利用判别理想改进DISPGB算法
Improving DISPGB Algorithm Using the Discriminant Ideal
摘要：
1992年，V.Weispfenning证明了综合Groebner基（CGB）的存在性，并给出了计算CGB的算法。这种算法不是很有效，也不是规范的。根据他的建议，A。Montes在2002年得到了一个更有效的算法（DISPGB）讨论参数Groebner基。受其哲学思想的启发，V.Weispfenning在2002年定义了如何获得参数多项式理想的规范综合Groebner基（CCGB），并提供了一种构造方法。本文利用Weispfenning的CCGB思想对Montes DISPGB算法进行了实质性的改进。它现在包括使用判别式理想重写讨论树，并提供紧凑有效的讨论。我们还描述了新的算法在DPGB库中包含改进的DISPGB以及新的例程来检查是否一个给定的基础是一个CGB或没有，并获得一个CGB。还提供了示例和测试。
英文摘要：
In 1992, V. Weispfenning proved the existence of Comprehensive Groebner Bases (CGB) and gave an algorithm to compute one. That algorithm was not very efficient and not canonical. Using his suggestions, A. Montes obtained in 2002 a more efficient algorithm (DISPGB) for Discussing Parametric Groebner Bases. Inspired in its philosophy, V. Weispfenning defined, in 2002, how to obtain a Canonical Comprehensive Groebner Basis (CCGB) for parametric polynomial ideals, and provided a constructive method. In this paper we use Weispfenning's CCGB ideas to make substantial improvements on Montes DISPGB algorithm. It now includes rewriting of the discussion tree using the Discriminant Ideal and provides a compact and effective discussion. We also describe the new algorithms in the DPGB library containing the improved DISPGB as well as new routines to check whether a given basis is a CGB or not, and to obtain a CGB. Examples and tests are also provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
