相关论文: Inverse-syst.lib, Singular library for computing M…
Since its original publication in 1916 under the title "The Algebraic Theory of Modular Systems", the book by F. S. Macaulay has attracted a lot of scientists with a view towards pure mathematics (D. Eisenbud,...) or applications to control…
The purpose of this paper is to characterize one-dimensional local domains, or more in general reduced, in terms of its Macaulay's inverse system. This leads to study almost finitely generated modules in the divided power ring. We…
Generalizing a result of Masuti and the second author, we describe inverse limits of Macaulay's inverse systems for Cohen-Macaulay factor algebras of formal power series or polynomial rings over an infinite field. On the way we find a…
Macaulay's Inverse System gives an effective method to construct Artinian Gorenstein k-algebras. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. In this paper we extend Macaulay's…
Macaulay's inverse system is an effective method to construct Artinian K-algebras with additional properties like, Gorenstein, level, more generally with any socle type. Recently, Elias and Rossi gave the structure of the inverse system of…
We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schemes.
This is a user guide for the first version of our developed Maple library, named Singularity. The first version here is designed for the qualitative study of local real zeros of scalar smooth maps. This library will be extended for symbolic…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…
The Macaulay2 package DecomposableSparseSystems implements methods for studying and numerically solving decomposable sparse polynomial systems. We describe the structure of decomposable sparse systems and explain how the methods in this…
Generalizing the concept of the Macaulay inverse system, we introduce a way to describe localizations of an ideal in a polynomial ring. This leads to an approach to the differential primary decomposition as a description of the affine…
We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of finite groups, the updated package adds functionality for…
In the last chapter of his book "The Algebraic Theory of Modular Systems " published in 1916, F. S. Macaulay developped specific techniques for dealing with " unmixed polynomial ideals " by introducing what he called " inverse systems ".…
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.
One-sided communication is a useful paradigm for irregular parallel applications, but most one-sided programming environments, including MPI's one-sided interface and PGAS programming languages, lack application level libraries to support…
During the last months or so we had the opportunity to read two papers trying to relate the study of Macaulay (1916) inverse systems with the so-called Riquier (1910)-Janet (1920) initial conditions for the integration of linear analytic…
GlobalBioIm is an open-source MATLAB library for solving inverse problems. The library capitalizes on the strong commonalities between forward models to standardize the resolution of a wide range of imaging inverse problems. Endowed with an…
In this paper, a library-based synthesis methodology for reversible circuits is proposed where a reversible specification is considered as a permutation comprising a set of cycles. To this end, a pre-synthesis optimization step is…
{\tt AbstractSimplicialComplexes.m2} is a computer algebra package written for the computer algebra system {\tt Macaulay2} \cite{M2}. It provides new infrastructure to work with abstract simplicial complexes and related homological…
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…
Inverse problem for Dirac systems with locally square summable potentials and rectangular Weyl functions is solved. For that purpose we use a new result on the linear similarity between operators from a subclass of triangular integral…