Sparse systems and algorithmic equidimensional decomposition
Algebraic Geometry
2026-01-19 v2
Abstract
We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the algorithm computes a witness set, namely a finite set obtained by intersecting the component with a generic linear variety of complementary dimension. The complexity of the algorithm is polynomial in combinatorial invariants associated to the supports of the polynomials involved.
Cite
@article{arxiv.2505.08097,
title = {Sparse systems and algorithmic equidimensional decomposition},
author = {Maria Isabel Herrero and Gabriela Jeronimo and Juan Sabia},
journal= {arXiv preprint arXiv:2505.08097},
year = {2026}
}
Comments
23 pages