PASCAL programs for identification of Lie algebras Part 3: LEVI decomposition and canonical basis

Title of program: CANONIK Catalogue Id: AAXO_v1_0 Nature of problem Given a Lie algebra L with structure constants which are either integers or polynomials with integer coefficients, LEVI determines a Levi decomposition of L into its radical R(L) and its (semi-)simple part S(L). The program CANONIK uses the methods of all three programs SPLIT, LEVI and RADICAL in order to express L in a standard basis: L is decomposed as a direct sum, each component L' is Levi-decomposed, each S(L') is decomposed as a direct sum, the nilradical of each R(L') is calculated, and f ... Versions of this program held in the CPC repository in Mendeley Data aaxo_v1_0; CANONIK; 10.1016/0010-4655(87)90007-5 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)程序名称：CANONIK 目录编号：AAXO_v1_0 问题本质： 给定结构常数为整数或整系数多项式的李代数(Lie algebra) L，LEVI程序可实现L的列维分解，将其拆分为根基R(L)与（半）单部分S(L)。本程序CANONIK融合SPLIT、LEVI与RADICAL三个程序的算法，将李代数L表示为标准基形式：将L分解为直和，对每个分量L'执行列维分解，将每个S(L')拆分为直和，计算每个R(L')的幂零根基，以及f…… 存放在Mendeley Data的CPC仓库中的该程序版本： aaxo_v1_0; CANONIK; 10.1016/0010-4655(87)90007-5 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019）