Hilbert Functions and the Buchberger Algorithm
Hilbert Functions and the Buchberger Algorithm
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DOI：
10.1006/jsco.1996.0056
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发表时间：
1996-10
期刊：
影响因子：
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通讯作者：
C. Traverso
中科院分区：
文献类型：
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作者：
C. Traverso
本文介绍了如何利用理想函数的Hilbert-Poincare级数知识来加速计算Grobner基的Buchberger算法。该算法在改变顺序和验证模计算中很有用，对于切锥排序也是有用的；如果理想是完全交集，则加速Grobner基的直接计算，例如在从参数方程计算笛卡尔时，可以验证或反驳理想是完全交集的猜想，并且当猜想为假时也是略微有用的。报道了一系列大型实验。
Abstract In this paper we show how to use the knowledge of the Hilbert–Poincare series of an idealIto speed up the Buchberger algorithm for the computation of a Grobner basis. The algorithm is useful in the change of ordering and in the validation of modular computations, also with tangent cone orderings; speeds the direct computation of a Grobner basis if the ideal is a complete intersection, e.g. in the computation of cartesian from parametric equations, can validate or disprove a conjecture that an ideal is a complete intersection, and is marginally useful also when the conjecture is false. A large set of experiments is reported.