An improvement upon unmixed decomposition of an algebraic variety

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 $\textbf{K[X]}$.