On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Canonical representatives for residue classes of a polynomial ideal
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
A theoretical basis for the reduction of polynomials to canonical forms
ACM SIGSAM Bulletin
Some properties of Gröbner-bases for polynomial ideals
ACM SIGSAM Bulletin
Some examples for solving systems of algebraic equations by calculating groebner bases
Journal of Symbolic Computation
A p-adic approach to the computation ofGröbner bases
Journal of Symbolic Computation
Modular algorithms for computing Gröbner bases
Journal of Symbolic Computation
Parallelization of Modular Algorithms
Journal of Symbolic Computation
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
| Hi-index | 0.00 |
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.