Exponential space computation of Gröbner bases Klaus Kühnle

Given a polynomial ideal and a term order, there is a unique reduced Grr obner basis and, for each polynomial, a unique normal form, namely the smallest (w.r.t. the term order) polynomial in the same coset. We consider the problem of nding this normal form for any given polynomial, without prior computation of the Grr obner basis. This is done by transforming a representation of the normal form into a system of linear equations and solving this system. Using the ability to nd normal forms, we show how to obtain the Grr obner basis in exponential space.