Algorithms for symmetric groups of simplexes

作者：Lin Shenggui Zhang Huiling^*

来源：Applied Mathematics and Computation, 2007, 188(2): 1610-1634.

DOI：10.1016/j.amc.2006.11.029

• exact computation
• simplex
• symmetric group
• rotation group
• regular tetrahedron

An algorithm is developed to solve a special case of reverse problems of linear systems, and as its application, a method is presented to solve optimal problem over the special orthogonal group. An algorithm is designed to find out an orthogonal matrix A such that A transforms a set of orthogonal vectors to another, and as its application, a method is given to generate subgroups of the orthogonal group preserving several orthogonal vectors fixed. It is prove that the symmetric (or rotational) group of the simplex S-n preserving its center fixed is isomorphic to the group consisting of all n x n permutational matrices. All algorithms in this paper can be realized by algebraic system CoCoA 4.3.

• 出版日期2007-5-15
• 单位福建师范大学