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
本程序LINA01用于哈密顿系统（Hamiltonian systems）的正向与逆向正则化，以及其形式运动积分的计算。LINA01的相关计算基于李正则变换（Lie canonical transformation）方法实现。该程序包基于REDUCE平台编写。

程序名称：LINA01
目录编号：ADUV_v1_0

问题本质
将给定哈密顿函数转化为标准形的变换（即正则化过程）是非线性哈密顿系统的经典处理手段之一[1-6]。近年来，除经典力学领域外，为探寻混沌的量子特征，标准形方法已被应用于混沌哈密顿系统的量子化研究[7]。除此之外，正则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...

存放在Mendeley数据的CPC库中的该程序版本：ADUV_v1_0；LINA01；10.1016/j.cpc.2004.10.010

本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018）