a, 2]- a(Subscript[a, 1])^(2))/ 2`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3}	`q[3] (3a[3]- 3a[1]*a[2]+ a(a[1])^(3))/ 3`	`Subscript[q, 3] (3Subscript[a, 3]- 3Subscript[a, 1]*Subscript[a, 2]+ a(Subscript[a, 1])^(3))/ 3`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{0} = 1}	`p[0] = 1`	`Subscript[p, 0] == 1`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{1} = \nu a_{1}}	`p[1] = nu*a[1]`	`Subscript[p, 1] == \[Nu]*Subscript[a, 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9#Ex21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2}	`p[2] = ((nu - 1)a(a[1])^(2)+ 2a[2])/ 2`	`Subscript[p, 2] == ((\[Nu]- 1)a(Subscript[a, 1])^(2)+ 2Subscript[a, 2])/ 2`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E63	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}}	`(f)^(m)(z) = sum(pochhammer(n + 1, m)a[n + m]*(z - z[0])^(n), n = 0..infinity)`	`(f)^(m)(z) == Sum[Pochhammer[n + 1, m]Subscript[a, n + m]*(z - Subscript[z, 0])^(n), {n, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
1.9.E64	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|z_{m,n}-z\| < \epsilon}	`abs(z[m , n]- z) < epsilon`	`Abs[Subscript[z, m , n]- z] < \[Epsilon]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E66	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{p,q} = \sum^{p}_{m=0}\sum^{q}_{n=0}\zeta_{m,n}}	`z[p , q] = sum(sum(zeta[m , n], n = 0..q), m = 0..p)`	`Subscript[z, p , q] == Sum[Sum[Subscript[\[Zeta], m , n], {n, 0, q}, GenerateConditions->None], {m, 0, p}, GenerateConditions->None]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.9.E71	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\diff{t} = \sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\diff{t}}	`int(sum(f[n](t), n = 0..infinity), t = a..b) = sum(int(f[n](t), t = a..b), n = 0..infinity)`	`Integrate[Sum[Subscript[f, n](t), {n, 0, Infinity}, GenerateConditions->None], {t, a, b}, GenerateConditions->None] == Sum[Integrate[Subscript[f, n](t), {t, a, b}, GenerateConditions->None], {n, 0, Infinity}, GenerateConditions->None]`	Successful	Error	-	Skipped - Because timed out
1.10.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\ln@{1+a_{n}(z)}\| \leq M_{n}}	`abs(ln(1 + a[n]*(z))) <= M[n]`	`Abs[Log[1 + Subscript[a, n]*(z)]] <= Subscript[M, n]`	Failure	Failure	Failed [126 / 300] `126/300]: [[.7588760888 <= -1.5 <- {z = 1/23^(1/2)+1/2I, M[n] = -1.5, a[n] = 1/23^(1/2)+1/2I, n = 1}` `.7588760888 <= -1.5 <- {z = 1/23^(1/2)+1/2I, M[n] = -1.5, a[n] = 1/23^(1/2)+1/2I, n = 2}` `.7588760888 <= -1.5 <- {z = 1/23^(1/2)+1/2I, M[n] = -1.5, a[n] = 1/23^(1/2)+1/2I, n = 3}` `1.465287519 <= -1.5 <- {z = 1/23^(1/2)+1/2I, M[n] = -1.5, a[n] = -1/2+1/2I3^(1/2), n = 1}` ... skip entries to safe data	Failed [246 / 300] `{LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
1.10.E21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=1}M_{n} < \infty}	`sum(M[n] , n = 1..infinity)< infinity`	`Sum[Subscript[M, n] , {n, 1, Infinity}, GenerateConditions->None]< Infinity`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.10.E22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}}	`P(z) = product((1 -(z)/(z[n])) exp(z/ z[n]), n = 1..infinity)`	`P(z) == Product[(1 -Divide[z,Subscript[z, n]]) Exp[z/ Subscript[z, n]], {n, 1, Infinity}, GenerateConditions->None]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{k} = \alpha b_{k+1}+a_{k}}	`b[k] = alpha*b[k + 1]+ a[k]`	`Subscript[b, k] == \[Alpha]*Subscript[b, k + 1]+ Subscript[a, k]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{k} = \alpha c_{k+1}+b_{k}}	`c[k] = alpha*c[k + 1]+ b[k]`	`Subscript[c, k] == \[Alpha]*Subscript[c, k + 1]+ Subscript[b, k]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#E10Xa	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sum_{1\leq j<k\leq n}z_{j}z_{k} = a_{n-2}/a_{n}}	`sum(sum(z[j]*z[k], k = j + 1..n), j = 1..k - 1) = a[n - 2]/ a[n]`	`Sum[Sum[Subscript[z, j]*Subscript[z, k], {k, j + 1, n}, GenerateConditions->None], {j, 1, k - 1}, GenerateConditions->None] == Subscript[a, n - 2]/ Subscript[a, n]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D = b^{2}-4ac}	`D = (b)^(2)- 4ac`	`D == (b)^(2)- 4ac`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3}}	`rho = -(1)/(2)+(1)/(2)*sqrt(- 3)`	`\[Rho] == -Divide[1,2]+Divide[1,2]*Sqrt[- 3]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho^{2} = e^{-2\pi i/3}}	`(rho)^(2) = exp(- 2PiI/ 3)`	`\[Rho]^(2) == Exp[- 2PiI/ 3]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = (-3a^{2}+8b)/8}	`p = (- 3(a)^(2)+ 8b)/ 8`	`p == (- 3(a)^(2)+ 8b)/ 8`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = (a^{3}-4ab+8c)/8}	`q = ((a)^(3)- 4ab + 8*c)/ 8`	`q == ((a)^(3)- 4ab + 8*c)/ 8`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = (-3a^{4}+16a^{2}b-64ac+256d)/256}	`r = (- 3(a)^(4)+ 16(a)^(2)* b - 64ac + 256*d)/ 256`	`r == (- 3(a)^(4)+ 16(a)^(2)* b - 64ac + 256*d)/ 256`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0}	`(z)^(3)- 2p(z)^(2)+((p)^(2)- 4r) z + (q)^(2) = 0`	`(z)^(3)- 2p(z)^(2)+((p)^(2)- 4r) z + (q)^(2) == 0`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q}	`sqrt(- theta[1])sqrt(- theta[2])sqrt(- theta[3]) = - q`	`Sqrt[- Subscript[\[Theta], 1]]Sqrt[- Subscript[\[Theta], 2]]Sqrt[- Subscript[\[Theta], 3]] == - q`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{n} = a+ib}	`(z)^(n) = a + I*b`	`(z)^(n) == a + I*b`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{1} = a_{1}}	`D[1] = a[1]`	`Subscript[D, 1] == Subscript[a, 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}}	`A[k] = b[k]A[k - 1]+ a[k]A[k - 2]`	`Subscript[A, k] == Subscript[b, k]Subscript[A, k - 1]+ Subscript[a, k]Subscript[A, k - 2]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}}	`B[k] = b[k]B[k - 1]+ a[k]B[k - 2]`	`Subscript[B, k] == Subscript[b, k]Subscript[B, k - 1]+ Subscript[a, k]Subscript[B, k - 2]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1} = 1}	`A[- 1] = 1`	`Subscript[A, - 1] == 1`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0} = b_{0}}	`A[0] = b[0]`	`Subscript[A, 0] == Subscript[b, 0]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-1} = 0}	`B[- 1] = 0`	`Subscript[B, - 1] == 0`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0} = 1}	`B[0] = 1`	`Subscript[B, 0] == 1`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}}	`A[n]B[n - 1]- B[n]A[n - 1] = (- 1)^(n - 1)* product(a[k], k = 1..n)`	`Subscript[A, n]Subscript[B, n - 1]- Subscript[B, n]Subscript[A, n - 1] == (- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}}	`C[n]- C[n - 1] = ((- 1)^(n - 1)* product(a[k], k = 1..n))/(B[n - 1]*B[n])`	`Subscript[C, n]- Subscript[C, n - 1] == Divide[(- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None],Subscript[B, n - 1]*Subscript[B, n]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}}	`a[n] = (A[n - 1]B[n]- A[n]B[n - 1])/(A[n - 1]B[n - 2]- A[n - 2]B[n - 1])`	`Subscript[a, n] == Divide[Subscript[A, n - 1]Subscript[B, n]- Subscript[A, n]Subscript[B, n - 1],Subscript[A, n - 1]Subscript[B, n - 2]- Subscript[A, n - 2]Subscript[B, n - 1]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}}	`a[n] = (B[n])/(B[n - 2])*(C[n - 1]- C[n])/(C[n - 1]- C[n - 2])`	`Subscript[a, n] == Divide[Subscript[B, n],Subscript[B, n - 2]]*Divide[Subscript[C, n - 1]- Subscript[C, n],Subscript[C, n - 1]- Subscript[C, n - 2]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}}	`b[n] = (A[n]B[n - 2]- A[n - 2]B[n])/(A[n - 1]B[n - 2]- A[n - 2]B[n - 1])`	`Subscript[b, n] == Divide[Subscript[A, n]Subscript[B, n - 2]- Subscript[A, n - 2]Subscript[B, n],Subscript[A, n - 1]Subscript[B, n - 2]- Subscript[A, n - 2]Subscript[B, n - 1]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}}	`b[n] = (B[n])/(B[n - 1])*(C[n]- C[n - 2])/(C[n - 1]- C[n - 2])`	`Subscript[b, n] == Divide[Subscript[B, n],Subscript[B, n - 1]]*Divide[Subscript[C, n]- Subscript[C, n - 2],Subscript[C, n - 1]- Subscript[C, n - 2]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0} = A_{0}}	`b[0] = A[0]`	`Subscript[b, 0] == Subscript[A, 0]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = B_{1}}	`b[1] = B[1]`	`Subscript[b, 1] == Subscript[B, 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1} = A_{1}-A_{0}B_{1}}	`a[1] = A[1]- A[0]*B[1]`	`Subscript[a, 1] == Subscript[A, 1]- Subscript[A, 0]*Subscript[B, 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}}	`C[n](w) = (A[n]+ A[n - 1]w)/(B[n]+ B[n - 1]*w)`	`Subscript[C, n](w) == Divide[Subscript[A, n]+ Subscript[A, n - 1]w,Subscript[B, n]+ Subscript[B, n - 1]*w]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}(0) = C_{n}}	`C[n]*(0) = C[n]`	`Subscript[C, n]*(0) == Subscript[C, n]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}(\infty) = C_{n-1}}	`C[n]*(infinity) = C[n - 1]`	`Subscript[C, n]*(Infinity) == Subscript[C, n - 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E25	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|b_{n}\| \geq \|a_{n}\|+1}	`abs(b[n]) >= abs(a[n])+ 1`	`Abs[Subscript[b, n]] >= Abs[Subscript[a, n]]+ 1`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}}	`-(1)/(2)*Pi + delta < argument(b[n])`	`-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[b, n]]`	Failure	Failure	Failed [27 / 300] `27/300]: [[-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2I3^(1/2), n = 1, n = 3}` `-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2I3^(1/2), n = 2, n = 3}` `-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2I3^(1/2), n = 3, n = 3}` `-.70796327e-1 < -2.617993878 <- {delta = 1.5, b[n] = -1/23^(1/2)-1/2I, n = 1, n = 3}` ... skip entries to safe data	Failed [49 / 100] `{Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.12.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta}	`argument(b[n]) < (1)/(2)*Pi - delta`	`Arg[Subscript[b, n]] < Divide[1,2]*Pi - \[Delta]`	Failure	Failure	Failed [72 / 300] `72/300]: [[3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 1, n = 3}` `3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 2, n = 3}` `3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 3, n = 3}` `3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -.5, n = 1, n = 3}` ... skip entries to safe data	Failed [64 / 100] `{Less[0.5235987755982988, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Less[2.0943951023931953, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.12.E27	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}}	`-(1)/(2)*Pi + delta < argument(C[n])`	`-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[C, n]]`	Failure	Failure	Failed [27 / 300] `27/300]: [[-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2I3^(1/2), n = 1, n = 3}` `-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2I3^(1/2), n = 2, n = 3}` `-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2I3^(1/2), n = 3, n = 3}` `-.70796327e-1 < -2.617993878 <- {delta = 1.5, C[n] = -1/23^(1/2)-1/2I, n = 1, n = 3}` ... skip entries to safe data	Failed [49 / 100] `{Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.12.E27	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta}	`argument(C[n]) < (1)/(2)*Pi - delta`	`Arg[Subscript[C, n]] < Divide[1,2]*Pi - \[Delta]`	Failure	Failure	Failed [72 / 300] `72/300]: [[3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 1, n = 3}` `3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 2, n = 3}` `3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 3, n = 3}` `3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -.5, n = 1, n = 3}` ... skip entries to safe data	Failed [64 / 100] `{Less[0.5235987755982988, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Less[2.0943951023931953, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.12.E28	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=1}\|b_{n}\| = \infty}	`sum(abs(b[n]), n = 1..infinity) = infinity`	`Sum[Abs[Subscript[b, n]], {n, 1, Infinity}, GenerateConditions->None] == Infinity`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.13.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = Aw_{1}(z)+Bw_{2}(z)}	`w(z) = Aw[1](z)+ Bw[2]*(z)`	`w(z) == ASubscript[w, 1](z)+ BSubscript[w, 2]*(z)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.13#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z_{0}) = 1}	`w[1]*(z[0]) = 1`	`Subscript[w, 1]*(Subscript[z, 0]) == 1`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.13#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z_{0}) = 0}	`w[2]*(z[0]) = 0`	`Subscript[w, 2]*(Subscript[z, 0]) == 0`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.13.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Aw_{1}(z)+Bw_{2}(z) = 0}	`Aw[1](z)+ Bw[2](z) = 0`	`ASubscript[w, 1](z)+ BSubscript[w, 2](z) == 0`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.13.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)}	`w(z) = w[0](z)+ Aw[1](z)+ Bw[2](z)`	`w(z) == Subscript[w, 0](z)+ ASubscript[w, 1](z)+ BSubscript[w, 2](z)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.13#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W(\xi) = w\left(\frac{1}{\xi}\right)}	`W(xi) = w((1)/(xi))`	`W(\[Xi]) == w(Divide[1,\[Xi]])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.13#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{U}{z}+IU = 0}	`diff(U, [z$(2)])+ I*U = 0`	`D[U, {z, 2}]+ I*U == 0`	Failure	Failure	Failed [300 / 300] `300/300]: [[.5000000004+.8660254040I <- {I = 1/23^(1/2)+1/2I, U = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `.5000000004+.8660254040I <- {I = 1/23^(1/2)+1/2I, U = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}` `.5000000004+.8660254040I <- {I = 1/23^(1/2)+1/2I, U = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)}` `.5000000004+.8660254040I <- {I = 1/23^(1/2)+1/2I, U = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Failed [210 / 210] `{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[Complex[0, 1], 1], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.7320508075688774, 0.9999999999999999] <- {Rule[Complex[0, 1], 2], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
1.13#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{V}{z}+JV = 0}	`diff(V, [z$(2)])+ J*V = 0`	`D[V, {z, 2}]+ J*V == 0`	Failure	Failure	Failed [300 / 300] `300/300]: [[.5000000004+.8660254040I <- {J = 1/23^(1/2)+1/2I, V = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `.5000000004+.8660254040I <- {J = 1/23^(1/2)+1/2I, V = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}` `.5000000004+.8660254040I <- {J = 1/23^(1/2)+1/2I, V = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)}` `.5000000004+.8660254040I <- {J = 1/23^(1/2)+1/2I, V = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Failed [300 / 300] `{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.15.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{n} = \sum_{k=0}^{n}a_{k}}	`s[n] = sum(a[k], k = 0..n)`	`Subscript[s, n] == Sum[Subscript[a, k], {k, 0, n}, GenerateConditions->None]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to 1-}\sum^{\infty}_{n=0}a_{n}x^{n} = s}	`limit(sum(a[n]*(x)^(n), n = 0..infinity), x = 1, left) = s`	`Limit[Sum[Subscript[a, n]*(x)^(n), {n, 0, Infinity}, GenerateConditions->None], x -> 1, Direction -> "FromBelow", GenerateConditions->None] == s`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\frac{n!}{(\alpha+1)_{n}}\sum^{n}_{k=0}\frac{(\alpha+1)_{k}}{k!}a_{n-k} = s}	`limit((factorial(n))/(alpha + 1[n])sum((alpha + 1[k])/(factorial(k))a[n - k], k = 0..n), n = infinity) = s`	`Limit[Divide[(n)!,Subscript[\[Alpha]+ 1, n]]Sum[Divide[Subscript[\[Alpha]+ 1, k],(k)!]Subscript[a, n - k], {k, 0, n}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == s`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{t\to\infty}e^{-t}\sum^{\infty}_{n=0}\frac{s_{n}}{n!}t^{n} = s}	`limit(exp(- t)sum((s[n])/(factorial(n))(t)^(n), n = 0..infinity), t = infinity) = s`	`Limit[Exp[- t]Sum[Divide[Subscript[s, n],(n)!](t)^(n), {n, 0, Infinity}, GenerateConditions->None], t -> Infinity, GenerateConditions->None] == s`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=0}a_{n} = s}	`sum(a[n], n = 0..infinity) = s`	`Sum[Subscript[a, n], {n, 0, Infinity}, GenerateConditions->None] == s`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1}	`(1)/(2Pi)int(P(r , theta), theta = 0..2Pi) = 1`	`Divide[1,2Pi]Integrate[P(r , \[Theta]), {\[Theta], 0, 2Pi}, GenerateConditions->None] == 1`	Successful	Error	-	Successful [Tested: 1]
1.15.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1}	`(1)/(2Pi)int(K[n](theta), theta = 0..2Pi) = 1`	`Divide[1,2Pi]Integrate[Subscript[K, n](\[Theta]), {\[Theta], 0, 2Pi}, GenerateConditions->None] == 1`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
1.15.E34	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1}	`(1)/(2Pi)int(P*(x , y), x = - infinity..infinity) = 1`	`Divide[1,2Pi]Integrate[P*(x , y), {x, - Infinity, Infinity}, GenerateConditions->None] == 1`	Successful	Successful	-	Successful [Tested: 3]
1.15.E39	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Phi(z) = \Phi(x+iy)}	`Phi((x + yI)) = Phi(x + Iy)`	`\[CapitalPhi]((x + yI)) == \[CapitalPhi](x + Iy)`	Successful	Successful	-	Successful [Tested: 180]
1.15.E42	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{\infty}_{-\infty}K_{R}(s)\diff{s} = 1}	`int(K[R]*(s), s = - infinity..infinity) = 1`	`Integrate[Subscript[K, R]*(s), {s, - Infinity, Infinity}, GenerateConditions->None] == 1`	Failure	Error	Failed [7 / 10] `7/10]: [[-.1339745960+.5000000000I <- {R = 1/23^(1/2)+1/2I}` `-1.500000000+.8660254040I <- {R = -1/2+1/2I3^(1/2)}` `-.5000000000-.8660254040I <- {R = 1/2-1/2I3^(1/2)}` `-1.866025404-.5000000000I <- {R = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Skipped - Because timed out
1.15.E48	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I^{\alpha}I^{\beta} = I^{\alpha+\beta}}	`(I)^(alpha)* (I)^(beta) = (I)^(alpha + beta)`	`(I)^\[Alpha]* (I)^\[Beta] == (I)^(\[Alpha]+ \[Beta])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E52	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D^{k}I^{\alpha} = D^{n}I^{\alpha+n-k}}	`(D)^(k)* (I)^(alpha) = (D)^(n)* (I)^(alpha + n - k)`	`(D)^(k)* (I)^\[Alpha] == (D)^(n)* (I)^(\[Alpha]+ n - k)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E53	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D^{\alpha}D^{\beta} = D^{\alpha+\beta}}	`(D)^(alpha)* (D)^(beta) = (D)^(alpha + beta)`	`(D)^\[Alpha]* (D)^\[Beta] == (D)^(\[Alpha]+ \[Beta])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} > -\frac{K}{n}}	`a[n] > -(K)/(n)`	`Subscript[a, n] > -Divide[K,n]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E55	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=0}a_{n} = s}	`sum(a[n], n = 0..infinity) = s`	`Sum[Subscript[a, n], {n, 0, Infinity}, GenerateConditions->None] == s`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.15.E56	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to 1-}(1-x)\sum^{\infty}_{n=0}a_{n}x^{n} = s}	`limit((1 - x)* sum(a[n]*(x)^(n), n = 0..infinity), x = 1, left) = s`	`Limit[(1 - x)* Sum[Subscript[a, n]*(x)^(n), {n, 0, Infinity}, GenerateConditions->None], x -> 1, Direction -> "FromBelow", GenerateConditions->None] == s`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Lambda(\alpha_{1}\phi_{1}+\alpha_{2}\phi_{2}) = \alpha_{1}\Lambda(\phi_{1})+\alpha_{2}\Lambda(\phi_{2})}	`Lambda(alpha[1]phi[1]+ alpha[2]phi[2]) = alpha[1]Lambda(phi[1])+ alpha[2]Lambda*(phi[2])`	`\[CapitalLambda](Subscript[\[Alpha], 1]Subscript[\[Phi], 1]+ Subscript[\[Alpha], 2]Subscript[\[Phi], 2]) == Subscript[\[Alpha], 1]\[CapitalLambda](Subscript[\[Phi], 1])+ Subscript[\[Alpha], 2]\[CapitalLambda]*(Subscript[\[Phi], 2])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\Lambda(\phi_{n}) = \Lambda(\phi)}	`limit(Lambda(phi[n]), n = infinity) = Lambda(phi)`	`Limit[\[CapitalLambda](Subscript[\[Phi], n]), n -> Infinity, GenerateConditions->None] == \[CapitalLambda](\[Phi])`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma_{n} = f^{(n)}(x_{0}+)-f^{(n)}(x_{0}-)}	`sigma[n] = (f)^(n)(x[0]+)- (f)^(n)(x[0]-)`	`Subscript[\[Sigma], n] == (f)^(n)(Subscript[x, 0]+)- (f)^(n)(Subscript[x, 0]-)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{\alpha}_{+} = x^{\alpha}\HeavisideH@{x}}	`(x[+])^(alpha) = (x)^(alpha)* Heaviside(x)`	`(Subscript[x, +])^\[Alpha] == (x)^\[Alpha]* HeavisideTheta[x]`	Error	Failure	-	Error
1.16.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Dx^{\alpha}_{+} = \alpha x_{+}^{\alpha-1}}	`D(x[+])^(alpha) = alpha(x[+])^(alpha - 1)`	`D(Subscript[x, +])^\[Alpha] == \[Alpha](Subscript[x, +])^(\[Alpha]- 1)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{\alpha}_{+} = \frac{1}{(\alpha+1)_{n}}D^{n}x_{+}^{\alpha+n}}	`(x[+])^(alpha) = (1)/(alpha + 1[n])(D)^(n) (x[+])^(alpha + n)`	`(Subscript[x, +])^\[Alpha] == Divide[1,Subscript[\[Alpha]+ 1, n]](D)^(n) (Subscript[x, +])^(\[Alpha]+ n)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x}	`(- 1)^(n)* factorial(n)(x[+])^(- 1 - n) = (D)^(n + 1) [+]ln()*x`	`(- 1)^(n)* (n)!(Subscript[x, +])^(- 1 - n) == Subscript[(D)^(n + 1) , +]Log[]*x`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E24	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|x^{N}\phi_{n}^{(k)}\| \leq c_{k,N}}	`abs((x)^(N)* phi(phi[n])^(k)) <= c[k , N]`	`Abs[(x)^(N)* \[Phi](Subscript[\[Phi], n])^(k)] <= Subscript[c, k , N]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E28	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|x^{m}\phi^{(k)}(x)\| \leq c_{m,k}}	`abs((x)^(m)* (phi)^(k)*(x)) <= c[m , k]`	`Abs[(x)^(m)* \[Phi]^(k)*(x)] <= Subscript[c, m , k]`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{\boldsymbol{{\alpha}}} = \iunit^{-\|\boldsymbol{{\alpha}}\|}D^{\boldsymbol{{\alpha}}}}	`D[alpha] = (I)^(-abs(alpha))* (D)^(alpha)`	`Subscript[D, \[Alpha]] == (I)^(-Abs[\[Alpha]])* (D)^\[Alpha]`	Failure	Failure	Failed [300 / 300] `300/300]: [[.8660254041+1.500000000I <- {D = 1/23^(1/2)+1/2I, alpha = 1.5, D[alpha] = 1/23^(1/2)+1/2I}` `-.4999999999+1.866025404I <- {D = 1/23^(1/2)+1/2I, alpha = 1.5, D[alpha] = -1/2+1/2I3^(1/2)}` `.5000000001+.1339745960I <- {D = 1/23^(1/2)+1/2I, alpha = 1.5, D[alpha] = 1/2-1/2I3^(1/2)}` `-.8660254039+.5000000000I <- {D = 1/23^(1/2)+1/2I, alpha = 1.5, D[alpha] = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Failed [300 / 300] `{Complex[0.8660254037844387, 1.5] <- {Rule[D, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[D, α], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.4999999999999998, 1.8660254037844388] <- {Rule[D, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[D, α], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
1.16.E33	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathscr{F}(P(\mathbf{D})\phi)(\mathbf{x}) = P(-\mathbf{x})\mathscr{F}\phi(\mathbf{x})}	`F(P(D)phi)(x) = P(- x) Fphi(x)`	`F(P(D)\[Phi])(x) == P(- x) F\[Phi](x)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E34	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathscr{F}(P\phi)(\mathbf{x}) = P(\mathbf{D})\mathscr{F}\phi(\mathbf{x})}	`F(Pphi)(x) = P(D)* Fphi(x)`	`F(P\[Phi])(x) == P(D)* F\[Phi](x)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{F}(P(D)u) = P(-\mathbf{x})\mathcal{F}(u)}	`F(P(D)u) = P(- x)* F*(u)`	`F(P(D)u) == P(- x)* F*(u)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{F}(Pu) = P(D)\mathcal{F}(u)}	`F(Pu) = P(D) F*(u)`	`F(Pu) == P(D) F*(u)`	Skipped - no semantic math	Skipped - no semantic math	-	-
1.16.E40	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{\infty}_{-\infty}\Diracdelta@{t}\expe^{\iunit xt}\diff{t} = 1}	`int(Dirac(t)exp(Ix*t), t = - infinity..infinity) = 1`	`Integrate[DiracDelta[t]Exp[Ix*t], {t, - Infinity, Infinity}, GenerateConditions->None] == 1`	Successful	Successful	-	Successful [Tested: 3]
1.16.E43	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\cpi}\int^{\infty}_{-\infty}\expe^{\iunit xt}\diff{t} = \Diracdelta@{x}}	`(1)/(2Pi)int(exp(Ixt), t = - infinity..infinity) = Dirac(x)`	`Divide[1,2Pi]Integrate[Exp[Ixt], {t, - Infinity, Infinity}, GenerateConditions->None] == DiracDelta[x]`	Successful	Failure	-	Failed [3 / 3] `{Complex[-0.07099199156997928, 3.003857199159988*^-16] <- {Rule[x, 1.5]}` `Complex[0.07742603591272186, 0.30312240144001046] <- {Rule[x, 0.5]}`
1.16.E44	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sign@{x} = 2\HeavisideH@{x}-1}	`signum(x) = 2*Heaviside(x)- 1`	`Sign[x] == 2*HeavisideTheta[x]- 1`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
1.17.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x} = 0}	`Dirac(x) = 0`	`DiracDelta[x] == 0`	Failure	Successful	Successful [Tested: 3]	Successful [Tested: 1]
1.17.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\Diracdelta@{x-a}\phi(x)\diff{x} = \phi(a)}	`int(Dirac(x - a)phi(x), x = - infinity..infinity) = phi*(a)`	`Integrate[DiracDelta[x - a]\[Phi](x), {x, - Infinity, Infinity}, GenerateConditions->None] == \[Phi]*(a)`	Successful	Successful	-	Successful [Tested: 10]
1.17.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \phi(a)}	`limit(sqrt((n)/(Pi))int(exp(- n(x - a)^(2))phi(x), x = - infinity..infinity), n = infinity) = phi*(a)`	`Limit[Sqrt[Divide[n,Pi]]Integrate[Exp[- n(x - a)^(2)]\[Phi](x), {x, - Infinity, Infinity}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == \[Phi]*(a)`	Successful	Error	-	Successful [Tested: 60]
1.17.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \tfrac{1}{2}\phi(a-)+\tfrac{1}{2}\phi(a+)}	`limit(sqrt((n)/(Pi))int(exp(- n(x - a)^(2))phi(x), x = - infinity..infinity), n = infinity) = (1)/(2)phi(a -)+(1)/(2)phi(a +)`	`Limit[Sqrt[Divide[n,Pi]]Integrate[Exp[- n(x - a)^(2)]\[Phi](x), {x, - Infinity, Infinity}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == Divide[1,2]\[Phi](a -)+Divide[1,2]\[Phi](a +)`	Error	Failure	-	Error
1.17.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left(\int_{-\infty}^{\infty}\phi(x)e^{itx}\diff{x}\right)\diff{t} = \phi(a)}	`(1)/(2Pi)int(exp(- Iat)(int(phi(x)* exp(Itx), x = - infinity..infinity)), t = - infinity..infinity) = phi*(a)`	`Divide[1,2Pi]Integrate[Exp[- Iat](Integrate[\[Phi](x)* Exp[Itx], {x, - Infinity, Infinity}, GenerateConditions->None]), {t, - Infinity, Infinity}, GenerateConditions->None] == \[Phi]*(a)`	Failure	Error	Failed [60 / 60] `60/60]: [[Float(undefined)+.7500000000I <- {a = -1.5, phi = 1/23^(1/2)+1/2I}` `Float(undefined)+1.299038106I <- {a = -1.5, phi = -1/2+1/2I3^(1/2)}` `Float(undefined)-1.299038106I <- {a = -1.5, phi = 1/2-1/2I3^(1/2)}` `Float(undefined)-.7500000000I <- {a = -1.5, phi = -1/23^(1/2)-1/2I}` ... skip entries to safe data	Skipped - Because timed out
1.17.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}\right)\phi(x)\diff{x} = \phi(a)}	`int(((1)/(2Pi)int(exp(I(x - a) t), t = - infinity..infinity))* phi(x), x = - infinity..infinity) = phi(a)`	`Integrate[(Divide[1,2Pi]Integrate[Exp[I(x - a) t], {t, - Infinity, Infinity}, GenerateConditions->None])* \[Phi](x), {x, - Infinity, Infinity}, GenerateConditions->None] == \[Phi](a)`	Successful	Error	-	Skipped - Because timed out
1.17.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\diff{t} = \sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}}	`(1)/(2Pi)int(exp(- (t)^(2)/(4n))exp(I(x - a) t), t = - infinity..infinity) = sqrt((n)/(Pi))exp(- n(x - a)^(2))`	`Divide[1,2Pi]Integrate[Exp[- (t)^(2)/(4n)]Exp[I(x - a) t], {t, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[n,Pi]]Exp[- n(x - a)^(2)]`	Failure	Successful	Successful [Tested: 54]	Successful [Tested: 54]
1.17.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}}	`Dirac(x - a) = (1)/(2Pi)int(exp(I(x - a) t), t = - infinity..infinity)`	`DiracDelta[x - a] == Divide[1,2Pi]Integrate[Exp[I(x - a) t], {t, - Infinity, Infinity}, GenerateConditions->None]`	Successful	Failure	-	Skipped - Because timed out
1.17.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = x\int_{0}^{\infty}t\BesselJ{\nu}@{xt}\BesselJ{\nu}@{at}\diff{t}}	`Dirac(x - a) = xint(tBesselJ(nu, xt)BesselJ(nu, a*t), t = 0..infinity)`	`DiracDelta[x - a] == xIntegrate[tBesselJ[\[Nu], xt]BesselJ[\[Nu], a*t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Error	Error	Skipped - Because timed out
1.17.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \int_{-\infty}^{\infty}\AiryAi@{t-x}\AiryAi@{t-a}\diff{t}}	`Dirac(x - a) = int(AiryAi(t - x)*AiryAi(t - a), t = - infinity..infinity)`	`DiracDelta[x - a] == Integrate[AiryAi[t - x]*AiryAi[t - a], {t, - Infinity, Infinity}, GenerateConditions->None]`	Failure	Error	Skipped - Because timed out	Skipped - Because timed out
1.17.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}\left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\diff{x}\right) = \phi(a)}	`(1)/(2Pi)sum(exp(- Ika)(int(phi(x)* exp(Ikx), x = - Pi..Pi)), k = - infinity..infinity) = phi*(a)`	`Divide[1,2Pi]Sum[Exp[- Ika](Integrate[\[Phi](x)* Exp[Ikx], {x, - Pi, Pi}, GenerateConditions->None]), {k, - Infinity, Infinity}, GenerateConditions->None] == \[Phi]*(a)`	Error	Failure	-	Successful [Tested: 60]
1.17.E21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}}	`Dirac(x - a) = (1)/(2Pi)sum(exp(Ik(x - a)), k = - infinity..infinity)`	`DiracDelta[x - a] == Divide[1,2Pi]Sum[Exp[Ik(x - a)], {k, - Infinity, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [18 / 18] `{Times[-0.15915494309189535, NSum[Power[E, Times[Complex[0.0, 3.0], k]] <- {k, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}` `Times[-0.15915494309189535, NSum[Power[E, Times[Complex[0.0, 2.0], k]] <- {k, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}`
1.17.E22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \sum_{k=0}^{\infty}(k+\tfrac{1}{2})\LegendrepolyP{k}@{x}\LegendrepolyP{k}@{a}}	`Dirac(x - a) = sum((k +(1)/(2))* LegendreP(k, x)*LegendreP(k, a), k = 0..infinity)`	`DiracDelta[x - a] == Sum[(k +Divide[1,2])* LegendreP[k, x]*LegendreP[k, a], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Error	Failed [18 / 18] `{Times[-1.0, NSum[Times[Plus[Rational[1, 2], k], LegendreP[k, -1.5], LegendreP[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}` `Times[-1.0, NSum[Times[Plus[Rational[1, 2], k], LegendreP[k, -1.5], LegendreP[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}`
1.17.E23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = e^{-(x+a)/2}\sum_{k=0}^{\infty}\LaguerrepolyL[]{k}@{x}\LaguerrepolyL[]{k}@{a}}	`Dirac(x - a) = exp(-(x + a)/ 2)sum(LaguerreL(k, x)LaguerreL(k, a), k = 0..infinity)`	`DiracDelta[x - a] == Exp[-(x + a)/ 2]Sum[LaguerreL[k, x]LaguerreL[k, a], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Error	Failed [18 / 18] `{Times[-1.0, NSum[Times[LaguerreL[k, -1.5], LaguerreL[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}` `Times[-1.6487212707001282, NSum[Times[LaguerreL[k, -1.5], LaguerreL[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}`
1.17.E24	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{e^{-(x^{2}+a^{2})/2}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{\HermitepolyH{k}@{x}\HermitepolyH{k}@{a}}{2^{k}k!}}	`Dirac(x - a) = (exp(-((x)^(2)+ (a)^(2))/ 2))/(sqrt(Pi))sum((HermiteH(k, x)HermiteH(k, a))/((2)^(k)* factorial(k)), k = 0..infinity)`	`DiracDelta[x - a] == Divide[Exp[-((x)^(2)+ (a)^(2))/ 2],Sqrt[Pi]]Sum[Divide[HermiteH[k, x]HermiteH[k, a],(2)^(k)* (k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [18 / 18] `{Times[-0.05946514461181468, NSum[Times[Power[2, Times[-1, k]], Power[Factorial[k], -1], HermiteH[k, -1.5], HermiteH[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}` `Times[-0.16164302202498515, NSum[Times[Power[2, Times[-1, k]], Power[Factorial[k], -1], HermiteH[k, -1.5], HermiteH[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}`
1.17.E25	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{\cos@@{\theta_{1}}-\cos@@{\theta_{2}}}\Diracdelta@{\phi_{1}-\phi_{2}} = \sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell}\sphharmonicY{\ell}{m}@{\theta_{1}}{\phi_{1}}\conj{\sphharmonicY{\ell}{m}@{\theta_{2}}{\phi_{2}}}}	`Dirac(cos(theta[1])- cos(theta[2]))Dirac(phi[1]- phi[2]) = sum(sum(SphericalY(ell, m, theta[1], phi[1])conjugate(SphericalY(ell, m, theta[2], phi[2])), m = - ell..ell), ell = 0..infinity)`	`DiracDelta[Cos[Subscript[\[Theta], 1]]- Cos[Subscript[\[Theta], 2]]]DiracDelta[Subscript[\[Phi], 1]- Subscript[\[Phi], 2]] == Sum[Sum[SphericalHarmonicY[\[ScriptL], m, Subscript[\[Theta], 1], Subscript[\[Phi], 1]]Conjugate[SphericalHarmonicY[\[ScriptL], m, Subscript[\[Theta], 2], Subscript[\[Phi], 2]]], {m, - \[ScriptL], \[ScriptL]}, GenerateConditions->None], {\[ScriptL], 0, Infinity}, GenerateConditions->None]`	Error	Failure	Skipped - Because timed out	Skipped - Because timed out

Results of Algebraic and Analytic Methods

Navigation menu

Search