Modular Algorithms for Computing Groebner Bases

Beth Arnold
Texas A&M University, College Station, Texas, USA

Intermediate coefficients swell is a well known difficulty associated with
Buchberger's algorithms for computing Groebner bases.  Modular algorithms limit
this growth.  I will present two algorithms, one which uses the Chinese
remainder theorem, and another which uses Hensel lifting techniques.  These
algorithms extend the modular algorithms for computing the greatest common
divisor of polynomials in one variable.  In particular, the concept of "lucky
primes" for modular Groebner basis computations and a method for checking the
result for correctness will be discussed and illustrated with examples.