A short proof for the parameter continuation theorem

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2024-08-03 DOI:10.1016/j.jsc.2024.102373

Viktoriia Borovik, Paul Breiding

引用次数: 0

Abstract

The Parameter Continuation Theorem is the theoretical foundation for polynomial homotopy continuation, which is one of the main tools in computational algebraic geometry. In this note, we give a short proof using Gröbner bases. Our approach gives a method for computing discriminants.

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参数延续定理的简短证明

参数延续定理是多项式同调延续的理论基础，是计算代数几何的主要工具之一。在本注释中，我们用格罗布纳基给出了一个简短的证明。我们的方法给出了计算判别式的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.