A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System - INRIA 2 Access content directly
Journal Articles Journal of Symbolic Computation Year : 2023

A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System

Christian Eder
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Mohab Safey El Din

Abstract

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 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.
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Dates and versions

hal-03590675 , version 1 (28-02-2022)
hal-03590675 , version 2 (22-02-2023)
hal-03590675 , version 3 (23-02-2023)
hal-03590675 , version 4 (10-03-2023)

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Christian Eder, Pierre Lairez, Rafael Mohr, Mohab Safey El Din. A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System. Journal of Symbolic Computation, 2023, 119, pp.1-21. ⟨10.1016/j.jsc.2023.02.001⟩. ⟨hal-03590675v4⟩
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