Weakly nonlocal Poisson brackets: Tools, examples, computations

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.我们在Maple、Reduce与Mathematica三款计算机代数系统（computer algebra systems）中，实现了一套用于计算弱非局域哈密顿算子（weakly nonlocal Hamiltonian operators）的舒滕括号（Schouten bracket）的算法。此类哈密顿算子几乎涵盖了(1+1)维可积演化偏微分方程（partial differential equations, PDE）理论中的绝大多数实例。