2013/09/16 by Bernard Parisse, Parisse, Bernard · 1 citation
Computer Science · #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #Numerical Methods and Algorithms #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC
paper · pdf · doi:10.48550/arxiv.1309.4044
openalex publication_date 2013/09/16 · arxiv created 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modular algorithm are widely used in computer algebra systems (CAS), for example to compute efficiently the gcd of multivariate polynomials. It is known to work to compute Groebner basis over \Q, but it does not seem to be popular among CAS implementers. In this paper, I will show how to check a candidate Groebner basis (obtained by reconstruction of several Groebner basis modulo distinct prime numbers) with a given error probability, that may be 0 if a certified Groebner basis is desired. This algorithm is now the default algorithm used by the Giac/Xcas computer algebra system with competitive timings, thanks to a trick that can accelerate computing Groebner basis modulo a prime once the computation has been done modulo another prime.