Computing the decomposition group of a zero-dimensional ideal by elimination method

2016/01/22 by Yongbin Li, Li, Yongbin
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Commutative Algebra and Its Applications #Polynomial and algebraic computation #cs.SC #math.AC

paper · pdf · doi:10.48550/arxiv.1601.06626

arxiv created 2016/01/22 · arxiv updated 2016/01/26

Abstract

In this note, we show that the decomposition group Dec(I) of a zero-dimensional radical ideal I in \bf K[x₁,…,x_n] can be represented as the direct sum of several symmetric groups of polynomials based upon using Gröbner bases. The new method makes a theoretical contribution to discuss the decomposition group of I by using Computer Algebra without considering the complexity. As one application, we also present an approach to yield new triangular sets in computing triangular decomposition of polynomial sets \mathbb P if Dec(<\mathbb P>) is known.

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