Related papers: Abstract simplicial complexes in {\tt Macaulay2}
We introduce the package LatticePolytopes for Macaulay2. The package provides methods for computations related to Cayley structures, local positivity and smoothness for lattice polytopes.
On behalf of the development team, I review the capabilities of the BAGEL program package in this article. BAGEL is a newly-developed full-fledged program package for electronic-structure computation in quantum chemistry, which is released…
simpcomp is an extension to GAP, the well known system for computational discrete algebra. It allows the user to work with simplicial complexes. In the latest version, support for simplicial blowups and discrete normal surfaces was added,…
This work describes the design and implementation of an abstract machine, Amalia, for the linguistic formalism ALE, which is based on typed feature structures. This formalism is one of the most widely accepted in computational linguistics…
Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…
We present the Macaulay2 package Resultants, which provides commands for the effective computation of multivariate resultants, discriminants, and Chow forms. We provide some background for the algorithms implemented and show, with a few…
We describe the \texttt{Imeall} package for the calculation and indexing of atomistic properties of grain boundaries in materials. The package provides a structured database for the storage of atomistic structures and their associated…
This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable to extract topological information from digital pictures. A simplicial complex is encoded in a (non-unique)…
This is the Hadamard package for Macaulay2 which computes the Hadamard product of projective subvarieties.
The MultiplicitySequence package for Macaulay2 computes the multiplicity sequence of a graded ideal in a standard graded ring over a field, as well as several invariants of monomial ideals related to integral dependence. We discuss two…
This note describes a package for computing seminormalization of rings within Macaulay2.
We introduce the Macaulay2 package $\mathtt{LinearTruncations}$ for finding and studying the truncations of a multigraded module over a standard multigraded ring that have linear resolutions.
We describe the main functions of the Macaulay2 package Quasidegrees. The purpose of this package is to compute the quasidegree set of a finitely generated A-graded module presented as the cokernel of a monomial matrix. We provide examples…
In this paper we introduce a new model of random simplicial complexes depending on multiple probability parameters. This model includes the well-known Linial - Meshulam random simplicial complexes and random clique complexes as special…
We provide dual algorithms for sampling the space of abstract simplicial complexes on a fixed number of vertices. We develop a generative and descriptive sampler designed with heuristics to help balance the combinatorial multiplicities of…
The following article is an application of commutative algebra to the study of multiparameter persistent homology in topological data analysis. In particular, the theory of finite free resolutions of modules over polynomial rings is applied…
We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to compute and manipulate subagebra bases -- which are also known as…
We formalise, in Coq, the opening sections of Parity Complexes [Street1991] up to and including the all important excision of extremals algorithm. Parity complexes describe the essential combinatorial structure exhibited by simplexes, cubes…
Cellular resolutions are a technique for constructing resolutions of monomial ideals by giving a cell complex labeled by monomials, or more generally, by monomial modules. This \verb|Macaulay2| package allows us to work with cellular…
The complexity of Gr\"{o}bner computations has inspired many improvements to Buchberger's algorithm over the years. Looking for further insights into the algorithm's performance, we offer a threaded implementation of classical Buchberger's…