Results of Painlevé Transcendents
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 32.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = 6w^{2}+z} | diff(w, [z$(2)]) = 6*(w)^(2)+ z |
D[w, {z, 2}] == 6*(w)^(2)+ z |
Failure | Failure | Failed [70 / 70] 70/70]: [[-3.866025406-5.696152424*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-2.500000002-6.062177828*I <- {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [70 / 70]
{Complex[-3.8660254037844397, -5.696152422706632] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.500000000000001, -6.06217782649107] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = 2w^{3}+zw+\alpha} | diff(w, [z$(2)]) = 2*(w)^(3)+ z*w + alpha |
D[w, {z, 2}] == 2*(w)^(3)+ z*w + \[Alpha] |
Failure | Failure | Failed [209 / 210] 209/210]: [[-2.000000001-2.866025406*I <- {alpha = 3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-.6339745966-2.500000002*I <- {alpha = 3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [209 / 210]
{Complex[-2.0, -2.8660254037844384] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Complex[-1.0, -2.8660254037844384] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 32.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = \frac{1}{w}\left(\deriv{w}{z}\right)^{2}-\frac{1}{z}\deriv{w}{z}+\frac{\alpha w^{2}+\beta}{z}+\gamma w^{3}+\frac{\delta}{w}} | diff(w, [z$(2)]) = (1)/(w)*(diff(w, z))^(2)-(1)/(z)*diff(w, z)+(alpha*(w)^(2)+ beta)/(z)+ gamma*(w)^(3)+(delta)/(w) |
D[w, {z, 2}] == Divide[1,w]*(D[w, z])^(2)-Divide[1,z]*D[w, z]+Divide[\[Alpha]*(w)^(2)+ \[Beta],z]+ \[Gamma]*(w)^(3)+Divide[\[Delta],w] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-3.598076212-.5772156656*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-1.000000000+2.020860546*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [299 / 300]
{Complex[-3.098076211353316, -0.8660254037844389] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.098076211353316, -1.8660254037844388] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = \frac{1}{2w}\left(\deriv{w}{z}\right)^{2}+\frac{3}{2}w^{3}+4zw^{2}+2(z^{2}-\alpha)w+\frac{\beta}{w}} | diff(w, [z$(2)]) = (1)/(2*w)*(diff(w, z))^(2)+(3)/(2)*(w)^(3)+ 4*z*(w)^(2)+ 2*((z)^(2)- alpha)* w +(beta)/(w) |
D[w, {z, 2}] == Divide[1,2*w]*(D[w, z])^(2)+Divide[3,2]*(w)^(3)+ 4*z*(w)^(2)+ 2*((z)^(2)- \[Alpha])* w +Divide[\[Beta],w] |
Failure | Failure | Failed [299 / 300] 299/300]: [[1.299038104-5.250000007*I <- {alpha = 3/2, beta = 3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}5.299038110+2.749999997*I <- {alpha = 3/2, beta = 3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[1.2990381056766576, -5.25] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5]}Complex[2.1650635094610964, -5.75] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 0.5]} |
| 32.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = \left(\frac{1}{2w}+\frac{1}{w-1}\right)\left(\deriv{w}{z}\right)^{2}-\frac{1}{z}\deriv{w}{z}+\frac{(w-1)^{2}}{z^{2}}\left(\alpha w+\frac{\beta}{w}\right)+\frac{\gamma w}{z}+\frac{\delta w(w+1)}{w-1}} | diff(w, [z$(2)]) = ((1)/(2*w)+(1)/(w - 1))*(diff(w, z))^(2)-(1)/(z)*diff(w, z)+((w - 1)^(2))/((z)^(2))*(alpha*w +(beta)/(w))+(gamma*w)/(z)+(delta*w*(w + 1))/(w - 1) |
D[w, {z, 2}] == (Divide[1,2*w]+Divide[1,w - 1])*(D[w, z])^(2)-Divide[1,z]*D[w, z]+Divide[(w - 1)^(2),(z)^(2)]*(\[Alpha]*w +Divide[\[Beta],w])+Divide[\[Gamma]*w,z]+Divide[\[Delta]*w*(w + 1),w - 1] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-3.206380793+1.517949194*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-3.834936494+2.791317281*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-3.495190528383291, 1.017949192431124] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.1291651245988517, -4.0801270189221945] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = \frac{1}{2}\left(\frac{1}{w}+\frac{1}{w-1}+\frac{1}{w-z}\right)\left(\deriv{w}{z}\right)^{2}-\left(\frac{1}{z}+\frac{1}{z-1}+\frac{1}{w-z}\right)\deriv{w}{z}+\frac{w(w-1)(w-z)}{z^{2}(z-1)^{2}}\left(\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+\frac{\delta z(z-1)}{(w-z)^{2}}\right)} | diff(w, [z$(2)]) = (1)/(2)*((1)/(w)+(1)/(w - 1)+(1)/(w - z))*(diff(w, z))^(2)-((1)/(z)+(1)/(z - 1)+(1)/(w - z))* diff(w, z)+(w*(w - 1)*(w - z))/((z)^(2)*(z - 1)^(2))*(alpha +(beta*z)/((w)^(2))+(gamma*(z - 1))/((w - 1)^(2))+(delta*z*(z - 1))/((w - z)^(2))) |
D[w, {z, 2}] == Divide[1,2]*(Divide[1,w]+Divide[1,w - 1]+Divide[1,w - z])*(D[w, z])^(2)-(Divide[1,z]+Divide[1,z - 1]+Divide[1,w - z])* D[w, z]+Divide[w*(w - 1)*(w - z),(z)^(2)*(z - 1)^(2)]*(\[Alpha]+Divide[\[Beta]*z,(w)^(2)]+Divide[\[Gamma]*(z - 1),(w - 1)^(2)]+Divide[\[Delta]*z*(z - 1),(w - z)^(2)]) |
Failure | Failure | Failed [269 / 300] 269/300]: [[-.9380246356e-1+1.316803425*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}1.739453154+1.182694224*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)} |
Failed [300 / 300]
{Indeterminate <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle W(\zeta) = \frac{a(z)w+b(z)}{c(z)w+d(z)}} | W*(zeta) = (a*(z)* w + b*(z))/(c*(z)* w + d*(z)) |
W*(\[Zeta]) == Divide[a*(z)* w + b*(z),c*(z)* w + d*(z)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \phi(z)} | zeta = phi*(z) |
\[Zeta] == \[Phi]*(z) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u}{\zeta} = \frac{1}{u}\left(\deriv{u}{\zeta}\right)^{2}-\frac{1}{\zeta}\deriv{u}{\zeta}+\frac{u^{2}(\alpha+\gamma u)}{4\zeta^{2}}+\frac{\beta}{4\zeta}+\frac{\delta}{4u}} | diff(u, [zeta$(2)]) = (1)/(u)*(diff(u, zeta))^(2)-(1)/(zeta)*diff(u, zeta)+((u)^(2)*(alpha + gamma*u))/(4*(zeta)^(2))+(beta)/(4*zeta)+(delta)/(4*u) |
D[u, {\[Zeta], 2}] == Divide[1,u]*(D[u, \[Zeta]])^(2)-Divide[1,\[Zeta]]*D[u, \[Zeta]]+Divide[(u)^(2)*(\[Alpha]+ \[Gamma]*u),4*\[Zeta]^(2)]+Divide[\[Beta],4*\[Zeta]]+Divide[\[Delta],4*u] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.074730384+.1153480418*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}.4374708571+.3969114845*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-1.0747595264191645, -0.029006350946109677] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.4374999999999999, 0.541265877365274] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u}{z}+\frac{1}{z}\deriv{u}{z} = \frac{2\alpha}{z}\sin@@{u}+2\gamma\sin@{2u}} | diff(u, [z$(2)])+(1)/(z)*diff(u, z) = (2*alpha)/(z)*sin(u)+ 2*gamma*sin(2*u) |
D[u, {z, 2}]+Divide[1,z]*D[u, z] == Divide[2*\[Alpha],z]*Sin[u]+ 2*\[Gamma]*Sin[2*u] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-4.496361213+.6291944644*I <- {alpha = 3/2, gamma = 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}-1.346900984+2.955916370*I <- {alpha = 3/2, gamma = 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)} |
Failed [300 / 300]
{Complex[-5.5647975539874, -0.7848783935570325] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.5418435125289267, -2.4153373252737342] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u}{\zeta} = 3u^{5}+2\zeta u^{3}+\left(\tfrac{1}{4}\zeta^{2}-\nu-\tfrac{1}{2}\right)u+\frac{\beta}{32u^{3}}} | diff(u, [zeta$(2)]) = 3*(u)^(5)+ 2*zeta*(u)^(3)+((1)/(4)*(zeta)^(2)- nu -(1)/(2))* u +(beta)/(32*(u)^(3)) |
D[u, {\[Zeta], 2}] == 3*(u)^(5)+ 2*\[Zeta]*(u)^(3)+(Divide[1,4]*\[Zeta]^(2)- \[Nu]-Divide[1,2])* u +Divide[\[Beta],32*(u)^(3)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[4.531088915-2.319150408*I <- {beta = 3/2, nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}5.263139725+.9129004010*I <- {beta = 3/2, nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[4.531088913245536, -2.3191504037844384] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[3.165063509461097, -2.685175807568877] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u}{\zeta} = -\frac{\alpha\cosh@@{u}}{2(\sinh@@{u})^{3}}-\frac{\beta\sinh@@{u}}{2(\cosh@@{u})^{3}}-\tfrac{1}{4}\gamma e^{\zeta}\sinh@{2u}-\tfrac{1}{8}\delta e^{2\zeta}\sinh@{4u}} | diff(u, [zeta$(2)]) = -(alpha*cosh(u))/(2*(sinh(u))^(3))-(beta*sinh(u))/(2*(cosh(u))^(3))-(1)/(4)*gamma*exp(zeta)*sinh(2*u)-(1)/(8)*delta*exp(2*zeta)*sinh(4*u) |
D[u, {\[Zeta], 2}] == -Divide[\[Alpha]*Cosh[u],2*(Sinh[u])^(3)]-Divide[\[Beta]*Sinh[u],2*(Cosh[u])^(3)]-Divide[1,4]*\[Gamma]*Exp[\[Zeta]]*Sinh[2*u]-Divide[1,8]*\[Delta]*Exp[2*\[Zeta]]*Sinh[4*u] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-10.15437375-4.132059394*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}-.1182986371-1.333346640*I <- {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-10.983749451492802, -3.604532198424999] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.3640397236276506, -1.2834088930332135] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(1-z)I\left(\int_{\infty}^{w}\frac{\diff{t}}{\sqrt{t(t-1)(t-z)}}\right) = \sqrt{w(w-1)(w-z)}\*\left(\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+(\delta-\tfrac{1}{2})\frac{z(z-1)}{(w-z)^{2}}\right)} | z*(1 - z)* I*(int((1)/(sqrt(t*(t - 1)*(t - z))), t = infinity..w)) = sqrt(w*(w - 1)*(w - z))*(alpha +(beta*z)/((w)^(2))+(gamma*(z - 1))/((w - 1)^(2))+(delta -(1)/(2))*(z*(z - 1))/((w - z)^(2))) |
z*(1 - z)* I*(Integrate[Divide[1,Sqrt[t*(t - 1)*(t - z)]], {t, Infinity, w}, GenerateConditions->None]) == Sqrt[w*(w - 1)*(w - z)]*(\[Alpha]+Divide[\[Beta]*z,(w)^(2)]+Divide[\[Gamma]*(z - 1),(w - 1)^(2)]+(\[Delta]-Divide[1,2])*Divide[z*(z - 1),(w - z)^(2)]) |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 32.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I = z(1-z)\deriv[2]{}{z}+(1-2z)\deriv{}{z}-\frac{1}{4}} | I = z*(1 - z)* diff(+(1 - 2*z)* diff(-, z), [z$(2)])(1)/(4) |
I == z*(1 - z)* D[+(1 - 2*z)* D[-, z], {z, 2}]Divide[1,4] |
Error | Failure | - | Error |
| 32.2#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{f_{1}}{z}+f_{1}(f_{2}-f_{3})+2\mu_{1} = 0} | diff(f[1], z)+ f[1]*(f[2]- f[3])+ 2*mu[1] = 0 |
D[Subscript[f, 1], z]+ Subscript[f, 1]*(Subscript[f, 2]- Subscript[f, 3])+ 2*Subscript[\[Mu], 1] == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.732050808+1.000000000*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I}-1.000000000+1.732050808*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[1] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[1.7320508075688774, 0.9999999999999999] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.9999999999999996, 1.7320508075688774] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{f_{2}}{z}+f_{2}(f_{3}-f_{1})+2\mu_{2} = 0} | diff(f[2], z)+ f[2]*(f[3]- f[1])+ 2*mu[2] = 0 |
D[Subscript[f, 2], z]+ Subscript[f, 2]*(Subscript[f, 3]- Subscript[f, 1])+ 2*Subscript[\[Mu], 2] == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.732050808+1.000000000*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I}-1.000000000+1.732050808*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[2] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[1.7320508075688774, 0.9999999999999999] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.9999999999999996, 1.7320508075688774] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{f_{3}}{z}+f_{3}(f_{1}-f_{2})+2\mu_{3} = 0} | diff(f[3], z)+ f[3]*(f[1]- f[2])+ 2*mu[3] = 0 |
D[Subscript[f, 3], z]+ Subscript[f, 3]*(Subscript[f, 1]- Subscript[f, 2])+ 2*Subscript[\[Mu], 3] == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.732050808+1.000000000*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[3] = 1/2*3^(1/2)+1/2*I}-1.000000000+1.732050808*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[3] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[1.7320508075688774, 0.9999999999999999] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.9999999999999996, 1.7320508075688774] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.2.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu_{1}+\mu_{2}+\mu_{3} = 1} | mu[1]+ mu[2]+ mu[3] = 1 |
Subscript[\[Mu], 1]+ Subscript[\[Mu], 2]+ Subscript[\[Mu], 3] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(z)+f_{2}(z)+f_{3}(z)+2z = 0} | f[1]*(z)+ f[2]*(z)+ f[3]*(z)+ 2*z = 0 |
Subscript[f, 1]*(z)+ Subscript[f, 2]*(z)+ Subscript[f, 3]*(z)+ 2*z == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha,\beta) = (\mu_{3}-\mu_{2},-2\mu_{1}^{2})} | (alpha , beta) (mu[3]- mu[2], - 2*mu(mu[1])^(2)) |
(\[Alpha], \[Beta]) (Subscript[\[Mu], 3]- Subscript[\[Mu], 2], - 2*\[Mu](Subscript[\[Mu], 1])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\deriv{f_{1}}{z} = f_{1}f_{3}(f_{2}-f_{4})+(\tfrac{1}{2}-\mu_{3})f_{1}+\mu_{1}f_{3}} | z*diff(f[1], z) = f[1]*f[3]*(f[2]- f[4])+((1)/(2)- mu[3])* f[1]+ mu[1]*f[3] |
z*D[Subscript[f, 1], z] == Subscript[f, 1]*Subscript[f, 3]*(Subscript[f, 2]- Subscript[f, 4])+(Divide[1,2]- Subscript[\[Mu], 3])* Subscript[f, 1]+ Subscript[\[Mu], 1]*Subscript[f, 3] |
Failure | Failure | Failed [298 / 300] 298/300]: [[-.4330127020-.2500000000*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I, mu[3] = 1/2*3^(1/2)+1/2*I}-1.799038106-.6160254036*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I, mu[3] = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 32.2#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\deriv{f_{2}}{z} = f_{2}f_{4}(f_{3}-f_{1})+(\tfrac{1}{2}-\mu_{4})f_{2}+\mu_{2}f_{4}} | z*diff(f[2], z) = f[2]*f[4]*(f[3]- f[1])+((1)/(2)- mu[4])* f[2]+ mu[2]*f[4] |
z*D[Subscript[f, 2], z] == Subscript[f, 2]*Subscript[f, 4]*(Subscript[f, 3]- Subscript[f, 1])+(Divide[1,2]- Subscript[\[Mu], 4])* Subscript[f, 2]+ Subscript[\[Mu], 2]*Subscript[f, 4] |
Failure | Failure | Failed [298 / 300] 298/300]: [[-.4330127020-.2500000000*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I, mu[4] = 1/2*3^(1/2)+1/2*I}-1.799038106-.6160254036*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I, mu[4] = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 32.2#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\deriv{f_{3}}{z} = f_{3}f_{1}(f_{4}-f_{2})+(\tfrac{1}{2}-\mu_{1})f_{3}+\mu_{3}f_{1}} | z*diff(f[3], z) = f[3]*f[1]*(f[4]- f[2])+((1)/(2)- mu[1])* f[3]+ mu[3]*f[1] |
z*D[Subscript[f, 3], z] == Subscript[f, 3]*Subscript[f, 1]*(Subscript[f, 4]- Subscript[f, 2])+(Divide[1,2]- Subscript[\[Mu], 1])* Subscript[f, 3]+ Subscript[\[Mu], 3]*Subscript[f, 1] |
Failure | Failure | Failed [298 / 300] 298/300]: [[-.4330127020-.2500000000*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I, mu[3] = 1/2*3^(1/2)+1/2*I}.9330127024+.1160254036*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I, mu[3] = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 32.2#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\deriv{f_{4}}{z} = f_{4}f_{2}(f_{1}-f_{3})+(\tfrac{1}{2}-\mu_{2})f_{4}+\mu_{4}f_{2}} | z*diff(f[4], z) = f[4]*f[2]*(f[1]- f[3])+((1)/(2)- mu[2])* f[4]+ mu[4]*f[2] |
z*D[Subscript[f, 4], z] == Subscript[f, 4]*Subscript[f, 2]*(Subscript[f, 1]- Subscript[f, 3])+(Divide[1,2]- Subscript[\[Mu], 2])* Subscript[f, 4]+ Subscript[\[Mu], 4]*Subscript[f, 2] |
Failure | Failure | Failed [298 / 300] 298/300]: [[-.4330127020-.2500000000*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I, mu[4] = 1/2*3^(1/2)+1/2*I}.9330127024+.1160254036*I <- {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I, mu[4] = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 32.2.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu_{1}+\mu_{2}+\mu_{3}+\mu_{4} = 1} | mu[1]+ mu[2]+ mu[3]+ mu[4] = 1 |
Subscript[\[Mu], 1]+ Subscript[\[Mu], 2]+ Subscript[\[Mu], 3]+ Subscript[\[Mu], 4] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(z)+f_{3}(z) = \sqrt{z}} | f[1]*(z)+ f[3]*(z) = sqrt(z) |
Subscript[f, 1]*(z)+ Subscript[f, 3]*(z) == Sqrt[z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(z)+f_{4}(z) = \sqrt{z}} | f[2]*(z)+ f[4]*(z) = sqrt(z) |
Subscript[f, 2]*(z)+ Subscript[f, 4]*(z) == Sqrt[z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha,\beta,\gamma,\delta) = (\tfrac{1}{2}\mu_{1}^{2},-\tfrac{1}{2}\mu_{3}^{2},\mu_{4}-\mu_{2},-\tfrac{1}{2})} | ((1)/(2)*mu(mu[1])^(2), -(1)/(2)*mu(mu[3])^(2), mu[4]- mu[2], -(1)/(2)) |
(Divide[1,2]*\[Mu](Subscript[\[Mu], 1])^(2), -Divide[1,2]*\[Mu](Subscript[\[Mu], 3])^(2), Subscript[\[Mu], 4]- Subscript[\[Mu], 2], -Divide[1,2]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \epsilon^{2}\zeta-\frac{6}{\epsilon^{10}}} | z = (epsilon)^(2)* zeta -(6)/((epsilon)^(10)) |
z == \[Epsilon]^(2)* \[Zeta]-Divide[6,\[Epsilon]^(10)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \frac{4}{\epsilon^{15}}} | alpha = (4)/((epsilon)^(15)) |
\[Alpha] == Divide[4,\[Epsilon]^(15)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{W}{\zeta} = 6W^{2}+\zeta+\epsilon^{6}(2W^{3}+\zeta W)} | diff(W, [zeta$(2)]) = 6*(W)^(2)+ zeta + (epsilon)^(6)*(2*(W)^(3)+ zeta*W) |
D[W, {\[Zeta], 2}] == 6*(W)^(2)+ \[Zeta]+ \[Epsilon]^(6)*(2*(W)^(3)+ \[Zeta]*W) |
Failure | Failure | Failed [300 / 300] 300/300]: [[-4.366025408-8.562177830*I <- {W = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, epsilon = 1}-35.86602547-189.1217784*I <- {W = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, epsilon = 2} |
Failed [300 / 300]
{Complex[-4.366025403784439, -8.56217782649107] <- {Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϵ, 1], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-35.86602540378445, -189.1217782649107] <- {Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϵ, 2], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 32.2#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = 1+\epsilon^{2}\zeta} | z = 1 + (epsilon)^(2)* zeta |
z == 1 + \[Epsilon]^(2)* \[Zeta] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = -\tfrac{1}{2}\epsilon^{-6}} | alpha = -(1)/(2)*(epsilon)^(- 6) |
\[Alpha] == -Divide[1,2]*\[Epsilon]^(- 6) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = \tfrac{1}{2}\epsilon^{-6}+2a\epsilon^{-3}} | beta = (1)/(2)*(epsilon)^(- 6)+ 2*a*(epsilon)^(- 3) |
\[Beta] == Divide[1,2]*\[Epsilon]^(- 6)+ 2*a*\[Epsilon]^(- 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = -\delta} | gamma = - delta |
\[Gamma] == - \[Delta] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = 2^{-2/3}\epsilon\zeta-\epsilon^{-3}} | z = (2)^(- 2/ 3)* epsilon*zeta - (epsilon)^(- 3) |
z == (2)^(- 2/ 3)* \[Epsilon]*\[Zeta]- \[Epsilon]^(- 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = -2a-\tfrac{1}{2}\epsilon^{-6}} | alpha = - 2*a -(1)/(2)*(epsilon)^(- 6) |
\[Alpha] == - 2*a -Divide[1,2]*\[Epsilon]^(- 6) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = -\tfrac{1}{2}\epsilon^{-12}} | beta = -(1)/(2)*(epsilon)^(- 12) |
\[Beta] == -Divide[1,2]*\[Epsilon]^(- 12) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \zeta^{2}} | z = (zeta)^(2) |
z == \[Zeta]^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \tfrac{1}{4}a\epsilon^{-1}+\tfrac{1}{8}c\epsilon^{-2}} | alpha = (1)/(4)*a*(epsilon)^(- 1)+(1)/(8)*c*(epsilon)^(- 2) |
\[Alpha] == Divide[1,4]*a*\[Epsilon]^(- 1)+Divide[1,8]*c*\[Epsilon]^(- 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = -\tfrac{1}{8}c\epsilon^{-2}} | beta = -(1)/(8)*c*(epsilon)^(- 2) |
\[Beta] == -Divide[1,8]*c*\[Epsilon]^(- 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = \tfrac{1}{4}\epsilon b} | gamma = (1)/(4)*epsilon*b |
\[Gamma] == Divide[1,4]*\[Epsilon]*b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta = \tfrac{1}{8}\epsilon^{2}d} | delta = (1)/(8)*(epsilon)^(2)* d |
\[Delta] == Divide[1,8]*\[Epsilon]^(2)* d |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = 1+\sqrt{2}\epsilon\zeta} | z = 1 +sqrt(2)*epsilon*zeta |
z == 1 +Sqrt[2]*\[Epsilon]*\[Zeta] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \tfrac{1}{2}\epsilon^{-4}} | alpha = (1)/(2)*(epsilon)^(- 4) |
\[Alpha] == Divide[1,2]*\[Epsilon]^(- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = \tfrac{1}{4}b} | beta = (1)/(4)*b |
\[Beta] == Divide[1,4]*b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = -\epsilon^{-4}} | gamma = - (epsilon)^(- 4) |
\[Gamma] == - \[Epsilon]^(- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta = a\epsilon^{-2}-\tfrac{1}{2}\epsilon^{-4}} | delta = a*(epsilon)^(- 2)-(1)/(2)*(epsilon)^(- 4) |
\[Delta] == a*\[Epsilon]^(- 2)-Divide[1,2]*\[Epsilon]^(- 4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = 1+\epsilon\zeta} | z = 1 + epsilon*zeta |
z == 1 + \[Epsilon]*\[Zeta] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = c\epsilon^{-1}-d\epsilon^{-2}} | gamma = c*(epsilon)^(- 1)- d*(epsilon)^(- 2) |
\[Gamma] == c*\[Epsilon]^(- 1)- d*\[Epsilon]^(- 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.2#Ex31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta = d\epsilon^{-2}} | delta = d*(epsilon)^(- 2) |
\[Delta] == d*\[Epsilon]^(- 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.3.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u}{x} = 3u^{5}+2xu^{3}+\left(\tfrac{1}{4}x^{2}-\nu-\tfrac{1}{2}\right)u} | diff(u, [x$(2)]) = 3*(u)^(5)+ 2*x*(u)^(3)+((1)/(4)*(x)^(2)- nu -(1)/(2))* u |
D[u, {x, 2}] == 3*(u)^(5)+ 2*x*(u)^(3)+(Divide[1,4]*(x)^(2)- \[Nu]-Divide[1,2])* u |
Failure | Failure | Failed [300 / 300] 300/300]: [[3.043949625-3.665224602*I <- {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 3/2}3.476962328-1.415224600*I <- {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[3.043949623616789, -3.6652245962155616] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.67792421983235, -4.031249999999999] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.3.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(x) = 2\sqrt{2}u_{k}^{2}(\sqrt{2}x,\nu)} | w*(x) = 2*sqrt(2)*(u[k])^(2)*(sqrt(2)*x , nu) |
w*(x) == 2*Sqrt[2]*(Subscript[u, k])^(2)*(Sqrt[2]*x , \[Nu]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.3.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u^{2} = -\tfrac{1}{3}x+\tfrac{1}{6}\sqrt{x^{2}+12\nu+6}} | (u)^(2) = -(1)/(3)*x +(1)/(6)*sqrt((x)^(2)+ 12*nu + 6) |
(u)^(2) == -Divide[1,3]*x +Divide[1,6]*Sqrt[(x)^(2)+ 12*\[Nu]+ 6] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.4#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\boldsymbol{{\Psi}}}{\lambda} = \mathbf{A}(z,\lambda)\boldsymbol{{\Psi}}} | diff(Psi, lambda) = A*(z , lambda)* Psi |
D[\[CapitalPsi], \[Lambda]] == A*(z , \[Lambda])* \[CapitalPsi] |
Failure | Failure | Error | Error |
| 32.4#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\boldsymbol{{\Psi}}}{z} = \mathbf{B}(z,\lambda)\boldsymbol{{\Psi}}} | diff(Psi, z) = B*(z , lambda)* Psi |
D[\[CapitalPsi], z] == B*(z , \[Lambda])* \[CapitalPsi] |
Failure | Failure | Error | Error |
| 32.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\mathbf{A}}{z}-\pderiv{\mathbf{B}}{\lambda}+\mathbf{A}\mathbf{B}-\mathbf{B}\mathbf{A} = 0} | diff(A, z)- diff(B, lambda)+ A*B - B*A = 0 |
D[A, z]- D[B, \[Lambda]]+ A*B - B*A == 0 |
Successful | Successful | - | Successful [Tested: 300] |
| 32.4.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha,\beta,\gamma,\delta) = \left(2\theta_{0},2(1-\theta_{\infty}),1,-1\right)} | (alpha , beta , gamma , delta) = (2*theta[0], 2*(1 - theta[infinity]), 1 , - 1) |
(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (2*Subscript[\[Theta], 0], 2*(1 - Subscript[\[Theta], Infinity]), 1 , - 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.4.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta_{0} = \frac{4v_{0}}{z}\left(\theta_{\infty}\left(1-\frac{z}{4v_{0}}\right)+\frac{z-2v_{0}}{2v_{0}v_{1}}u_{0}+u_{1}v_{1}\right)} | theta[0] = (4*v[0])/(z)*(theta[infinity]*(1 -(z)/(4*v[0]))+(z - 2*v[0])/(2*v[0]*v[1])*u[0]+ u[1]*v[1]) |
Subscript[\[Theta], 0] == Divide[4*Subscript[v, 0],z]*(Subscript[\[Theta], Infinity]*(1 -Divide[z,4*Subscript[v, 0]])+Divide[z - 2*Subscript[v, 0],2*Subscript[v, 0]*Subscript[v, 1]]*Subscript[u, 0]+ Subscript[u, 1]*Subscript[v, 1]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}} | K*(z , zeta) = k*AiryAi((z + zeta)/(2))+((k)^(2))/(4)* int(int(K*(z , s)* AiryAi((s + t)/(2))*AiryAi((t + zeta)/(2)), s = z..infinity), t = z..infinity) |
K*(z , \[Zeta]) == k*AiryAi[Divide[z + \[Zeta],2]]+Divide[(k)^(2),4]* Integrate[Integrate[K*(z , s)* AiryAi[Divide[s + t,2]]*AiryAi[Divide[t + \[Zeta],2]], {s, z, Infinity}, GenerateConditions->None], {t, z, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Error |
| 32.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = K(z,z)} | w*(z) = K*(z , z) |
w*(z) == K*(z , z) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.6#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{q}{z} = \pderiv{\mathrm{H}}{p}} | diff(q, z) = diff(H, p) |
D[q, z] == D[H, p] |
Successful | Successful | - | Successful [Tested: 300] |
| 32.6#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{p}{z} = -\pderiv{\mathrm{H}}{q}} | diff(p, z) = - diff(H, q) |
D[p, z] == - D[H, q] |
Successful | Successful | - | Successful [Tested: 300] |
| 32.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha,\beta,\gamma,\delta) = \left(-2\kappa_{\infty}\theta_{\infty},2\kappa_{0}(\theta_{0}+1),\kappa_{\infty}^{2},-\kappa_{0}^{2}\right)} | (- 2*kappa[infinity]*theta[infinity], 2*kappa[0]*(theta[0]+ 1), kappa(kappa[infinity])^(2), - kappa(kappa[0])^(2)) |
(- 2*Subscript[\[Kappa], Infinity]*Subscript[\[Theta], Infinity], 2*Subscript[\[Kappa], 0]*(Subscript[\[Theta], 0]+ 1), \[Kappa](Subscript[\[Kappa], Infinity])^(2), - \[Kappa](Subscript[\[Kappa], 0])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.6.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha,\beta,\gamma,\delta) = \left(-4\eta_{\infty}\theta_{\infty},4\eta_{0}(\theta_{0}+1),4\eta_{\infty}^{2},-4\eta_{0}^{2}\right)} | (- 4*eta[infinity]*theta[infinity], 4*eta[0]*(theta[0]+ 1), 4*eta(eta[infinity])^(2), - 4*eta(eta[0])^(2)) |
(- 4*Subscript[\[Eta], Infinity]*Subscript[\[Theta], Infinity], 4*Subscript[\[Eta], 0]*(Subscript[\[Theta], 0]+ 1), 4*\[Eta](Subscript[\[Eta], Infinity])^(2), - 4*\[Eta](Subscript[\[Eta], 0])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.6.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha,\beta,\gamma,\delta) = \left(2\kappa_{\infty},\kappa_{0}(\theta-1),0,-\kappa_{0}^{2}\right)} | (alpha , beta , gamma , delta) (2*kappa[infinity], kappa[0]*(theta - 1), 0 , - kappa(kappa[0])^(2)) |
(\[Alpha], \[Beta], \[Gamma], \[Delta]) (2*Subscript[\[Kappa], Infinity], Subscript[\[Kappa], 0]*(\[Theta]- 1), 0 , - \[Kappa](Subscript[\[Kappa], 0])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\alpha+\tfrac{1}{2}}{w_{\alpha+1}+w_{\alpha}}+\frac{\alpha-\tfrac{1}{2}}{w_{\alpha}+w_{\alpha-1}}+2w_{\alpha}^{2}+z = 0} | (alpha +(1)/(2))/(w[alpha + 1]+ w[alpha])+(alpha -(1)/(2))/(w[alpha]+ w[alpha - 1])+ 2*(w[alpha])^(2)+ z = 0 |
Divide[\[Alpha]+Divide[1,2],Subscript[w, \[Alpha]+ 1]+ Subscript[w, \[Alpha]]]+Divide[\[Alpha]-Divide[1,2],Subscript[w, \[Alpha]]+ Subscript[w, \[Alpha]- 1]]+ 2*(Subscript[w, \[Alpha]])^(2)+ z == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (-\alpha_{0},-\beta_{0},\gamma_{0},\delta_{0})} | (alpha[1], beta[1], gamma[1], delta[1]) = (- alpha[0], - beta[0], gamma[0], delta[0]) |
(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (- Subscript[\[Alpha], 0], - Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\delta_{0},-\gamma_{0})} | (alpha[2], beta[2], gamma[2], delta[2]) = (- beta[0], - alpha[0], - delta[0], - gamma[0]) |
(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], - Subscript[\[Delta], 0], - Subscript[\[Gamma], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1} = \alpha_{3}} | alpha[1] = alpha[3] |
Subscript[\[Alpha], 1] == Subscript[\[Alpha], 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2} = \alpha_{4}} | alpha[2] = alpha[4] |
Subscript[\[Alpha], 2] == Subscript[\[Alpha], 4] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{1} = \beta_{2}} | beta[1] = beta[2] |
Subscript[\[Beta], 1] == Subscript[\[Beta], 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{3} = \beta_{4}} | beta[3] = beta[4] |
Subscript[\[Beta], 3] == Subscript[\[Beta], 4] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{5} = \beta_{0}+2} | beta[5] = beta[0]+ 2 |
Subscript[\[Beta], 5] == Subscript[\[Beta], 0]+ 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{6} = \beta_{0}-2} | beta[6] = beta[0]- 2 |
Subscript[\[Beta], 6] == Subscript[\[Beta], 0]- 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \tfrac{1}{2}\zeta^{2}} | z = (1)/(2)*(zeta)^(2) |
z == Divide[1,2]*\[Zeta]^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1}^{+} = \tfrac{1}{4}\left(2-2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right)} | (alpha[1])^(+) = (1)/(4)*(2 - 2*alpha[0]+ 3*sqrt(- 2*beta[0])) |
(Subscript[\[Alpha], 1])^(+) == Divide[1,4]*(2 - 2*Subscript[\[Alpha], 0]+ 3*Sqrt[- 2*Subscript[\[Beta], 0]]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{1}^{+} = -\tfrac{1}{2}\left(1+\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}} | (beta[1])^(+) = -(1)/(2)*(1 + alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2) |
(Subscript[\[Beta], 1])^(+) == -Divide[1,2]*(1 + Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2}^{+} = -\tfrac{1}{4}\left(2+2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right)} | (alpha[2])^(+) = -(1)/(4)*(2 + 2*alpha[0]+ 3*sqrt(- 2*beta[0])) |
(Subscript[\[Alpha], 2])^(+) == -Divide[1,4]*(2 + 2*Subscript[\[Alpha], 0]+ 3*Sqrt[- 2*Subscript[\[Beta], 0]]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{2}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}} | (beta[2])^(+) = -(1)/(2)*(1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2) |
(Subscript[\[Beta], 2])^(+) == -Divide[1,2]*(1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{3}^{+} = \tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}}} | (alpha[3])^(+) = (3)/(2)-(1)/(2)*alpha[0]-(3)/(4)*sqrt(- 2*beta[0]) |
(Subscript[\[Alpha], 3])^(+) == Divide[3,2]-Divide[1,2]*Subscript[\[Alpha], 0]-Divide[3,4]*Sqrt[- 2*Subscript[\[Beta], 0]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{3}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}} | (beta[3])^(+) = -(1)/(2)*(1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2) |
(Subscript[\[Beta], 3])^(+) == -Divide[1,2]*(1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{4}^{+} = -\tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}}} | (alpha[4])^(+) = -(3)/(2)-(1)/(2)*alpha[0]-(3)/(4)*sqrt(- 2*beta[0]) |
(Subscript[\[Alpha], 4])^(+) == -Divide[3,2]-Divide[1,2]*Subscript[\[Alpha], 0]-Divide[3,4]*Sqrt[- 2*Subscript[\[Beta], 0]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{4}^{+} = -\tfrac{1}{2}\left(-1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}} | (beta[4])^(+) = -(1)/(2)*(- 1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2) |
(Subscript[\[Beta], 4])^(+) == -Divide[1,2]*(- 1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1} = -z_{0}} | z[1] = - z[0] |
Subscript[z, 1] == - Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{2} = z_{0}} | z[2] = z[0] |
Subscript[z, 2] == Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\gamma_{0},\delta_{0})} | (alpha[1], beta[1], gamma[1], delta[1]) = (alpha[0], beta[0], - gamma[0], delta[0]) |
(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (Subscript[\[Alpha], 0], Subscript[\[Beta], 0], - Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\gamma_{0},\delta_{0})} | (alpha[2], beta[2], gamma[2], delta[2]) = (- beta[0], - alpha[0], - gamma[0], delta[0]) |
(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], - Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1} = \tfrac{1}{8}\left(\gamma_{0}+\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2}} | alpha[1] = (1)/(8)*(gamma[0]+ varepsilon[1]*(1 - varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])))^(2) |
Subscript[\[Alpha], 1] == Divide[1,8]*(Subscript[\[Gamma], 0]+ Subscript[\[CurlyEpsilon], 1]*(1 - Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]]))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{1} = -\tfrac{1}{8}\left(\gamma_{0}-\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2}} | beta[1] = -(1)/(8)*(gamma[0]- varepsilon[1]*(1 - varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])))^(2) |
Subscript[\[Beta], 1] == -Divide[1,8]*(Subscript[\[Gamma], 0]- Subscript[\[CurlyEpsilon], 1]*(1 - Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]]))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{1} = \varepsilon_{1}\left(\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)} | gamma[1] = varepsilon[1]*(varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])) |
Subscript[\[Gamma], 1] == Subscript[\[CurlyEpsilon], 1]*(Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \sqrt{2\zeta}} | z = sqrt(2*zeta) |
z == Sqrt[2*\[Zeta]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = {\left((\beta-\varepsilon\alpha+2)^{2}/32,-(\beta+\varepsilon\alpha-2)^{2}/32,-\varepsilon,0\right)}} | (alpha[0], beta[0], gamma[0], delta[0]) = ((beta - varepsilon*alpha + 2)^(2)/ 32 , -(beta + varepsilon*alpha - 2)^(2)/ 32 , - varepsilon , 0) |
(Subscript[\[Alpha], 0], Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) == ((\[Beta]- \[CurlyEpsilon]*\[Alpha]+ 2)^(2)/ 32 , -(\[Beta]+ \[CurlyEpsilon]*\[Alpha]- 2)^(2)/ 32 , - \[CurlyEpsilon], 0) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1} = 1/z_{0}} | z[1] = 1/ z[0] |
Subscript[z, 1] == 1/ Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{2} = 1-z_{0}} | z[2] = 1 - z[0] |
Subscript[z, 2] == 1 - Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{3} = 1/z_{0}} | z[3] = 1/ z[0] |
Subscript[z, 3] == 1/ Subscript[z, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\delta_{0}+\tfrac{1}{2},-\gamma_{0}+\tfrac{1}{2})} | (alpha[1], beta[1], gamma[1], delta[1]) = (alpha[0], beta[0], - delta[0]+(1)/(2), - gamma[0]+(1)/(2)) |
(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (Subscript[\[Alpha], 0], Subscript[\[Beta], 0], - Subscript[\[Delta], 0]+Divide[1,2], - Subscript[\[Gamma], 0]+Divide[1,2]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (\alpha_{0},-\gamma_{0},-\beta_{0},\delta_{0})} | (alpha[2], beta[2], gamma[2], delta[2]) = (alpha[0], - gamma[0], - beta[0], delta[0]) |
(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (Subscript[\[Alpha], 0], - Subscript[\[Gamma], 0], - Subscript[\[Beta], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha_{3},\beta_{3},\gamma_{3},\delta_{3}) = (-\beta_{0},-\alpha_{0},\gamma_{0},\delta_{0})} | (alpha[3], beta[3], gamma[3], delta[3]) = (- beta[0], - alpha[0], gamma[0], delta[0]) |
(Subscript[\[Alpha], 3], Subscript[\[Beta], 3], Subscript[\[Gamma], 3], Subscript[\[Delta], 3]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\alpha,\beta,\gamma,\delta) = \left(\tfrac{1}{2}(\theta_{\infty}-1)^{2},-\tfrac{1}{2}\theta_{0}^{2},\tfrac{1}{2}\theta_{1}^{2},\tfrac{1}{2}(1-\theta_{2}^{2})\right)} | ((1)/(2)*(theta[infinity]- 1)^(2), -(1)/(2)*theta(theta[0])^(2),(1)/(2)*theta(theta[1])^(2),(1)/(2)*(1 - theta(theta[2])^(2))) |
(Divide[1,2]*(Subscript[\[Theta], Infinity]- 1)^(2), -Divide[1,2]*\[Theta](Subscript[\[Theta], 0])^(2),Divide[1,2]*\[Theta](Subscript[\[Theta], 1])^(2),Divide[1,2]*(1 - \[Theta](Subscript[\[Theta], 2])^(2))) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E43 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (A,B,C,D) = \left(\tfrac{1}{2}(\Theta_{\infty}-1)^{2},-\tfrac{1}{2}\Theta_{0}^{2},\tfrac{1}{2}\Theta_{1}^{2},\tfrac{1}{2}(1-\Theta_{2}^{2})\right)} | ((1)/(2)*(Theta[infinity]- 1)^(2), -(1)/(2)*Theta(Theta[0])^(2),(1)/(2)*Theta(Theta[1])^(2),(1)/(2)*(1 - Theta(Theta[2])^(2))) |
(Divide[1,2]*(Subscript[\[CapitalTheta], Infinity]- 1)^(2), -Divide[1,2]*\[CapitalTheta](Subscript[\[CapitalTheta], 0])^(2),Divide[1,2]*\[CapitalTheta](Subscript[\[CapitalTheta], 1])^(2),Divide[1,2]*(1 - \[CapitalTheta](Subscript[\[CapitalTheta], 2])^(2))) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E44 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta_{j} = \Theta_{j}+\tfrac{1}{2}\sigma} | theta[j] = Theta[j]+(1)/(2)*sigma |
Subscript[\[Theta], j] == Subscript[\[CapitalTheta], j]+Divide[1,2]*\[Sigma] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E45 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma = \theta_{0}+\theta_{1}+\theta_{2}+\theta_{\infty}-1} | sigma = theta[0]+ theta[1]+ theta[2]+ theta[infinity]- 1 |
\[Sigma] == Subscript[\[Theta], 0]+ Subscript[\[Theta], 1]+ Subscript[\[Theta], 2]+ Subscript[\[Theta], Infinity]- 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{1}(\zeta_{1}) = \frac{(1-w)(w-z)}{(1+\sqrt{z})^{2}w}} | u[1]*(zeta[1]) = ((1 - w)*(w - z))/((1 +sqrt(z))^(2)* w) |
Subscript[u, 1]*(Subscript[\[Zeta], 1]) == Divide[(1 - w)*(w - z),(1 +Sqrt[z])^(2)* w] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{1} = \left(\frac{1-\sqrt{z}}{1+\sqrt{z}}\right)^{2}} | zeta[1] = ((1 -sqrt(z))/(1 +sqrt(z)))^(2) |
Subscript[\[Zeta], 1] == (Divide[1 -Sqrt[z],1 +Sqrt[z]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{2}(\zeta_{2}) = \frac{(w^{2}-z)^{2}}{4w(w-1)(w-z)}} | u[2]*(zeta[2]) = (((w)^(2)- z)^(2))/(4*w*(w - 1)*(w - z)) |
Subscript[u, 2]*(Subscript[\[Zeta], 2]) == Divide[((w)^(2)- z)^(2),4*w*(w - 1)*(w - z)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{2} = z} | zeta[2] = z |
Subscript[\[Zeta], 2] == z |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E49 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{3}(\zeta_{3}) = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{2}\left(\frac{\sqrt{w}+z^{1/4}}{\sqrt{w}-z^{1/4}}\right)^{2}} | u[3]*(zeta[3]) = ((1 - (z)^(1/ 4))/(1 + (z)^(1/ 4)))^(2)*((sqrt(w)+ (z)^(1/ 4))/(sqrt(w)- (z)^(1/ 4)))^(2) |
Subscript[u, 3]*(Subscript[\[Zeta], 3]) == (Divide[1 - (z)^(1/ 4),1 + (z)^(1/ 4)])^(2)*(Divide[Sqrt[w]+ (z)^(1/ 4),Sqrt[w]- (z)^(1/ 4)])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.7.E50 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{3} = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{4}} | zeta[3] = ((1 - (z)^(1/ 4))/(1 + (z)^(1/ 4)))^(4) |
Subscript[\[Zeta], 3] == (Divide[1 - (z)^(1/ 4),1 + (z)^(1/ 4)])^(4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{2}(z) = z^{3}+4} | Q[2]*(z) = (z)^(3)+ 4 |
Subscript[Q, 2]*(z) == (z)^(3)+ 4 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{3}(z) = z^{6}+20z^{3}-80} | Q[3]*(z) = (z)^(6)+ 20*(z)^(3)- 80 |
Subscript[Q, 3]*(z) == (z)^(6)+ 20*(z)^(3)- 80 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{4}(z) = z^{10}+60z^{7}+11200z} | Q[4]*(z) = (z)^(10)+ 60*(z)^(7)+ 11200*z |
Subscript[Q, 4]*(z) == (z)^(10)+ 60*(z)^(7)+ 11200*z |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{5}(z) = z^{15}+140z^{12}+2800z^{9}+78400z^{6}-3\;13600z^{3}-62\;72000} | Q[5]*(z) = (z)^(15)+ 140*(z)^(12)+ 2800*(z)^(9)+ 78400*(z)^(6)- 313600*(z)^(3)- 6272000 |
Subscript[Q, 5]*(z) == (z)^(15)+ 140*(z)^(12)+ 2800*(z)^(9)+ 78400*(z)^(6)- 313600*(z)^(3)- 6272000 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{6}(z) = z^{21}+280z^{18}+18480z^{15}+6\;27200z^{12}-172\;48000z^{9}+14488\;32000z^{6}+1\;93177\;60000z^{3}-3\;86355\;20000} | Q[6]*(z) = (z)^(21)+ 280*(z)^(18)+ 18480*(z)^(15)+ 627200*(z)^(12)- 17248000*(z)^(9)+ 1448832000*(z)^(6)+ 19317760000*(z)^(3)- 38635520000 |
Subscript[Q, 6]*(z) == (z)^(21)+ 280*(z)^(18)+ 18480*(z)^(15)+ 627200*(z)^(12)- 17248000*(z)^(9)+ 1448832000*(z)^(6)+ 19317760000*(z)^(3)- 38635520000 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{m=0}^{\infty}p_{m}(z)\lambda^{m} = \exp@{z\lambda-\tfrac{4}{3}\lambda^{3}}} | sum(p[m]*(z)* (lambda)^(m), m = 0..infinity) = exp(z*lambda -(4)/(3)*(lambda)^(3)) |
Sum[Subscript[p, m]*(z)* \[Lambda]^(m), {m, 0, Infinity}, GenerateConditions->None] == Exp[z*\[Lambda]-Divide[4,3]*\[Lambda]^(3)] |
Failure | Failure | Skipped - Because timed out | Failed [300 / 300]
{Plus[Complex[-1.4719523959894307, 0.7427233484952657], NSum[Times[Power[E, Times[Complex[0, Rational[1, 3]], Pi]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], m]] <- {m, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-1.4719523959894307, 0.7427233484952657], NSum[Times[Power[E, Times[Complex[0, Rational[5, 6]], Pi]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], m]] <- {m, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, m], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.8.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha+\beta = 4n} | alpha + beta = 4*n |
\[Alpha]+ \[Beta] == 4*n |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \ifrac{P_{m}(z)}{Q_{m}(z)}} | w*(z) = (P[m]*(z))/(Q[m]*(z)) |
w*(z) == Divide[Subscript[P, m]*(z),Subscript[Q, m]*(z)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = m} | alpha = m |
\[Alpha] == m |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = -2(1+2n-m)^{2}} | beta = - 2*(1 + 2*n - m)^(2) |
\[Beta] == - 2*(1 + 2*n - m)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mspace{12.0mu }\alpha = m} | alpha = m |
\[Alpha] == m |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = -2(\tfrac{1}{3}+2n-m)^{2}} | beta = - 2*((1)/(3)+ 2*n - m)^(2) |
\[Beta] == - 2*(Divide[1,3]+ 2*n - m)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \lambda z+\mu+(\ifrac{P_{n-1}(z)}{Q_{n}(z)})} | w*(z) = lambda*z + mu +((P[n - 1]*(z))/(Q[n]*(z))) |
w*(z) == \[Lambda]*z + \[Mu]+(Divide[Subscript[P, n - 1]*(z),Subscript[Q, n]*(z)]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.8.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a+b+c+d = 2n+1} | a + b + c + d = 2*n + 1 |
a + b + c + d == 2*n + 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = 2n} | beta = 2*n |
\[Beta] == 2*n |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \ifrac{P_{n^{2}+1}(\zeta)}{Q_{n^{2}}(\zeta)}} | w*(z) = (P[(n)^(2)+ 1]*(zeta))/(Q[(n)^(2)]*(zeta)) |
w*(z) == Divide[Subscript[P, (n)^(2)+ 1]*(\[Zeta]),Subscript[Q, (n)^(2)]*(\[Zeta])] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.9.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mspace{17.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{2}\mu^{2},-\tfrac{1}{8}(2n-1)^{2},-1)} | (alpha , beta , gamma) = ((1)/(2)*(mu)^(2), -(1)/(8)*(2*n - 1)^(2), - 1) |
(\[Alpha], \[Beta], \[Gamma]) == (Divide[1,2]*\[Mu]^(2), -Divide[1,8]*(2*n - 1)^(2), - 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.9.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mspace{5.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{8}(2n-1)^{2},-\tfrac{1}{2}\mu^{2},1)} | (alpha , beta , gamma) = ((1)/(8)*(2*n - 1)^(2), -(1)/(2)*(mu)^(2), 1) |
(\[Alpha], \[Beta], \[Gamma]) == (Divide[1,8]*(2*n - 1)^(2), -Divide[1,2]*\[Mu]^(2), 1) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \ifrac{P_{n^{2}-n+1}(\zeta)}{Q_{n^{2}-n}(\zeta)}} | w*(z) = (P[(n)^(2)- n + 1]*(zeta))/(Q[(n)^(2)- n]*(zeta)) |
w*(z) == Divide[Subscript[P, (n)^(2)- n + 1]*(\[Zeta]),Subscript[Q, (n)^(2)- n]*(\[Zeta])] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = n+\tfrac{1}{2}} | alpha = n +(1)/(2) |
\[Alpha] == n +Divide[1,2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = C_{1}\AiryAi@{-2^{-1/3}z}+C_{2}\AiryBi@{-2^{-1/3}z}} | phi*(z) = C[1]*AiryAi(- (2)^(- 1/ 3)* z)+ C[2]*AiryBi(- (2)^(- 1/ 3)* z) |
\[Phi]*(z) == Subscript[C, 1]*AiryAi[- (2)^(- 1/ 3)* z]+ Subscript[C, 2]*AiryBi[- (2)^(- 1/ 3)* z] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.2986692739+.5787509238*I <- {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}.3018910357e-1+.1740730853*I <- {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-0.29866927421000106, 0.5787509234724151] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.03018910341830547, 0.174073084997731] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.10.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{1}\alpha+\varepsilon_{2}\beta = 4n+2} | varepsilon[1]*alpha + varepsilon[2]*beta = 4*n + 2 |
Subscript[\[CurlyEpsilon], 1]*\[Alpha]+ Subscript[\[CurlyEpsilon], 2]*\[Beta] == 4*n + 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = z^{\nu}\left(C_{1}\BesselJ{\nu}@{\zeta}+C_{2}\BesselY{\nu}@{\zeta}\right)} | phi*(z) = (z)^(nu)*(C[1]*BesselJ(nu, zeta)+ C[2]*BesselY(nu, zeta)) |
\[Phi]*(z) == (z)^\[Nu]*(Subscript[C, 1]*BesselJ[\[Nu], \[Zeta]]+ Subscript[C, 2]*BesselY[\[Nu], \[Zeta]]) |
Failure | Failure | Failed [300 / 300] 300/300]: [[.6857713611+1.049278090*I <- {nu = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}-.1639325500+1.038275666*I <- {nu = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.6857713606630202, 1.0492780901981935] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.16393255022963316, 1.0382756660889538] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.10.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = -2(2n+1+\varepsilon\alpha)^{2}} | beta = - 2*(2*n + 1 + varepsilon*alpha)^(2) |
\[Beta] == - 2*(2*n + 1 + \[CurlyEpsilon]*\[Alpha])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = -2n^{2}} | beta = - 2*(n)^(2) |
\[Beta] == - 2*(n)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = \left(C_{1}\paraU@{a}{\sqrt{2}z}+C_{2}\paraV@{a}{\sqrt{2}z}\right)\exp@{\tfrac{1}{2}\varepsilon z^{2}}} | phi*(z) = (C[1]*CylinderU(a, sqrt(2)*z)+ C[2]*CylinderV(a, sqrt(2)*z))* exp((1)/(2)*varepsilon*(z)^(2)) |
\[Phi]*(z) == (Subscript[C, 1]*ParabolicCylinderD[- 1/2 -(a), Sqrt[2]*z]+ Subscript[C, 2]*Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, Sqrt[2]*z] + ParabolicCylinderD[-(a) - 1/2, -(Sqrt[2]*z)]))* Exp[Divide[1,2]*\[CurlyEpsilon]*(z)^(2)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.6213533818-.8057984780*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I, varepsilon = 1}1.542195596-1.017130546*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I, varepsilon = 2} |
Failed [300 / 300] {Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-1.165517214154348, -0.5387865015105858], Plus[Complex[0.9001043151387932, 0.6347232005321619], Times[Complex[-6.562724044143109*^-17, -2.768827103772538*^-17], GAMMA[-1.0]]]]] <- {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-1.0681394822800956, -1.2559298845291706], Plus[Complex[0.9001043151387932, 0.6347232005321619], Times[Complex[-6.562724044143109*^-17, -2.768827103772538*^-17], GAMMA[-1.0]]]]] <- {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0,
|
| 32.10.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a+b+\varepsilon_{3}\gamma = 2n+1} | a + b + varepsilon[3]*gamma = 2*n + 1 |
a + b + Subscript[\[CurlyEpsilon], 3]*\[Gamma] == 2*n + 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a-n)(b-n) = 0} | (a - n)*(b - n) = 0 |
(a - n)*(b - n) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = \frac{C_{1}\WhittakerconfhyperM{\kappa}{\mu}@{\zeta}+C_{2}\WhittakerconfhyperW{\kappa}{\mu}@{\zeta}}{\zeta^{(a-b+1)/2}}\exp@{\tfrac{1}{2}\zeta}} | phi*(z) = (C[1]*WhittakerM(kappa, mu, zeta)+ C[2]*WhittakerW(kappa, mu, zeta))/((zeta)^((a - b + 1)/ 2))*exp((1)/(2)*zeta) |
\[Phi]*(z) == Divide[Subscript[C, 1]*WhittakerM[\[Kappa], \[Mu], \[Zeta]]+ Subscript[C, 2]*WhittakerW[\[Kappa], \[Mu], \[Zeta]],\[Zeta]^((a - b + 1)/ 2)]*Exp[Divide[1,2]*\[Zeta]] |
Failure | Failure | Manual Skip! | Skipped - Because timed out |
| 32.10.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a+b+c+d = 2n+1} | a + b + c + d = 2*n + 1 |
a + b + c + d == 2*n + 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \frac{\zeta-1}{a\phi(\zeta)}\deriv{\phi}{\zeta}} | w*(z) = (zeta - 1)/(a*phi*(zeta))*diff(phi, zeta) |
w*(z) == Divide[\[Zeta]- 1,a*\[Phi]*(\[Zeta])]*D[\[Phi], \[Zeta]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.5000000004+.8660254040*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}.5000000004+.8660254040*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \frac{1}{1-z}} | zeta = (1)/(1 - z) |
\[Zeta] == Divide[1,1 - z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.10.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(\zeta) = C_{1}\hyperF@{b}{-a}{b+c}{\zeta}+C_{2}\zeta^{-b+1-c}\*\hyperF@{-a-b-c+1}{-c+1}{2-b-c}{\zeta}} | phi*(zeta) = C[1]*hypergeom([b, - a], [b + c], zeta)+ C[2]*(zeta)^(- b + 1 - c)* hypergeom([- a - b - c + 1, - c + 1], [2 - b - c], zeta) |
\[Phi]*(\[Zeta]) == Subscript[C, 1]*Hypergeometric2F1[b, - a, b + c, \[Zeta]]+ Subscript[C, 2]*\[Zeta]^(- b + 1 - c)* Hypergeometric2F1[- a - b - c + 1, - c + 1, 2 - b - c, \[Zeta]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[Float(infinity)+Float(infinity)*I <- {a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}Float(infinity)+Float(infinity)*I <- {a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 32.10.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u = \int_{0}^{\Lambda}\frac{\diff{t}}{\sqrt{t(t-1)(t-z)}}} | u = int((1)/(sqrt(t*(t - 1)*(t - z))), t = 0..Lambda) |
u == Integrate[Divide[1,Sqrt[t*(t - 1)*(t - z)]], {t, 0, \[CapitalLambda]}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 32.10.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(1-z)\deriv[2]{\phi}{z}+(1-2z)\deriv{\phi}{z}-\tfrac{1}{4}\phi = 0} | z*(1 - z)* diff(phi, [z$(2)])+(1 - 2*z)* diff(phi, z)-(1)/(4)*phi = 0 |
z*(1 - z)* D[\[Phi], {z, 2}]+(1 - 2*z)* D[\[Phi], z]-Divide[1,4]*\[Phi] == 0 |
Failure | Failure | Failed [70 / 70] 70/70]: [[-.2165063510-.1250000000*I <- {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-.2165063510-.1250000000*I <- {phi = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [70 / 70]
{Complex[-0.21650635094610968, -0.12499999999999999] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.12499999999999994, -0.21650635094610968] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x) = (24)^{1/4}\left(\tfrac{4}{5}|x|^{5/4}-\tfrac{5}{8}d^{2}\ln@@{|x|}\right)} | phi*(x) = (24)^(1/ 4)*((4)/(5)*(abs(x))^(5/ 4)-(5)/(8)*(d)^(2)* ln(abs(x))) |
\[Phi]*(x) == (24)^(1/ 4)*(Divide[4,5]*(Abs[x])^(5/ 4)-Divide[5,8]*(d)^(2)* Log[Abs[x]]) |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.359899020+1.235754628*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}-.7909045934-.5804030210*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[-1.3598990205302544, 1.2357546278215892] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-3.408937126206912, 1.7847927334982474] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x) = \tfrac{2}{3}|x|^{3/2}-\tfrac{3}{4}d^{2}\ln@@{|x|}} | phi*(x) = (2)/(3)*(abs(x))^(3/ 2)-(3)/(4)*(d)^(2)* ln(abs(x)) |
\[Phi]*(x) == Divide[2,3]*(Abs[x])^(3/ 2)-Divide[3,4]*(d)^(2)* Log[Abs[x]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.2263426496+1.013357313*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}-.626197514e-1-.2002123003*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[0.22634264982563074, 1.0133573129774054] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.8226954558510269, 1.5623954186540636] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d^{2} = -\pi^{-1}\ln@{1-k^{2}}} | (d)^(2) = - (Pi)^(- 1)* ln(1 - (k)^(2)) |
(d)^(2) == - (Pi)^(- 1)* Log[1 - (k)^(2)] |
Failure | Failure | Failed [30 / 30] 30/30]: [[Float(-infinity)+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, k = 1}.8496991530+1.866025404*I <- {d = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [30 / 30]
{DirectedInfinity[-1] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1]}Complex[0.84969915256606, 1.8660254037844386] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2]} |
| 32.11.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta_{0} = \tfrac{3}{2}d^{2}\ln@@{2}+\phase@@{\EulerGamma@{1-\tfrac{1}{2}id^{2}}}+\tfrac{1}{4}\pi(1-2\sign@{k})} | theta[0] = (3)/(2)*(d)^(2)* ln(2)+ argument(GAMMA(1 -(1)/(2)*I*(d)^(2)))+(1)/(4)*Pi*(1 - 2*signum(k)) |
Subscript[\[Theta], 0] == Divide[3,2]*(d)^(2)* Log[2]+ Arg[Gamma[1 -Divide[1,2]*I*(d)^(2)]]+Divide[1,4]*Pi*(1 - 2*Sign[k]) |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.126938891-.4004246008*I <- {d = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, theta[0] = 1/2*3^(1/2)+1/2*I, k = 1}1.126938891-.4004246008*I <- {d = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, theta[0] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[1.1269388909194178, -0.4004246003897078] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[θ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.1269388909194178, -0.4004246003897078] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[θ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 32.11.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x) = \tfrac{2}{3}|x|^{3/2}+\tfrac{3}{4}d^{2}\ln@@{|x|}} | phi*(x) = (2)/(3)*(abs(x))^(3/ 2)+(3)/(4)*(d)^(2)* ln(abs(x)) |
\[Phi]*(x) == Divide[2,3]*(Abs[x])^(3/ 2)+Divide[3,4]*(d)^(2)* Log[Abs[x]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.777561816e-1+.4866426869*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}.4572406346+.7002123003*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[-0.0777561812554926, 0.48664268702259433] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.1267942869321503, 1.0356807926992524] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \chi+\tfrac{3}{2}d^{2}\ln@@{2}-\tfrac{1}{4}\pi-\phase@@{\EulerGamma@{\tfrac{1}{2}id^{2}}} = n\pi} | chi +(3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi - argument(GAMMA((1)/(2)*I*(d)^(2))) = n*Pi |
\[Chi]+Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi - Arg[Gamma[Divide[1,2]*I*(d)^(2)]] == n*Pi |
Failure | Failure | Failed [60 / 60] 60/60]: [[-4.109048867-.4004246008*I <- {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), n = 1}-7.250641521-.4004246008*I <- {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), n = 2} |
Failed [60 / 60]
{Complex[-4.10904886506357, -0.4004246003897078] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[n, 1], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-7.250641518653364, -0.4004246003897078] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[n, 2], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 32.11.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d^{2} = \pi^{-1}\ln@{1+k^{2}}} | (d)^(2) = (Pi)^(- 1)* ln(1 + (k)^(2)) |
(d)^(2) == (Pi)^(- 1)* Log[1 + (k)^(2)] |
Failure | Failure | Failed [30 / 30] 30/30]: [[.2793644003+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, k = 1}-.122999981e-1+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [30 / 30]
{Complex[0.2793643998473485, 0.8660254037844386] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1]}Complex[-0.012299998726776007, 0.8660254037844386] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2]} |
| 32.11.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \chi+\tfrac{3}{2}d^{2}\ln@@{2}-\tfrac{1}{4}\pi-\phase@@{\EulerGamma@{\tfrac{1}{2}id^{2}}} \neq n\pi} | chi +(3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi - argument(GAMMA((1)/(2)*I*(d)^(2))) <> n*Pi |
\[Chi]+Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi - Arg[Gamma[Divide[1,2]*I*(d)^(2)]] \[NotEqual]n*Pi |
Failure | Failure | Successful [Tested: 60] | Failed [60 / 60]
{Plus[Complex[-0.4392331450329683, -0.4004246003897078], Times[-3.141592653589793, StringJoin[0.5282230664408086, 1.0]]] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[n, 1], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.4392331450329683, -0.4004246003897078], Times[-3.141592653589793, StringJoin[0.5282230664408086, 2.0]]] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[n, 2], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 32.11.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi(x) = \tfrac{2}{3}\sqrt{2}x^{3/2}-\tfrac{3}{2}\rho^{2}\ln@@{x}} | psi*(x) = (2)/(3)*sqrt(2)*(x)^(3/ 2)-(3)/(2)*(rho)^(2)* ln(x) |
\[Psi]*(x) == Divide[2,3]*Sqrt[2]*(x)^(3/ 2)-Divide[3,2]*\[Rho]^(2)* Log[x] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.1289138697+1.276714626*I <- {psi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, x = 3/2}-.4201810172-.6504246006*I <- {psi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[-0.12891387081109584, 1.276714625954811] <- {Rule[x, 1.5], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.1779519764877535, 1.8257527316314692] <- {Rule[x, 1.5], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma = -\sign@{\imagpart@@{s}}} | sigma = - signum(Im(s)) |
\[Sigma] == - Sign[Im[s]] |
Failure | Failure | Failed [200 / 200] 200/200]: [[-.1339745960+.5000000000*I <- {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), sigma = 1/2*3^(1/2)+1/2*I}-1.500000000+.8660254040*I <- {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), sigma = -1/2+1/2*I*3^(1/2)} |
Failed [200 / 200]
{Complex[-0.1339745962155613, 0.49999999999999994] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.8660254037844388, 0.49999999999999994] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho^{2} = \pi^{-1}\ln@{(1+|s|^{2})/|2\imagpart@@{s}|}} | (rho)^(2) = (Pi)^(- 1)* ln((1 +(abs(s))^(2))/abs(2*Im(s))) |
\[Rho]^(2) == (Pi)^(- 1)* Log[(1 +(Abs[s])^(2))/Abs[2*Im[s]]] |
Failure | Failure | Failed [200 / 200] 200/200]: [[.2989013521+.8660254040*I <- {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), rho = 1/2*3^(1/2)+1/2*I}-.7010986487-.8660254040*I <- {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), rho = -1/2+1/2*I*3^(1/2)} |
Failed [200 / 200]
{Complex[0.2989013519411052, 0.8660254037844386] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.3675975407110632, 0.8660254037844386] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta = -\tfrac{3}{4}\pi-\tfrac{7}{2}\rho^{2}\ln{2}+\phase@{1+s^{2}}+\phase@@{\EulerGamma@{i\rho^{2}}}} | theta = -(3)/(4)*Pi -(7)/(2)*(rho)^(2)* ln(2)+ argument(1 + (s)^(2))+ argument(GAMMA(I*(rho)^(2))) |
\[Theta] == -Divide[3,4]*Pi -Divide[7,2]*\[Rho]^(2)* Log[2]+ Arg[1 + (s)^(2)]+ Arg[Gamma[I*\[Rho]^(2)]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.925696688-1.600990735*I <- {chi = 1/2*3^(1/2)+1/2*I, d = 1/2*3^(1/2)+1/2*I, rho = -1/2+1/2*I*3^(1/2), theta = 1/2*3^(1/2)+1/2*I}.5596712830-1.234965331*I <- {chi = 1/2*3^(1/2)+1/2*I, d = 1/2*3^(1/2)+1/2*I, rho = -1/2+1/2*I*3^(1/2), theta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.6978889663556802, -1.6009907342426515] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[2.496658442211441, -1.6009907342426515] <- {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma = (2/\pi)\asin@{\pi\lambda}} | sigma = (2/ Pi)* arcsin(Pi*lambda) |
\[Sigma] == (2/ Pi)* ArcSin[Pi*\[Lambda]] |
Failure | Failure | Failed [100 / 100] 100/100]: [[.2138525505-.6623078870*I <- {lambda = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I}-1.152172854-.2962824830*I <- {lambda = 1/2*3^(1/2)+1/2*I, sigma = -1/2+1/2*I*3^(1/2)} |
Failed [100 / 100]
{Complex[0.2138525499640901, -0.6623078873679977] <- {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.1521728538203484, -0.296282483583559] <- {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B = 2^{-2\sigma}\frac{\EulerGamma^{2}@{\tfrac{1}{2}(1-\sigma)}\EulerGamma@{\tfrac{1}{2}(1+\sigma)+\nu}}{\EulerGamma^{2}@{\tfrac{1}{2}(1+\sigma)}\EulerGamma@{\tfrac{1}{2}(1-\sigma)+\nu}}} | B = (2)^(- 2*sigma)*((GAMMA((1)/(2)*(1 - sigma)))^(2)* GAMMA((1)/(2)*(1 + sigma)+ nu))/((GAMMA((1)/(2)*(1 + sigma)))^(2)* GAMMA((1)/(2)*(1 - sigma)+ nu)) |
B == (2)^(- 2*\[Sigma])*Divide[(Gamma[Divide[1,2]*(1 - \[Sigma])])^(2)* Gamma[Divide[1,2]*(1 + \[Sigma])+ \[Nu]],(Gamma[Divide[1,2]*(1 + \[Sigma])])^(2)* Gamma[Divide[1,2]*(1 - \[Sigma])+ \[Nu]]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[3.808977659-.2371191295*I <- {B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I}.9147008442+.353764288e-1*I <- {B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, sigma = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[3.808977656026658, -0.23711913260929035] <- {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.914700843688173, 0.035376428936519655] <- {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h^{*} = \ifrac{1}{\left(\pi^{1/2}\EulerGamma@{\nu+1}\right)}} | (h)^(*) = (1)/((Pi)^(1/ 2)* GAMMA(nu + 1)) |
(h)^(*) == Divide[1,(Pi)^(1/ 2)* Gamma[\[Nu]+ 1]] |
Error | Failure | - | Error |
| 32.11.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x) = \tfrac{1}{3}\sqrt{3}x^{2}-\tfrac{4}{3}d^{2}\sqrt{3}\ln@{\sqrt{2}|x|}} | phi*(x) = (1)/(3)*sqrt(3)*(x)^(2)-(4)/(3)*(d)^(2)*sqrt(3)*ln(sqrt(2)*abs(x)) |
\[Phi]*(x) == Divide[1,3]*Sqrt[3]*(x)^(2)-Divide[4,3]*(d)^(2)*Sqrt[3]*Log[Sqrt[2]*Abs[x]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.8683794902+2.254077396*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}-.1115135772-.4431471813*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[0.8683794899108137, 2.2540773967762746] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.180658615765844, 2.8031155024529326] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d^{2} = -\tfrac{1}{4}\sqrt{3}\pi^{-1}\ln@{1-|\mu|^{2}}} | (d)^(2) = -(1)/(4)*sqrt(3)*(Pi)^(- 1)* ln(1 -(abs(mu))^(2)) |
(d)^(2) == -Divide[1,4]*Sqrt[3]*(Pi)^(- 1)* Log[1 -(Abs[\[Mu]])^(2)] |
Failure | Failure | Failed [100 / 100] 100/100]: [[Float(-infinity)+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I}Float(-infinity)+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, mu = -1/2+1/2*I*3^(1/2)} |
Failed [100 / 100]
{DirectedInfinity[-1] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}DirectedInfinity[-1] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta_{0} = \tfrac{1}{3}d^{2}\sqrt{3}\ln@@{3}+\tfrac{2}{3}\pi\nu+\tfrac{7}{12}\pi+\phase@@{\mu}+\phase@@{\EulerGamma@{-\tfrac{2}{3}i\sqrt{3}d^{2}}}} | theta[0] = (1)/(3)*(d)^(2)*sqrt(3)*ln(3)+(2)/(3)*Pi*nu +(7)/(12)*Pi + argument(mu)+ argument(GAMMA(-(2)/(3)*I*sqrt(3)*(d)^(2))) |
Subscript[\[Theta], 0] == Divide[1,3]*(d)^(2)*Sqrt[3]*Log[3]+Divide[2,3]*Pi*\[Nu]+Divide[7,12]*Pi + Arg[\[Mu]]+ Arg[Gamma[-Divide[2,3]*I*Sqrt[3]*(d)^(2)]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-3.888102442-1.096503697*I <- {d = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, theta[0] = 1/2*3^(1/2)+1/2*I}-5.254127846-.7304782927*I <- {d = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, theta[0] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-3.888102439563878, -1.0965036955306524] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[θ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-5.254127843348316, -0.7304782917462136] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[θ, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.11.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = 1+\left(\ifrac{2ih\pi^{3/2}\exp@{-i\pi\nu}}{\EulerGamma@{-\nu}}\right)} | mu = 1 +((2*I*h*(Pi)^(3/ 2)* exp(- I*Pi*nu))/(GAMMA(- nu))) |
\[Mu] == 1 +(Divide[2*I*h*(Pi)^(3/ 2)* Exp[- I*Pi*\[Nu]],Gamma[- \[Nu]]]) |
Failure | Failure | Failed [300 / 300] 300/300]: [[241.2310915-105.5149067*I <- {h = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = -1/2+1/2*I*3^(1/2)}-1.289758519+2.890481636*I <- {h = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = -1/2*3^(1/2)-1/2*I} |
Failed [300 / 300]
{Complex[241.23109103950634, -105.514906477147] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[-1.289758518042884, 2.89048163412207] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} |
| 32.13.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v_{t}-6v^{2}v_{x}+v_{xxx} = 0} | v[t]- 6*(v)^(2)* v[x]+ v[x*x*x] = 0 |
Subscript[v, t]- 6*(v)^(2)* Subscript[v, x]+ Subscript[v, x*x*x] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x(3t)^{-1/3}} | (x + y*I) = x*(3*t)^(- 1/ 3) |
(x + y*I) == x*(3*t)^(- 1/ 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v(x,t) = (3t)^{-1/3}w(z)} | v*(x , t) = (3*t)^(- 1/ 3)* w*((x + y*I)) |
v*(x , t) == (3*t)^(- 1/ 3)* w*((x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{t}+6uu_{x}+u_{xxx} = 0} | u[t]+ 6*u*u[x]+ u[x*x*x] = 0 |
Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x*x*x] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x(3t)^{-1/3}} | (x + y*I) = x*(3*t)^(- 1/ 3) |
(x + y*I) == x*(3*t)^(- 1/ 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x+3\lambda t^{2}} | (x + y*I) = x + 3*lambda*(t)^(2) |
(x + y*I) == x + 3*\[Lambda]*(t)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(x,t) = W(z)-\lambda t} | u*(x , t) = W*((x + y*I))- lambda*t |
u*(x , t) == W*((x + y*I))- \[Lambda]*t |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{xt} = \sin@@{u}} | u[x*t] = sin(u) |
Subscript[u, x*t] == Sin[u] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.70450695e-2+.1624035369*I <- {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, u[x*t] = 1/2*3^(1/2)+1/2*I}-1.358980334+.5284289409*I <- {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, u[x*t] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.007045069484300837, 0.16240353677712993] <- {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[u, Times[t, x]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.3589803343001376, 0.5284289405615687] <- {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[u, Times[t, x]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 32.13#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = xt} | (x + y*I) = x*t |
(x + y*I) == x*t |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(x,t) = v(z)} | u*(x , t) = v*((x + y*I)) |
u*(x , t) == v*((x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{tt} = u_{xx}-6(u^{2})_{xx}+u_{xxxx}} | u[t*t] = u[x*x]- 6*(u)^(2)[x*x]+ u[x*x*x*x] |
Subscript[u, t*t] == Subscript[u, x*x]- 6*Subscript[(u)^(2), x*x]+ Subscript[u, x*x*x*x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = x-ct} | (x + y*I) = x - c*t |
(x + y*I) == x - c*t |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.13#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(x,t) = v(z)} | u*(x , t) = v*((x + y*I)) |
u*(x , t) == v*((x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\exp@{-\tfrac{1}{4}\xi^{4}-z\xi^{2}}p_{m}(\xi)p_{n}(\xi)\diff{\xi} = \Kroneckerdelta{m}{n}} | int(exp(-(1)/(4)*(xi)^(4)- z*(xi)^(2))*p[m]*(xi)* p[n]*(xi), xi = - infinity..infinity) = KroneckerDelta[m, n] |
Integrate[Exp[-Divide[1,4]*\[Xi]^(4)- z*\[Xi]^(2)]*Subscript[p, m]*(\[Xi])* Subscript[p, n]*(\[Xi]), {\[Xi], - Infinity, Infinity}, GenerateConditions->None] == KroneckerDelta[m, n] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.5089051774+.3195154069*I <- {z = 1/2*3^(1/2)+1/2*I, p[m] = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}.4910948226+.3195154069*I <- {z = 1/2*3^(1/2)+1/2*I, p[m] = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 2} |
Failed [300 / 300]
{Complex[-0.5089051767265081, 0.31951540648426185] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.49109482327349185, 0.31951540648426185] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 32.15.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n+1}(z)p_{n+1}(\xi) = \xi p_{n}(\xi)-a_{n}(z)p_{n-1}(\xi)} | a[n + 1]*(z)* p[n + 1]*(xi) = xi*p[n]*(xi)- a[n]*(z)* p[n - 1]*(xi) |
Subscript[a, n + 1]*(z)* Subscript[p, n + 1]*(\[Xi]) == \[Xi]*Subscript[p, n]*(\[Xi])- Subscript[a, n]*(z)* Subscript[p, n - 1]*(\[Xi]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 32.15.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (u_{n+1}+u_{n}+u_{n-1})u_{n} = n-2zu_{n}} | (u[n + 1]+ u[n]+ u[n - 1])* u[n] = n - 2*z*u[n] |
(Subscript[u, n + 1]+ Subscript[u, n]+ Subscript[u, n - 1])* Subscript[u, n] == n - 2*z*Subscript[u, n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |