Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety
Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety
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DOI：
10.1016/j.amc.2013.12.165
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发表时间：
2014-03-15
影响因子：
4
通讯作者：
Wampler, Charles W.
中科院分区：
文献类型：
--
作者：
Bates, Daniel J.;Decker, Wolfram;Wampler, Charles W.
多项式方程组出现在数学、工程和科学中。因此，求多项式系统的解集是数学和应用领域的一个基本问题。本文的重点是比较两个根本不同的方法来计算和表示多项式系统的解决方案：数值同伦连续和符号计算。几个说明性的例子被认为是，使用软件包贝尔蒂尼和奇异。(C)2014 Elsevier Inc. All rights reserved.
Systems of polynomial equations arise throughout mathematics, engineering, and the sciences. It is therefore a fundamental problem both in mathematics and in application areas to find the solution sets of polynomial systems. The focus of this paper is to compare two fundamentally different approaches to computing and representing the solutions of polynomial systems: numerical homotopy continuation and symbolic computation. Several illustrative examples are considered, using the software packages Bertini and Singular. (C) 2014 Elsevier Inc. All rights reserved.