Details:
Title  Modular algorithms for computing Gröbner bases  Author(s)  Elizabeth A. Arnold  Type  Article in Journal  Abstract  Intermediate coefficient swell is a wellknown difficulty with Buchberger‘s algorithm for computing Gröbner bases over the rational numbers. pAdic and modular methods have been successful in limiting intermediate coefficient growth in other computations, and in particular in the Euclidian algorithm for computing the greatest common divisor (GCD) of polynomials in one variable. In this paper we present two modular algorithms for computing a Gröbner basis for an ideal in Q[x1, ... ,xy] which extend the modular GCD algorithms. These algorithms improve upon previously proposed modular techniques for computing Gröbner bases in that we test primes before lifting, and also provide an algorithm for checking the result for correctness. A complete characterization of unlucky primes is also given. Finally, we give some preliminary timings which indicate that these modular algorithms can provide considerable time improvements in examples where intermediate coefficient growth is a problem.  Length  17  ISSN  07477171 
File 
 Language  English  Journal  Journal of Symbolic Computation  Volume  35  Number  4  Pages  403419  Publisher  Academic Press, Inc.  Address  Duluth, MN, USA  Year  2003  Month  April  Edition  0  Translation 
No  Refereed 
No  Organization 
Texas A&M University 
