Painlevé Transcendents - 32.4 Isomonodromy Problems

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
32.4#Ex1	${\displaystyle{\displaystyle\frac{\partial\boldsymbol{{\Psi}}}{\partial\lambda}=\mathbf{A}(z,\lambda)\boldsymbol{{\Psi}}}}$ \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	${\displaystyle{\displaystyle\frac{\partial\boldsymbol{{\Psi}}}{\partial z}=\mathbf{B}(z,\lambda)\boldsymbol{{\Psi}}}}$ \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	${\displaystyle{\displaystyle\frac{\partial\mathbf{A}}{\partial z}-\frac{\partial\mathbf{B}}{\partial\lambda}+\mathbf{A}\mathbf{B}-\mathbf{B}\mathbf{A}=0}}$ \pderiv{\mathbf{A}}{z}-\pderiv{\mathbf{B}}{\lambda}+\mathbf{A}\mathbf{B}-\mathbf{B}\mathbf{A} = 0		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	${\displaystyle{\displaystyle(\alpha,\beta,\gamma,\delta)=\left(2\theta_{0},2(1-\theta_{\infty}),1,-1\right)}}$ (\alpha,\beta,\gamma,\delta) = \left(2\theta_{0},2(1-\theta_{\infty}),1,-1\right)		(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	${\displaystyle{\displaystyle\theta_{0}=\frac{4v_{0}}{z}\left(\theta_{\infty}\left(1-\frac{z}{4v_{0}}\right)+\frac{z-2v_{0}}{2v_{0}v_{1}}u_{0}+u_{1}v_{1}\right)}}$ \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)		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	-	-