对合除法技术：若干推广与优化
Involutive Division Technique: Some Generalizations and Optimizations
AI总结：
本文提出一类由容许单项式序诱导的新对合除法，证明其诺特性与构造性，并基于完成序选择和变量重算提出两种优化，用于高效计算对合格罗布纳基。
摘要：
本文在先前引入的对合除法之外，考虑了一类由容许单项式序诱导的新除法。我们证明了这些除法是诺特性的且是构造性的。因此，它们中的每一个都允许通过依次检验非乘法延拓的乘法约化来计算多项式理想的对合格罗布纳基。我们研究了对合算法对完成序的依赖性。基于特定对合除法的性质，提出了两种计算优化。其一在于对完成序的特殊选择。另一种优化与在算法过程中重新计算乘法变量和非乘法变量有关。
英文摘要：
In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them allows one to compute an involutive Groebner basis of a polynomial ideal by sequentially examining multiplicative reductions of nonmultiplicative prolongations. We study dependence of involutive algorithms on the completion ordering. Based on properties of particular involutive divisions two computational optimizations are suggested. One of them consists in a special choice of the completion ordering. Another optimization is related to recomputing multiplicative and nonmultiplicative variables in the course of the algorithm.
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。
