A Syzygial Method for Equidimensional Decomposition

TL;DR

This paper introduces a new algorithm for equidimensional decomposition of algebraic sets that leverages syzygy computations and Gr"obner bases, improving efficiency over previous methods.

Contribution

The authors present a novel syzygy-based algorithm that avoids elimination and homological algebra, streamlining equidimensional decomposition.

Findings

Algorithm outperforms existing methods in experiments

Avoids complex algebraic processes like elimination

Demonstrates practical efficiency improvements

Abstract

Based on a theorem by Vasconcelos, we give an algorithm for equidimensional decomposition of algebraic sets using syzygy computations via Gr\"obner bases. This algorithm avoids the use of elimination, homological algebra and processing the input equations one-by-one present in previous algorithms. We experimentally demonstrate the practical interest of our algorithm compared to the state of the art.