Painlevé Transcendents - 32.4 Isomonodromy Problems
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 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}}}
\pderiv{\boldsymbol{{\Psi}}}{\lambda} = \mathbf{A}(z,\lambda)\boldsymbol{{\Psi}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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}}}
\pderiv{\boldsymbol{{\Psi}}}{z} = \mathbf{B}(z,\lambda)\boldsymbol{{\Psi}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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}
\pderiv{\mathbf{A}}{z}-\pderiv{\mathbf{B}}{\lambda}+\mathbf{A}\mathbf{B}-\mathbf{B}\mathbf{A} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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) = \left(2\theta_{0},2(1-\theta_{\infty}),1,-1\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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} = \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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | - | - |