Painlevé Transcendents - 32.6 Hamiltonian Structure
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 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}}
\deriv{q}{z} = \pderiv{\mathrm{H}}{p} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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}}
\deriv{p}{z} = -\pderiv{\mathrm{H}}{q} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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)}
(\alpha,\beta,\gamma,\delta) = \left(-2\kappa_{\infty}\theta_{\infty},2\kappa_{0}(\theta_{0}+1),\kappa_{\infty}^{2},-\kappa_{0}^{2}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | 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)}
(\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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | 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) = \left(2\kappa_{\infty},\kappa_{0}(\theta-1),0,-\kappa_{0}^{2}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | - | - |