Related papers: Software for multiplier ideals
Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic…
In this paper we study the normality of monomial ideals using linear programming and graph theory. We give normality criteria for monomial ideals, for ideals generated by monomials of degree two, and for edge ideals of graphs and clutters…
Symbolic powers are a classical commutative algebra topic that relates to primary decomposition, consisting, in some circumstances, of the functions that vanish up to a certain order on a given variety. However, these are notoriously…
We introduce the package LatticePolytopes for Macaulay2. The package provides methods for computations related to Cayley structures, local positivity and smoothness for lattice polytopes.
We describe an algorithm for computing Macaulay dual spaces for multi-graded ideals. For homogeneous ideals, the natural grading is inherited by the Macaulay dual space which has been leveraged to develop algorithms to compute the Macaulay…
We shortly describe the algorithms behind some of the functions provided by the Macaulay2 package MultiprojectiveVarieties, a package for multi-projective varieties and rational maps between them.
This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.
The Package Miura contains functions that compute divisor class group arithmetic for nonsingular curves. The package reduces computation in a divisor class group to that in the ideal class group via the isomorphism. The underlying quotient…
We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical…
The Macaulay2 package Cremona performs some computations on rational and birational maps between irreducible projective varieties. For instance, it provides methods to compute degrees and projective degrees of rational maps without any…
With a particular focus on explicit computations and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals of this thesis are the following: Analyze the Koszul homology of monomial ideals and apply it to…
This note describes a package for computing seminormalization of rings within Macaulay2.
This article highlights the ToricHigherDirectImages package in Macaulay2. The central feature is a method for computing (higher) direct images of line bundles under surjective toric morphisms.
We describe the Macaulay2 package "A1BrouwerDegrees" for computing local and global $\mathbb{A}^1$-Brouwer degrees and studying symmetric bilinear forms over the complex numbers, the real numbers, the rational numbers, and finite fields of…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
In this note we calculate the multiplier ideal associated to an arbitrary monomial ideal in C^n. We discuss applications to the calculation of log canonical thresholds.
We describe a Macaulay2 package for computing Schur complexes. This package expands on the ChainComplexOperations package by David Eisenbud.
We introduce the Brackets package for the computer algebra system Macaulay2, which provides convenient syntax for computations involving the classical invariants of the special linear group. We describe our implementation of bracket rings…
We present two novel applications of symmetries for mixed-integer linear programming. First we propose two variants of a new heuristic to improve the objective value of a feasible solution using symmetries. These heuristics can use either…
We introduce the MatrixSchubert package for the computer algebra system Macaulay2. This package has tools to construct and study matrix Schubert varieties and alternating sign matrix (ASM) varieties. The package also introduces tools for…