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arXiv · 2505.08097

Sparse systems and algorithmic equidimensional decomposition

Maria Isabel Herrero·Gabriela Jeronimo·Juan Sabia
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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.

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Maria Isabel Herrero, Gabriela Jeronimo, Juan Sabia. 2025-05-12. Sparse systems and algorithmic equidimensional decomposition. https://arxiv.org/abs/2505.08097

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