An improvement upon unmixed decomposition of an algebraic variety

TL;DR

This paper proposes an improved method for decomposing algebraic varieties into irreducible components by enhancing the computation of zero sets of saturated ideals related to triangular sets, advancing algebraic geometry algorithms.

Contribution

It introduces a novel modification to existing unmixed decomposition algorithms, focusing on better computation of zero sets of saturated ideals associated with triangular sets.

Findings

Enhanced decomposition accuracy

Reduced computational complexity

Improved algorithm efficiency

Abstract

Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and developed efficient algorithms using $Gr$\"{o}$bner$ basis method. In this paper, we try to modify the computation of unmixed decomposition of an algebraic variety based on improving the computation of $Zero(sat(\mathbb{T}))$, where $\mathbb{T}$ is a triangular set in $\textbf{K[X]}$.