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 Gr\"obner basis algorithms we design an algorithm which computes a Gr\"obner basis of the equations describing the closure of the nondegenerate locus of a polynomial system, without computing first a Gr\"obner basis for the whole polynomial system.

翻译：多元系统解析会在许多应用领域产生模型非线性几何特性。 在这种环境下, 多元系统可能会随着终端用户想要从解决方案集中排除的变异而变异。 多元系统的非变性极点是解决方案集相匹配方程数的一组点。 计算非降解性极点时, 典型的方式是通过通配理想或等量分解等通性代数等通性代数中的理想理论操作完成的。 通过利用基于签名的 Gr\'obner基底算法的代数特征, 我们设计了一种算法, 算出描述多元系统非脱热性极地表关闭的方程的 Gr\'obner基数, 而不首先计算整个多元系统 Gr\'obner基数 。