Related papers: The Slice Algorithm For Irreducible Decomposition …

Let $S=K[x_1,\ldots,x_n]$ be the ring of polynomials in $n$ variables over an arbitrary field $K$. Given a finitely generated multigraded module $M$, its Stanley length, denoted by $\operatorname{slength}(M)$, is the minimal length of a…

In this paper we study the problem of computing a Kolchin characteristic set of a radical differential ideal. The central part of the article is the presentation of algorithms solving this problem in two principal cases: for ordinary…

This is an expository version of our paper [arXiv:1902.07384]. Our aim is to present recent Macaulay2 algorithms for computation of mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over…

We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…

We study Stanley decompositions and show that Stanley's conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals…

The aims of this work are to study Rees algebras of filtrations of monomial ideals associated to covering polyhedra of rational matrices with non-negative entries and non-zero columns using combinatorial optimization and integer…

A polynomial is a direct sum if it can be written as a sum of two non-zero polynomials in some distinct sets of variables, up to a linear change of variables. We analyze criteria for a homogeneous polynomial to be decomposable as a direct…

We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.

This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the…

A simple formula computing the multiplier ideal of a monomial ideal on an arbitrary affine toric variety is given. Variants for the multiplier module and test ideals are also treated.

Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…

Using the Newton polytope and polyhedron, we study analytic spread and ideal reductions of monomial ideals. We determine a bound for analytic spread based on halfspaces and hyperplanes of the Newton polytope, and we classify basic monomial…

Let $k$ be a field with characteristic zero, $R$ be the ring $k[x_1, \cdots, x_n]$ and $I$ be a monomial ideal of $R$. We study the Artinian local algebra $R/I$ when considered as an $R$-module $M$. We show that the largest reduced…

We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…

Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…

It is well known that for a first order system of linear difference equations with rational function coefficients, a solution that is holomorphic in some left half plane can be analytically continued to a meromorphic solution in the whole…

In this paper, we propose a MCMC algorithm based on elliptical slice sampling with the purpose to improve sampling efficiency. During sampling, a mixture distribution is fitted periodically to previous samples. The components of the mixture…

An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case…

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…