Using symmetries in the eigenvalue method for polynomial systems

被引:6
|
作者
Corless, Robert M. [1 ]
Gatermann, Karin [2 ]
Kotsireas, Ilias S. [3 ]
机构
[1] Univ Western Ontario, Dept Appl Math, Ontario Res Ctr Comp Algebra, London, ON N6A 5B7, Canada
[2] Univ Western Ontario, Dept Comp Sci, London, ON N6A 5B7, Canada
[3] Wilfrid Laurier Univ, Dept Phys & Comp Sci, Waterloo, ON N2L 3C5, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
GROBNER BASES; SAGBI-BASES;
D O I
10.1016/j.jsc.2008.11.009
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
One way of solving polynomial systems of equations is by computing a Grobner basis, setting up an eigenvalue problem and then computing the eigenvalues numerically. This so-called eigenvalue method is an excellent bridge between symbolic and numeric computation, enabling the solution of larger systems than with purely symbolic methods. We investigate the case that the system of polynomial equations has symmetries. For systems with symmetry, some matrices in the eigenvalue method turn out to have special structure. The exploitation of this special structure is the aim of this paper. For theoretical development we make use of SAGBI bases of invariant rings. Examples from applications illustrate our new approach. (C) 2009 Published by Elsevier Ltd
引用
收藏
页码:1536 / 1550
页数:15
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