We implement an algorithm for the computation of Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems: Maple, Reduce and Mathematica. This class of Hamiltonian operators encompass almost all the examples coming from the theory of (1+1)-integrable evolutionary PDEs. Program summary: Program Title: Jacobi (Maple), CDE module cde_weaklynl.red (Reduce, official distribution), nlPVA (Mathematica) CPC Library link to program files: https://doi.org/10.17632/synmrvr74g.1 Developer's repository link: https://gdeq.org/Weakly_nonlocal_Poisson_brackets Licensing provisions: BSD 2-clause Programming language: Maple, Reduce (Rlisp), Mathematica Supplementary material: Example program files in the three languages (Maple, Reduce, Mathematica) Nature of problem: Calculating the Jacobi identity for weakly nonlocal Poisson brackets Solution method: Bringing the Jacobi identity to a canonical form Additional comments including restrictions and unusual features: Use a 2020 Maple or Mathematica version, or a 2021 Reduce snapshot
Casati, M., Lorenzoni, P., Valeri, D., Vitolo, R. (2022). Weakly nonlocal Poisson brackets: Tools, examples, computations. COMPUTER PHYSICS COMMUNICATIONS, 274(May 2022) [10.1016/j.cpc.2022.108284].
Weakly nonlocal Poisson brackets: Tools, examples, computations
Lorenzoni P.
;
2022
Abstract
We implement an algorithm for the computation of Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems: Maple, Reduce and Mathematica. This class of Hamiltonian operators encompass almost all the examples coming from the theory of (1+1)-integrable evolutionary PDEs. Program summary: Program Title: Jacobi (Maple), CDE module cde_weaklynl.red (Reduce, official distribution), nlPVA (Mathematica) CPC Library link to program files: https://doi.org/10.17632/synmrvr74g.1 Developer's repository link: https://gdeq.org/Weakly_nonlocal_Poisson_brackets Licensing provisions: BSD 2-clause Programming language: Maple, Reduce (Rlisp), Mathematica Supplementary material: Example program files in the three languages (Maple, Reduce, Mathematica) Nature of problem: Calculating the Jacobi identity for weakly nonlocal Poisson brackets Solution method: Bringing the Jacobi identity to a canonical form Additional comments including restrictions and unusual features: Use a 2020 Maple or Mathematica version, or a 2021 Reduce snapshot
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