Probabilistic Algorithms for Geometric Elimination

Abstract.

We develop probabilistic algorithms that solve problems of geometric elimination theory using small memory resources. These algorithms are obtained by means of the adaptation of a general transformation due to A. Borodin which converts uniform boolean circuit depth into sequential (Turing machine) space. The boolean circuits themselves are developed using techniques based on the computation of a primitive element of a suitable zero-dimensional algebra and diophantine considerations.

Our algorithms improve considerably the space requirements of the elimination algorithms based on rewriting techniques (Gröbner solving), having simultaneously a time performance of the same kind of them.