Computational methods for t-spread monomial ideals

Abstract

Let $K$ be a field and $S=K[x_1,\ldots,x_n]$ a standard polynomial ring over $K$. In this paper, some new optimized algorithms to compute the smallest $t$-spread lexicographic set and the smallest $t$-spread strongly stable set containing a given set of $t$-spread monomials of $S$ are presented. Some technical tools allowing to compute the cardinality of $t$-spread strongly stable sets avoiding their construction are given. Then, a \emph{Macaulay2} package, \texttt{TSpreadIdeals}, providing methods to easily manage $t$-spread monomials and $t$-spread ideals is implemented. Some functions to ease the calculation of well known results about algebraic invariants for $t$-spread ideals are also provided.