Probabilistic algorithms for geometric elimination

We develop probabilistic algorithms that solve problems of geometric elimin ation theory using small memory resources. These algorithms are obtained by means of the adaptation of a general transformation due to A. Borodin whic h converts uniform boolean circuit depth into sequential (Turing machine) s pace. The boolean circuits themselves are developed using techniques based on the computation of a primitive element of a suitable zero-dimensional al gebra and diophantine considerations. Our algorithms improve considerably the space requirements of the eliminati on algorithms based on rewriting techniques (Grobner solving), having simul taneously a time performance of the same kind of them.