  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.
