Related papers: simpcomp -- A GAP toolbox for simplicial complexes
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds,…
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial…
The immediate snapshot complexes were introduced as combinatorial models for the protocol complexes in the context of theoretical distributed computing. In the previous work we have developed a formal language of witness structures in order…
We develop a package using the computer algebra system GAP for computing the decomposition of a representation $\rho$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser…
In this work we study the framework of mathematical morphology on simplicial complex spaces. Simplicial complexes are widely used to represent multidimensional data, such as meshes, that are two dimensional complexes, or graphs, that can be…
Modern large scale cosmological hydrodynamic simulations require robust tools capable of analysing their data outputs in a parallel and efficient manner. We introduce SOAP (Spherical Overdensity and Aperture Processor), a Python package…
We define two different simplicial complexes, the common divisor simplicial complex and the prime divisor simplicial complex, from a set of integers, and explore their similarities. We will define a map between the two simplicial complexes,…
The Simplex algorithm for solving linear programs-one of Computing in Science & Engineering's top 10 most influential algorithms of the 20th century-is an important topic in many algorithms courses. While the Simplex algorithm relies on…
Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant…
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…
In this paper we study the classifying spaces of graph products of simplicial groups and connected Hopf algebras over a field, and show that they can be uniformly treated under the framework of polyhedral products. It turns out that these…
Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes…
Suppose $X$ is a 1-connected simplicial set with finitely many nondegenerate simplices. We give an effective algorithm to calculate a simplicial set with the $n$-type of the loop space $\Omega X$. Iterating gives an algorithm to calculate…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
This is a collection of examples showing how the GAP system can be used to compute information about the generating graphs of finite groups. It includes all examples that were needed for the computational results in the paper "Hamiltonian…
SymJAX is a symbolic programming version of JAX simplifying graph input/output/updates and providing additional functionalities for general machine learning and deep learning applications. From an user perspective SymJAX provides a la…
CompHEP is a package for automatic calculations of elementary particle decay and collision properties in the lowest order of perturbation theory (the tree approximation). The main idea prescribed into the CompHEP is to make available…
Algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple Lie algebra, up to linear equivalence. The algorithms have been used to obtain classifications of the semisimple…
We present a library autgradalg.lib for the free computer algebra system Singular to compute automorphisms of integral, finitely generated $\mathbb{C}$-algebras that are graded pointedly by a finitely generated abelian group. It implements…