The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

Given an ideal I in a polynomial ring K [x 1,…, xn] over a field K, we present a complete
algorithm to compute the binomial part of I, ie, the subideal Bin (I) of I generated by all …

Primary decomposition of commutative monoid congruences is insensitive to certain
features of primary decomposition in commutative rings. These features are captured by the …

Abstract The Macaulay2 package Binomials contains implementations of specialized
algorithms for binomial ideals, including primary decomposition into binomial ideals. The …

We present Binomials, a package for the computer algebra system Macaulay 2, which
specializes well-known algorithms to binomial ideals. These come up frequently in algebraic …

An explicit lattice point realization is provided for the primary components of an arbitrary
binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free …

We study the eigenscheme of a matrix which encodes information about the eigenvectors
and generalized eigenvectors of a square matrix. The two main results in this paper are a …

Motivated by applications to the theory of error-correcting codes, we give an algorithmic
method for computing a generating set for the ideal generated by $\beta $-graded …

We extend the notion of standard pairs to the context of monomial ideals in semigroup rings.
Standard pairs can be used as a data structure to encode such monomial ideals, providing …

THE JOIN-MEET IDEAL OF A FINITE LATTICE 1. Introduction. Let L be a finite lattice and K[L]
the polynomial ring over a field K w Page 1 JOURNAL OF COMMUTATIVE ALGEBRA Volume …