Painlevé Transcendents - 32.6 Hamiltonian Structure

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
32.6#Ex1 d q d z = ∂ ⁡ H ∂ ⁡ p derivative 𝑞 𝑧 partial-derivative H 𝑝 {\displaystyle{\displaystyle\frac{\mathrm{d}q}{\mathrm{d}z}=\frac{\partial% \mathrm{H}}{\partial p}}}
\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 d p d z = - ∂ ⁡ H ∂ ⁡ q derivative 𝑝 𝑧 partial-derivative H 𝑞 {\displaystyle{\displaystyle\frac{\mathrm{d}p}{\mathrm{d}z}=-\frac{\partial% \mathrm{H}}{\partial q}}}
\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 ( α , β , γ , δ ) = ( - 2 ⁢ κ ∞ ⁢ θ ∞ , 2 ⁢ κ 0 ⁢ ( θ 0 + 1 ) , κ ∞ 2 , - κ 0 2 ) 𝛼 𝛽 𝛾 𝛿 2 subscript 𝜅 subscript 𝜃 2 subscript 𝜅 0 subscript 𝜃 0 1 superscript subscript 𝜅 2 superscript subscript 𝜅 0 2 {\displaystyle{\displaystyle(\alpha,\beta,\gamma,\delta)=\left(-2\kappa_{% \infty}\theta_{\infty},2\kappa_{0}(\theta_{0}+1),\kappa_{\infty}^{2},-\kappa_{% 0}^{2}\right)}}
(\alpha,\beta,\gamma,\delta) = \left(-2\kappa_{\infty}\theta_{\infty},2\kappa_{0}(\theta_{0}+1),\kappa_{\infty}^{2},-\kappa_{0}^{2}\right)		 

(alpha , beta , gamma , delta) = (- 2*kappa[infinity]*theta[infinity], 2*kappa[0]*(theta[0]+ 1), (kappa[infinity])^(2), - (kappa[0])^(2))
 
(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (- 2*Subscript[\[Kappa], Infinity]*Subscript[\[Theta], Infinity], 2*Subscript[\[Kappa], 0]*(Subscript[\[Theta], 0]+ 1), (Subscript[\[Kappa], Infinity])^(2), - (Subscript[\[Kappa], 0])^(2))
 Skipped - no semantic math Skipped - no semantic math - -
32.6.E27 ( α , β , γ , δ ) = ( - 4 ⁢ η ∞ ⁢ θ ∞ , 4 ⁢ η 0 ⁢ ( θ 0 + 1 ) , 4 ⁢ η ∞ 2 , - 4 ⁢ η 0 2 ) 𝛼 𝛽 𝛾 𝛿 4 subscript 𝜂 subscript 𝜃 4 subscript 𝜂 0 subscript 𝜃 0 1 4 superscript subscript 𝜂 2 4 superscript subscript 𝜂 0 2 {\displaystyle{\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)}}
(\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)		 

(alpha , beta , gamma , delta) = (- 4*eta[infinity]*theta[infinity], 4*eta[0]*(theta[0]+ 1), 4*(eta[infinity])^(2), - 4*(eta[0])^(2))
 
(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (- 4*Subscript[\[Eta], Infinity]*Subscript[\[Theta], Infinity], 4*Subscript[\[Eta], 0]*(Subscript[\[Theta], 0]+ 1), 4*(Subscript[\[Eta], Infinity])^(2), - 4*(Subscript[\[Eta], 0])^(2))
 Skipped - no semantic math Skipped - no semantic math - -
32.6.E35 ( α , β , γ , δ ) = ( 2 ⁢ κ ∞ , κ 0 ⁢ ( θ - 1 ) , 0 , - κ 0 2 ) 𝛼 𝛽 𝛾 𝛿 2 subscript 𝜅 subscript 𝜅 0 𝜃 1 0 superscript subscript 𝜅 0 2 {\displaystyle{\displaystyle(\alpha,\beta,\gamma,\delta)=\left(2\kappa_{\infty% },\kappa_{0}(\theta-1),0,-\kappa_{0}^{2}\right)}}
(\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[0])^(2))
 
(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (2*Subscript[\[Kappa], Infinity], Subscript[\[Kappa], 0]*(\[Theta]- 1), 0 , - (Subscript[\[Kappa], 0])^(2))
 Skipped - no semantic math Skipped - no semantic math - -
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