论文标题
用于计算饱和理想基础（F4SAT）和结肠理想的新的有效算法（稀疏FGLM-COLON）
New efficient algorithms for computing Gröbner bases of saturation ideals (F4SAT) and colon ideals (Sparse-FGLM-colon)
论文作者
论文摘要
本文涉及基于线性代数的方法，用于通过所谓的gröbner碱基求解准确的多项式系统，这些方法允许一个人计算输入方程生成的多项式理想。这是非线性代数的主题问题，在计算数学中更广泛地是由于其在工程和计算科学中的众多应用。这样的应用通常需要几何计算功能，例如表示两个解决方案集的设置差与给定的多项式系统的闭合。从代数上讲，这归结为计算结肠和/或饱和多项式理想的Gröbner基础。在本文中，我们描述和分析了针对此任务的新Gröbner算法，并且实现了与最先进的软件相比，这些算法的效率更高。
This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gröbner bases, which allow one to compute modulo the polynomial ideal generated by the input equations. This is a topical issue in non-linear algebra and more broadly in computational mathematics because of its numerous applications in engineering and computing sciences. Such applications often require geometric computing features such as representing the closure of the set difference of two solution sets to given polynomial systems. Algebraically, this boils down to computing Gröbner bases of colon and/or saturation polynomial ideals. In this paper, we describe and analyze new Gröbner bases algorithms for this task and present implementations which are more efficient by several orders of magnitude than the state-of-the-art software.
