Year: 2022
Type: preprint
Abstract: To decompose the parameter space of a parametric system of polynomial equations with respect to the number of real solutions that the system attains, first the discriminant variety of the system should be computed. This is an elimination type problem because the discriminant variety is the union of the projections into the parameter space of the intersection of the variety of the original system with one or several new hypersurfaces. Despite the popularity of Gröbner Bases (GBs) for this task, in this work we focus on a lesser used alternative tool, namely resultants. We develop new approaches to build the discriminant variety using different resultant methods such as Dixon resultant and iterated univariate resultants. We discuss how the minimal discriminant variety, the discriminant varieties computed by our methods, and the known border polynomials are related. We demonstrate with numerous examples from population dynamics and chemical reaction network theory that our new approach successfully handles larger size examples than a GB can.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G3744967713
OpenAlex ID: W4221160796