两个多项式的保重三角集分解
Multiplicity Preserving Triangular Set Decomposition of Two Polynomials
摘要：
本文对两个多项式组提出了一个保重三角集分解算法。该算法将多项式系统定义的簇分解成三角形集合表示的非混合分量，这些分量可能具有负重数。在二元情形下，我们给出了一个完整的算法，将系统分解成多重性保持的正三角集。我们还分析了算法的复杂性在双变量的情况下。我们实现了我们的算法，并通过大量的实验证明了该方法的有效性。
英文摘要：
In this paper, a multiplicity preserving triangular set decomposition algorithm is proposed for a system of two polynomials. The algorithm decomposes the variety defined by the polynomial system into unmixed components represented by triangular sets, which may have negative multiplicities. In the bivariate case, we give a complete algorithm to decompose the system into multiplicity preserving triangular sets with positive multiplicities. We also analyze the complexity of the algorithm in the bivariate case. We implement our algorithm and show the effectiveness of the method with extensive experiments.
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