A p-adic approach to the computation of Gröbner bases. (English) Zbl 0669.13009

To deal with the problem of coefficient growth in the computation of Gröbner bases of polynomial ideals over the rational number field \({\mathbb{Q}}\) the paper presents a lifting algorithm that computes a p-adic approximation to the normalized reduced Gröbner basis for the ideal generated by a finite set of polynomials F in \({\mathbb{Q}}[x_ 1,...,x_ v]\). For the lucky prime p for F (it is shown that almost all primes are lucky) a normalized reduced Gröbner basis for F modulo p is computed and then lifted to the desired result.
Reviewer: E.Ederle


13F20 Polynomial rings and ideals; rings of integer-valued polynomials
68W30 Symbolic computation and algebraic computation
13-04 Software, source code, etc. for problems pertaining to commutative algebra


Algorithm 628
Full Text: DOI


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