Elimination for generic sparse polynomial systems

TL;DR

This paper introduces a probabilistic symbolic algorithm for computing the Zariski closure of projections of varieties defined by generic sparse polynomial systems, with complexity depending polynomially on combinatorial invariants.

Contribution

A novel probabilistic algorithm that efficiently computes projections of varieties defined by sparse polynomial systems, with complexity tied to support invariants.

Findings

Algorithm successfully computes Zariski closures for generic sparse systems.

Complexity is polynomial in combinatorial support invariants.

Applicable to varieties in affine spaces with fixed supports.

Abstract

We present a new probabilistic symbolic algorithm that, given a variety defined in an n-dimensional affine space by a generic sparse system with fixed supports, computes the Zariski closure of its projection to an l-dimensional coordinate affine space with l < n. The complexity of the algorithm depends polynomially on combinatorial invariants associated to the supports.