A Signaturebased Algorithm for Computing the Nondegenerate Locus of a Polynomial System
Abstract
Polynomial system solving arises in many application areas to model nonlinear geometric properties. In such settings, polynomial systems may come with degeneration which the enduser 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 idealtheoretic operations in commutative algebra such as saturation ideals or equidimensional decompositions to extract the component of maximal codimension. By exploiting the algebraic features of signaturebased 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 DOI:
 10.48550/arXiv.2202.13784
 arXiv:
 arXiv:2202.13784
 Bibcode:
 2022arXiv220213784E
 Keywords:

 Computer Science  Symbolic Computation;
 13P10;
 13P05;
 I.1.2;
 G.4
 EPrint:
 22 pages, 2 figures. Substantial rewrite of content of the parts of the paper involving signaturebased Gr\"obner basis algorithms, both the exposition and the description of the core algorithm of the paper changed