多项式系统三角分解的算法
Algorithms for Computing Triangular Decompositions of Polynomial Systems
摘要：
我们提出了新的算法计算三角分解的多项式系统递增。相对于以前的工作，我们的改进是基于{ \em weakened}的多项式GCD模一个规则链的概念，这允许大大简化和优化的子算法。从类似的昂贵计算中提取共同的工作也是我们算法的一个关键特征。在我们的实验结果中，我们的新算法的实现，实现了与{\RegularChains }库中的{\Maple }，优于具有类似规格的求解器的几个数量级上足够困难的问题。
英文摘要：
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which permits to greatly simplify and optimize the sub-algorithms. Extracting common work from similar expensive computations is also a key feature of our algorithms. In our experimental results the implementation of our new algorithms, realized with the {\RegularChains} library in {\Maple}, outperforms solvers with similar specifications by several orders of magnitude on sufficiently difficult problems.
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