A signature-based algorithm for computing the nondegenerate locus of a polynomial system

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 exclude from solution set. The nondegenerate locus of a is set points where codimension matches number equations. Computing classically done through ideal-theoretic operations commutative algebra as saturation ideals or equidimensional decompositions extract component maximal codimension. By exploiting algebraic features signature-based Gr\"obner basis algorithms we design an algorithm computes equations describing closure system, without computing first for whole system.