2024/04/21 by Anna Maria Bigatti, Bigatti, Anna Maria, Elisa Palezzato +3
Computer Science · Engineering · #Numerical Methods and Algorithms #Advanced Numerical Analysis Techniques #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2404.13514
A Comprehensive Grobner system for a parametric ideal I in K(A)[X] represents the collection of all Grobner bases of the ideals I' in K[X] obtained as the values of the parameters A vary in K. The recent algorithms for computing them comprehensive Grobner systems consider the corresponding ideal J in K[A,X], and are based on stability of Grobner bases of ideals under specializations of the parameters. Starting from a Grobner basis of J, the computation splits recursively depending on the vanishing of the evaluation of some ``coefficients'' in K[A]. In this paper, taking inspiration from the algorithm described by Nabeshima, we create a new iterative algorithm to compute comprehensive Grobner systems. We show how we keep track of the sub-cases to be considered, and how we avoid some redundant computation branches using ``comparatively-cheap'' ideal-membership tests, instead of radical-membership tests.