A REDUCE program for the normalization of polynomial Hamiltonians

Abstract The program LINA01 is proposed for the direct and the inverse normalization of Hamiltonian systems and for the calculation of formal integrals of motion of them. The calculations required in LINA01 are made on the basis of Lie canonical transformation method. The program package of LINA01 is written on REDUCE. Title of program: LINA01 Catalogue Id: ADUV_v1_0 Nature of problem The transformation bringing a given Hamiltonian function into the normal form (namely, the normalization) is one of the conventional methods for non-linear Hamiltonian systems [1-6]. Recently, beyond classical mechanics, the normal form method has been applied to quantization of chaotic Hamiltonian systems with the aim of finding quantum signature of chaos [7]. Besides those utilities, the normalization requires quite cumbersome algebraic calculations of polynomials, so that the computer algebra ... Versions of this program held in the CPC repository in Mendeley Data ADUV_v1_0; LINA01; 10.1016/j.cpc.2004.10.010 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)摘要 本文提出的LINA01程序，可实现哈密顿系统的直接归一化与逆归一化，并可计算其形式运动积分。LINA01所需的计算基于李正则变换（Lie canonical transformation）方法完成，该程序包基于REDUCE平台编写。 程序名称：LINA01；目录编号：ADUV_v1_0；问题属性： 将给定哈密顿函数转化为正则形式（即归一化）的变换，是非线性哈密顿系统的经典处理方法之一[1-6]。近年来，除经典力学领域外，正则形式方法已被应用于混沌哈密顿系统的量子化研究，以期揭示混沌的量子特征[7]。除上述应用场景外，归一化过程需要开展极为繁琐的多项式代数运算，因此计算机代数…… 本程序在Mendeley数据集中的CPC仓库版本为ADUV_v1_0；LINA01；DOI:10.1016/j.cpc.2004.10.010。本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）。