多元代数方程组解的重数的计算

The Computation of the Multiplicity of Solutions of System of Algebraic Equations

本文利用多项式理想对偶基的理论给出了当代数方程组只有孤立解（即零维理想的零点）时解的重数的一个算法，同时得到了零维理想有重零点的几个判定准则．

In this paper, an algorithm and some criterions are given based on dual base theory of polynanial ideal. When the system of algebraic equations has only isolated solutions, this algorithm can compute the multiplicity of solutions of the system and the criterions can decide whether the system has multiple zero point. These generalize the results from unary to multivariate.