Work

p-adic algorithm for bivariate Gröbner bases

Year: 2023

Type: conference-paper

Abstract: We present a p-adic algorithm to recover the lexicographic Gröbner basis of an ideal in with a generating set in , with a complexity that is less than cubic in terms of the dimension of and softly linear in the height of its coefficients. We observe that previous results of Lazard’s that use Hermite normal forms to compute Gröbner bases for ideals with two generators can be generalized to a set of generators. We use this result to obtain a bound on the height of the coefficients of , and to control the probability of choosing a good prime p to build the p-adic expansion of .

Source: International Symposium on Symbolic and Algebraic Computation

DOI: 10.1145/3597066.3597086

Authors: Éric Schost, Catherine St-Pierre

Institutions: University of Waterloo, Université Paris-Saclay, Centre Inria de Saclay, MATHEXP: Calcul formel, mathématiques expérimentales et interactions

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze