论文标题
一种基于签名的算法，用于计算多项式系统的非等级基因座
A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System
论文作者
论文摘要
在许多应用区域中出现了多项式系统来建模非线性几何特性。在这种设置中，多项式系统可能会带有最终用户希望从解决方案集中排除的变性。多项式系统的非排定基因座是解决方案集合匹配方程数的一组点。计算非字体基因座是通过理想理论操作在交换代数（例如饱和理想或等二二维分解）中进行的，以提取最大编成的组成部分。通过利用基于签名的Gröbner基础算法的代数特征，我们设计了一种算法，该算法计算了描述多项式系统非排定基因座的方程式的gröbner基础，而没有首先计算整个多项式系统的GRöbner基础。
Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-user wants to exclude from the solution set. The nondegenerate locus of a polynomial system is the set of points where the codimension of the solution set matches the number of equations. Computing the nondegenerate locus is classically done through ideal-theoretic operations in commutative algebra such as saturation ideals or equidimensional decompositions to extract the component of maximal codimension. By exploiting the algebraic features of signature-based Gröbner basis algorithms we design an algorithm which computes a Gröbner basis of the equations describing the closure of the nondegenerate locus of a polynomial system, without computing first a Gröbner basis for the whole polynomial system.
