Some comments on the modular approach to Gröbner-bases
G.L. Ebert · ACM SIGSAM Bulletin · 1983
The problem of finding a modular algorithm for constructing Gröbner-bases is of interest to many computer algebraists. In particular, given a prime p and a set of (multivariate) polynomials with integer coefficients, it has been queried if the number of basis polynomials in a minimal normed Gröbner-basis for the polynomial ideal generated mod p has to be less than or equal to the corresponding number for the polynomial ideal generated over the rationals. In this paper we answer this question and related questions concerning the modular approach to Gröbner-bases, illustrating with several interesting examples, and we propose a criterion for determining "luckiness" of primes in the binomial case.