Results of Algebraic and Analytic Methods

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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)} n*a +(1)/(2)*n*(n - 1)* d = (1)/(2)*n*(a + ell) n*a +Divide[1,2]*n*(n - 1)* d == Divide[1,2]*n*(a + \[ScriptL]) Skipped - no semantic math Skipped - no semantic math - -
1.2.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(r) = 0} M*(r) = 0 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$(2)]) (f)^(2)*(x) == D[f, {x, 2}] Failure Failure
Failed [30 / 30]
30/30]: [[.7500000006+1.299038106*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5}
.2500000002+.4330127020*I <- {f = 1/2*3^(1/2)+1/2*I, x = .5}
1.000000001+1.732050808*I <- {f = 1/2*3^(1/2)+1/2*I, x = 2}
-.7500000006-1.299038106*I <- {f = -1/2+1/2*I*3^(1/2), x = 1.5}
... skip entries to safe data
Skip - symbolical successful subtest
1.4.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)} diff(f, [x$(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-.2500000000*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 1}
-.2500000002-.4330127020*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 2}
-.1616869430e-9-.5000000005*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 3}
.4330127020+.2500000000*I <- {f = 1/2*3^(1/2)+1/2*I, 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+.7500000000*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 1}
-.1160254034+.7990381060*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 2}
-.4999999999+.6339745980*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 3}
-.5669872980+.2500000000*I <- {f = 1/2*3^(1/2)+1/2*I, x = .5, n = 1}
... skip entries to safe data
Failed [84 / 90]
{Complex[0.299038105676658, 0.7499999999999999] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}
Complex[-0.11602540378443849, 0.799038105676658] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]}
1.4.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}} int(f*g, x) = (int(f, x))* g - int((int(f, x))* diff(g, x), x) Integrate[f*g, x, GenerateConditions->None] == (Integrate[f, x, GenerateConditions->None])* g - Integrate[(Integrate[f, x, GenerateConditions->None])* D[g, x], x, GenerateConditions->None] Successful Successful - Successful [Tested: 100]
1.4.E36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{n} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}} R[n] = ((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+2.448557159*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 1}
.8660254040+3.875000000*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 2}
-.6527245960+3.130552164*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 3}
.6250000000+2.814582563*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = -1/2+1/2*I*3^(1/2), n = 1}
... skip entries to safe data
Failed [300 / 300]
{Complex[1.9910254037844388, 2.4485571585149866] <- {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.8660254037844387, 3.875] <- {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
1.5.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{y} = D_{y}f} diff(f, y) = D[y]*f D[f, y] == Subscript[D, y]*f Failure Failure
Failed [300 / 300]
300/300]: [[-.5000000004-.8660254040*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I}
.8660254040-.5000000004*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2+1/2*I*3^(1/2)}
-.8660254040+.5000000004*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2-1/2*I*3^(1/2)}
.5000000004+.8660254040*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Failed [300 / 300]
{Complex[-0.5000000000000001, -0.8660254037844386] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.8660254037844387, -0.49999999999999994] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{y}f = f_{y}} D[y]*f = f[y] Subscript[D, y]*f == Subscript[f, y] Failure Failure
Failed [300 / 300]
300/300]: [[-.3660254036+.3660254040*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = 1/2*3^(1/2)+1/2*I}
1.000000000+0.*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = -1/2+1/2*I*3^(1/2)}
.4e-9+1.732050808*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = 1/2-1/2*I*3^(1/2)}
1.366025404+1.366025404*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Failed [300 / 300]
{Complex[-0.3660254037844386, 0.36602540378443865] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.9999999999999999, -1.1102230246251565*^-16] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = r\cos@@{\phi}} x = r*cos(phi) x == r*Cos[\[Phi]] Failure Failure
Failed [180 / 180]
180/180]: [[2.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}
1.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}
3.095814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 2}
.404185472+.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = 1.5, x = 1.5}
... skip entries to safe data
Failed [180 / 180]
{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\phi}} y = r*sin(phi) y == r*Sin[\[Phi]] Failure Failure
Failed [300 / 300]
300/300]: [[-.211529498+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}
2.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}
.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -.5}
1.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = .5}
... skip entries to safe data
Failed [300 / 300]
{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}} 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-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}
1.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}
3.095814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 2}
.404185472+.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = 1.5, x = 1.5}
... skip entries to safe data
Failed [180 / 180]
{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\phi}} y = r*sin(phi) y == r*Sin[\[Phi]] Failure Failure
Failed [300 / 300]
300/300]: [[-.211529498+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}
2.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}
.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -.5}
1.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = .5}
... skip entries to safe data
Failed [300 / 300]
{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = z} z = z 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 + y*I), diff( f, temp$(2) ) ) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) Successful Successful - Successful [Tested: 300]
1.5#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \rho\sin@@{\theta}\cos@@{\phi}} x = rho*sin(theta)*cos(phi) x == \[Rho]*Sin[\[Theta]]*Cos[\[Phi]] Failure Failure
Failed [300 / 300]
300/300]: [[.7933233780-.2990618885*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = 1.5}
-.2066766220-.2990618885*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = .5}
1.293323378-.2990618885*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = 2}
2.075937432-.6992275886*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = -1/2+1/2*I*3^(1/2), x = 1.5}
... skip entries to safe data
Failed [300 / 300]
{Complex[0.7933233783531031, -0.29906188871772155] <- {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.1325168401075085, -1.15603698835011] <- {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \rho\sin@@{\theta}\sin@@{\phi}} y = rho*sin(theta)*sin(phi) y == \[Rho]*Sin[\[Theta]]*Sin[\[Phi]] Failure Failure
Failed [300 / 300]
300/300]: [[-1.750303606-.8142131232*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = -1.5}
1.249696394-.8142131232*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = 1.5}
-.7503036064-.8142131232*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = -.5}
.2496963936-.8142131232*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = .5}
... skip entries to safe data
Failed [300 / 300]
{Complex[-1.750303605777159, -0.8142131229438421] <- {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.49444885508381575, -0.009630141394747549] <- {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \rho\cos@@{\theta}} z = rho*cos(theta) z == \[Rho]*Cos[\[Theta]] Failure Failure
Failed [300 / 300]
300/300]: [[.348818158e-1+.4784968852*I <- {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
-1.331143588+.8445222892*I <- {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
-.3311435882-.8875285188*I <- {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}
-1.697168992-.5215031148*I <- {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Failed [300 / 300]
{Complex[0.03488181560898618, 0.4784968849905366] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.8875285187939019, -0.3311435881754526] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.5.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)} diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = (1)/((rho)^(2))*diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))*diff(f, [phi$(2)]), rho)+(1)/((rho)^(2)* sin(theta))*diff(sin(theta)*diff(f, theta), theta) D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == Divide[1,\[Rho]^(2)]*D[(\[Rho]^(2)* D[f, \[Rho]])+Divide[1,\[Rho]^(2)* (Sin[\[Theta]])^(2)]*D[f, {\[Phi], 2}], \[Rho]]+Divide[1,\[Rho]^(2)* Sin[\[Theta]]]*D[Sin[\[Theta]]*D[f, \[Theta]], \[Theta]] Successful Successful - Successful [Tested: 300]
1.5.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{x} = \pderiv{f}{y}} 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 + y*I) Subscript[\[Psi], 1]*(x , y) <= (x + y*I) Skipped - no semantic math Skipped - no semantic math - -
1.6#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{a} = (a_{1},a_{2},a_{3})} 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-.3969495503*I <- {a = -1.5, b = -1.5, theta = 1/2*3^(1/2)+1/2*I}
.227765517+.4690753764*I <- {a = -1.5, b = -1.5, theta = -1/2+1/2*I*3^(1/2)}
.227765517+.4690753764*I <- {a = -1.5, b = -1.5, theta = 1/2-1/2*I*3^(1/2)}
-.2694569811-.3969495503*I <- {a = -1.5, b = -1.5, theta = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Failed [300 / 300]
{Complex[-0.2694569809427748, -0.3969495502290325] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.2277655168641104, 0.46907537626850365] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.6.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{a} = a_{1}\mathbf{i}+a_{2}\mathbf{j}+a_{3}\mathbf{k}} 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 + y*I, u)*(u[0], v[0])* k Subscript[T, u] == D[x, u]*(Subscript[u, 0], Subscript[v, 0])* I + D[y, u]*(Subscript[u, 0], Subscript[v, 0])* j + D[x + y*I, u]*(Subscript[u, 0], Subscript[v, 0])* k Failure Failure
Failed [300 / 300]
300/300]: [[.8660254040+.5000000000*I <- {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 1}
.8660254040+.5000000000*I <- {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 2}
.8660254040+.5000000000*I <- {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 3}
.8660254040+.5000000000*I <- {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 2, k = 1}
... skip entries to safe data
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 + y*I, v)*(u[0], v[0])* k Subscript[T, v] == D[x, v]*(Subscript[u, 0], Subscript[v, 0])* I + D[y, v]*(Subscript[u, 0], Subscript[v, 0])* j + D[x + y*I, v]*(Subscript[u, 0], Subscript[v, 0])* k Failure Failure
Failed [300 / 300]
300/300]: [[.8660254040+.5000000000*I <- {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 1}
.8660254040+.5000000000*I <- {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 2}
.8660254040+.5000000000*I <- {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 3}
.8660254040+.5000000000*I <- {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 2, k = 1}
... skip entries to safe data
Error
1.7.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 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/ omega)*cos(2*n*Pi*x), n = 1..infinity)) Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/ \[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}, GenerateConditions->None]) Failure Successful Successful [Tested: 15] Successful [Tested: 15]
1.9.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x+iy} (x + y*I) = x + I*y (x + y*I) == x + I*y Successful Successful - Successful [Tested: 1]
1.9#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{z} = x} 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-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = 1.5}
1.595814528-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = .5}
3.095814528-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = 2}
3.341648276+.7036130646*I <- {r = -1.5, theta = -1/2+1/2*I*3^(1/2), x = 1.5}
... skip entries to safe data
Failed [180 / 180]
{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.9#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = r\sin@@{\theta}} y = r*sin(theta) y == r*Sin[\[Theta]] Failure Failure
Failed [300 / 300]
300/300]: [[-.211529498+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = -1.5}
2.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = 1.5}
.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = -.5}
1.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = .5}
... skip entries to safe data
Failed [300 / 300]
{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.9.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = (x^{2}+y^{2})^{1/2}} r = ((x)^(2)+ (y)^(2))^(1/ 2) 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 = 1/2*3^(1/2)+1/2*I}
2.5 <- {r = -1.5, z = -1/2+1/2*I*3^(1/2)}
2.5 <- {r = -1.5, z = 1/2-1/2*I*3^(1/2)}
2.5 <- {r = -1.5, z = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Failed [39 / 42]
{2.5 <- {Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
2.5 <- {Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.9#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{z} = \theta+2n\pi} argument(z) = theta + 2*n*Pi Arg[z] == \[Theta]+ 2*n*Pi Error Failure -
Failed [70 / 70]
{Complex[-19.191982549724898, -0.49999999999999994] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-17.82595714594046, -0.8660254037844387] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.9#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\realpart@@{z}| \leq |z|} 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 = r*exp(I*theta) z == r*Exp[I*\[Theta]] Skipped - no semantic math Skipped - no semantic math - -
1.9.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{i\theta} = \cos@@{\theta}+i\sin@@{\theta}} exp(I*theta) = cos(theta)+ I*sin(theta) Exp[I*\[Theta]] == Cos[\[Theta]]+ I*Sin[\[Theta]] Successful Successful - Successful [Tested: 10]
1.9.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \conj{z} = x-iy} conjugate(x + y*I) = x - I*y Conjugate[x + y*I] == x - I*y Failure Failure Successful [Tested: 18] Successful [Tested: 18]
1.9.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\conj{z}| = |z|} 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 + y*I[1]+x + y*I[2] = x[1]+ x[2]+ I*(y[1]+ y[2]) Subscript[x + y*I, 1]+Subscript[x + y*I, 2] == Subscript[x, 1]+ Subscript[x, 2]+ I*(Subscript[y, 1]+ Subscript[y, 2]) Failure Failure Error
Failed [300 / 300]
{Plus[Complex[-0.7320508075688775, -2.732050807568877], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[-0.3660254037844388, -1.3660254037844388], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.9.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}- z_{2} = x_{1}- x_{2}+\iunit(y_{1}- y_{2})} x + y*I[1]-x + y*I[2] = x[1]- x[2]+ I*(y[1]- y[2]) Subscript[x + y*I, 1]-Subscript[x + y*I, 2] == Subscript[x, 1]- Subscript[x, 2]+ I*(Subscript[y, 1]- Subscript[y, 2]) Failure Failure Error
Failed [300 / 300]
{Plus[Subscript[Complex[1.5, -1.5], 1], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[-0.36602540378443876, -1.3660254037844384], Subscript[Complex[1.5, -1.5], 1], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.9.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}z_{2} = x_{1}x_{2}-y_{1}y_{2}+i(x_{1}y_{2}+x_{2}y_{1})} x + y*I[1]*x + y*I[2] = x[1]*x[2]- y[1]*y[2]+ I*(x[1]*y[2]+ x[2]*y[1]) Subscript[x + y*I, 1]*Subscript[x + y*I, 2] == Subscript[x, 1]*Subscript[x, 2]- Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 1]*Subscript[y, 2]+ Subscript[x, 2]*Subscript[y, 1]) Skipped - no semantic math Skipped - no semantic math - -
1.9.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}} (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] = 1/2*3^(1/2)+1/2*I, z[2] = -1.5}
-6.283185308 <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = -.5}
-6.283185308 <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = -2}
-6.283185309 <- {z[1] = -1/2+1/2*I*3^(1/2), z[2] = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data
Failed [25 / 100]
{-6.283185307179587 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], -1.5]}
-6.283185307179587 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], -0.5]}
1.9.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\frac{z_{1}}{z_{2}}} = \frac{|z_{1}|}{|z_{2}|}} abs((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+1/2*I*3^(1/2), z[2] = -1/2*3^(1/2)-1/2*I}
6.283185308 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -1/2+1/2*I*3^(1/2)}
6.283185307 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -1.5}
6.283185307 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -.5}
... skip entries to safe data
Failed [25 / 100]
{-6.283185307179586 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
6.283185307179586 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.9.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{n\theta}+i\sin@@{n\theta} = (\cos@@{\theta}+i\sin@@{\theta})^{n}} cos(n*theta)+ I*sin(n*theta) = (cos(theta)+ I*sin(theta))^(n) Cos[n*\[Theta]]+ I*Sin[n*\[Theta]] == (Cos[\[Theta]]+ I*Sin[\[Theta]])^(n) Error Successful - Successful [Tested: 10]
1.9.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{\abs{z_{1}}-\abs{z_{2}}} \leq \abs{z_{1}+z_{2}}} abs(abs(z[1])- abs(z[2])) <= 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)/(2*Pi)*int(u*(z + r*exp(I*phi)), phi = 0..2*Pi) u*(z) == Divide[1,2*Pi]*Integrate[u*(z + r*Exp[I*\[Phi]]), {\[Phi], 0, 2*Pi}, GenerateConditions->None] Successful Successful - Successful [Tested: 300]
1.9.E34 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(re^{i\theta}) = \frac{1}{2\pi}\int^{2\pi}_{0}\frac{(R^{2}-r^{2})h(Re^{i\phi})\diff{\phi}}{R^{2}-2Rr\cos@{\phi-\theta}+r^{2}}} u*(r*exp(I*theta)) = (1)/(2*Pi)*int((((R)^(2)- (r)^(2))* h*(R*exp(I*phi)))/((R)^(2)- 2*R*r*cos(phi - theta)+ (r)^(2)), phi = 0..2*Pi) u*(r*Exp[I*\[Theta]]) == Divide[1,2*Pi]*Integrate[Divide[((R)^(2)- (r)^(2))* h*(R*Exp[I*\[Phi]]),(R)^(2)- 2*R*r*Cos[\[Phi]- \[Theta]]+ (r)^(2)], {\[Phi], 0, 2*Pi}, GenerateConditions->None] 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 = (d*w - b)/(- c*w + a) z == Divide[d*w - b,- c*w + a] Skipped - no semantic math Skipped - no semantic math - -
1.9.E48 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{f^{(n)}(z_{0})}{n!}} a[n] = ((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] (3*a[3]- 3*a[1]*a[2]+ a(a[1])^(3))/ 3 Subscript[q, 3] (3*Subscript[a, 3]- 3*Subscript[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)+ 2*a[2])/ 2 Subscript[p, 2] == ((\[Nu]- 1)*a(Subscript[a, 1])^(2)+ 2*Subscript[a, 2])/ 2 Skipped - no semantic math Skipped - no semantic math - -
1.9.E63 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}} (f)^(m)*(z) = sum(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 = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 1}
.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 2}
.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 3}
1.465287519 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = -1/2+1/2*I*3^(1/2), n = 1}
... skip entries to safe data
Failed [246 / 300]
{LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
1.10.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=1}M_{n} < \infty} sum(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)- 4*a*c D == (b)^(2)- 4*a*c Skipped - no semantic math Skipped - no semantic math - -
1.11#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3}} rho = -(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(- 2*Pi*I/ 3) \[Rho]^(2) == Exp[- 2*Pi*I/ 3] Skipped - no semantic math Skipped - no semantic math - -
1.11#Ex13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = (-3a^{2}+8b)/8} p = (- 3*(a)^(2)+ 8*b)/ 8 p == (- 3*(a)^(2)+ 8*b)/ 8 Skipped - no semantic math Skipped - no semantic math - -
1.11#Ex14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = (a^{3}-4ab+8c)/8} q = ((a)^(3)- 4*a*b + 8*c)/ 8 q == ((a)^(3)- 4*a*b + 8*c)/ 8 Skipped - no semantic math Skipped - no semantic math - -
1.11#Ex15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = (-3a^{4}+16a^{2}b-64ac+256d)/256} r = (- 3*(a)^(4)+ 16*(a)^(2)* b - 64*a*c + 256*d)/ 256 r == (- 3*(a)^(4)+ 16*(a)^(2)* b - 64*a*c + 256*d)/ 256 Skipped - no semantic math Skipped - no semantic math - -
1.11.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0} (z)^(3)- 2*p*(z)^(2)+((p)^(2)- 4*r)* z + (q)^(2) = 0 (z)^(3)- 2*p*(z)^(2)+((p)^(2)- 4*r)* z + (q)^(2) == 0 Skipped - no semantic math Skipped - no semantic math - -
1.11.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q} sqrt(- theta[1])*sqrt(- theta[2])*sqrt(- theta[3]) = - q 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] = 1/2-1/2*I*3^(1/2), n = 1, n = 3}
-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 2, n = 3}
-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 3, n = 3}
-.70796327e-1 < -2.617993878 <- {delta = 1.5, b[n] = -1/2*3^(1/2)-1/2*I, n = 1, n = 3}
... skip entries to safe data
Failed [49 / 100]
{Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.12.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta} 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] = 1/2-1/2*I*3^(1/2), n = 1, n = 3}
-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 2, n = 3}
-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 3, n = 3}
-.70796327e-1 < -2.617993878 <- {delta = 1.5, C[n] = -1/2*3^(1/2)-1/2*I, n = 1, n = 3}
... skip entries to safe data
Failed [49 / 100]
{Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.12.E27 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta} 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) = A*w[1]*(z)+ B*w[2]*(z) w*(z) == A*Subscript[w, 1]*(z)+ B*Subscript[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} A*w[1]*(z)+ B*w[2]*(z) = 0 A*Subscript[w, 1]*(z)+ B*Subscript[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)+ A*w[1]*(z)+ B*w[2]*(z) w*(z) == Subscript[w, 0]*(z)+ A*Subscript[w, 1]*(z)+ B*Subscript[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$(2)])+ I*U = 0 D[U, {z, 2}]+ I*U == 0 Failure Failure
Failed [300 / 300]
300/300]: [[.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}
.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Failed [210 / 210]
{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[Complex[0, 1], 1], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.7320508075688774, 0.9999999999999999] <- {Rule[Complex[0, 1], 2], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
1.13#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{V}{z}+JV = 0} diff(V, [z$(2)])+ J*V = 0 D[V, {z, 2}]+ J*V == 0 Failure Failure
Failed [300 / 300]
300/300]: [[.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}
.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Failed [300 / 300]
{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.15.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{n} = \sum_{k=0}^{n}a_{k}} s[n] = sum(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)/(2*Pi)*int(P*(r , theta), theta = 0..2*Pi) = 1 Divide[1,2*Pi]*Integrate[P*(r , \[Theta]), {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1 Successful 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)/(2*Pi)*int(K[n]*(theta), theta = 0..2*Pi) = 1 Divide[1,2*Pi]*Integrate[Subscript[K, n]*(\[Theta]), {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1 Failure Failure Successful [Tested: 3] Successful [Tested: 3]
1.15.E34 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1} (1)/(2*Pi)*int(P*(x , y), x = - infinity..infinity) = 1 Divide[1,2*Pi]*Integrate[P*(x , y), {x, - Infinity, Infinity}, GenerateConditions->None] == 1 Successful Successful - Successful [Tested: 3]
1.15.E39 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Phi(z) = \Phi(x+iy)} Phi*((x + y*I)) = Phi*(x + I*y) \[CapitalPhi]*((x + y*I)) == \[CapitalPhi]*(x + I*y) Successful Successful - Successful [Tested: 180]
1.15.E42 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{\infty}_{-\infty}K_{R}(s)\diff{s} = 1} int(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+.5000000000*I <- {R = 1/2*3^(1/2)+1/2*I}
-1.500000000+.8660254040*I <- {R = -1/2+1/2*I*3^(1/2)}
-.5000000000-.8660254040*I <- {R = 1/2-1/2*I*3^(1/2)}
-1.866025404-.5000000000*I <- {R = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Skipped - Because timed out
1.15.E48 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I^{\alpha}I^{\beta} = I^{\alpha+\beta}} (I)^(alpha)* (I)^(beta) = (I)^(alpha + beta) (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+1.500000000*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = 1/2*3^(1/2)+1/2*I}
-.4999999999+1.866025404*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = -1/2+1/2*I*3^(1/2)}
.5000000001+.1339745960*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = 1/2-1/2*I*3^(1/2)}
-.8660254039+.5000000000*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Failed [300 / 300]
{Complex[0.8660254037844387, 1.5] <- {Rule[D, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[D, α], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.4999999999999998, 1.8660254037844388] <- {Rule[D, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[D, α], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
1.16.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)* F*phi*(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*(P*phi)*(x) = P*(D)* F*phi*(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*(P*u) = P*(D)* F*(u) F*(P*u) == P*(D)* F*(u) Skipped - no semantic math Skipped - no semantic math - -
1.16.E40 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int^{\infty}_{-\infty}\Diracdelta@{t}\expe^{\iunit xt}\diff{t} = 1} int(Dirac(t)*exp(I*x*t), t = - infinity..infinity) = 1 Integrate[DiracDelta[t]*Exp[I*x*t], {t, - Infinity, Infinity}, GenerateConditions->None] == 1 Successful Successful - Successful [Tested: 3]
1.16.E43 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\cpi}\int^{\infty}_{-\infty}\expe^{\iunit xt}\diff{t} = \Diracdelta@{x}} (1)/(2*Pi)*int(exp(I*x*t), t = - infinity..infinity) = Dirac(x) Divide[1,2*Pi]*Integrate[Exp[I*x*t], {t, - Infinity, Infinity}, GenerateConditions->None] == DiracDelta[x] Successful Failure -
Failed [3 / 3]
{Complex[-0.07099199156997928, 3.003857199159988*^-16] <- {Rule[x, 1.5]}
Complex[0.07742603591272186, 0.30312240144001046] <- {Rule[x, 0.5]}
1.16.E44 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sign@{x} = 2\HeavisideH@{x}-1} 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)/(2*Pi)*int(exp(- I*a*t)*(int(phi*(x)* exp(I*t*x), x = - infinity..infinity)), t = - infinity..infinity) = phi*(a) Divide[1,2*Pi]*Integrate[Exp[- I*a*t]*(Integrate[\[Phi]*(x)* Exp[I*t*x], {x, - Infinity, Infinity}, GenerateConditions->None]), {t, - Infinity, Infinity}, GenerateConditions->None] == \[Phi]*(a) Failure Error
Failed [60 / 60]
60/60]: [[Float(undefined)+.7500000000*I <- {a = -1.5, phi = 1/2*3^(1/2)+1/2*I}
Float(undefined)+1.299038106*I <- {a = -1.5, phi = -1/2+1/2*I*3^(1/2)}
Float(undefined)-1.299038106*I <- {a = -1.5, phi = 1/2-1/2*I*3^(1/2)}
Float(undefined)-.7500000000*I <- {a = -1.5, phi = -1/2*3^(1/2)-1/2*I}
... skip entries to safe data
Skipped - Because timed out
1.17.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}\right)\phi(x)\diff{x} = \phi(a)} int(((1)/(2*Pi)*int(exp(I*(x - a)* t), t = - infinity..infinity))* phi*(x), x = - infinity..infinity) = phi*(a) Integrate[(Divide[1,2*Pi]*Integrate[Exp[I*(x - a)* t], {t, - Infinity, Infinity}, GenerateConditions->None])* \[Phi]*(x), {x, - Infinity, Infinity}, GenerateConditions->None] == \[Phi]*(a) Successful 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)/(2*Pi)*int(exp(- (t)^(2)/(4*n))*exp(I*(x - a)* t), t = - infinity..infinity) = sqrt((n)/(Pi))*exp(- n*(x - a)^(2)) Divide[1,2*Pi]*Integrate[Exp[- (t)^(2)/(4*n)]*Exp[I*(x - a)* t], {t, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[n,Pi]]*Exp[- n*(x - a)^(2)] Failure Successful Successful [Tested: 54] Successful [Tested: 54]
1.17.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}} Dirac(x - a) = (1)/(2*Pi)*int(exp(I*(x - a)* t), t = - infinity..infinity) DiracDelta[x - a] == Divide[1,2*Pi]*Integrate[Exp[I*(x - a)* t], {t, - Infinity, Infinity}, GenerateConditions->None] Successful Failure - Skipped - Because timed out
1.17.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = x\int_{0}^{\infty}t\BesselJ{\nu}@{xt}\BesselJ{\nu}@{at}\diff{t}} Dirac(x - a) = x*int(t*BesselJ(nu, x*t)*BesselJ(nu, a*t), t = 0..infinity) DiracDelta[x - a] == x*Integrate[t*BesselJ[\[Nu], x*t]*BesselJ[\[Nu], a*t], {t, 0, Infinity}, GenerateConditions->None] Failure 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)/(2*Pi)*sum(exp(- I*k*a)*(int(phi*(x)* exp(I*k*x), x = - Pi..Pi)), k = - infinity..infinity) = phi*(a) Divide[1,2*Pi]*Sum[Exp[- I*k*a]*(Integrate[\[Phi]*(x)* Exp[I*k*x], {x, - Pi, Pi}, GenerateConditions->None]), {k, - Infinity, Infinity}, GenerateConditions->None] == \[Phi]*(a) Error Failure - Successful [Tested: 60]
1.17.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)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity) DiracDelta[x - a] == Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}, GenerateConditions->None] Failure Failure Skipped - Because timed out
Failed [18 / 18]
{Times[-0.15915494309189535, NSum[Power[E, Times[Complex[0.0, 3.0], k]] <- {k, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}
Times[-0.15915494309189535, NSum[Power[E, Times[Complex[0.0, 2.0], k]] <- {k, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}
1.17.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Diracdelta@{x-a} = \sum_{k=0}^{\infty}(k+\tfrac{1}{2})\LegendrepolyP{k}@{x}\LegendrepolyP{k}@{a}} 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