
HAP
 Referenced in 40 articles
[sw04870]
 homological algebra library for use with the GAP computer algebra system, and is still under ... Recent additions include some functions for computing homology of crossed modules and simplicial groups...

Homology
 Referenced in 31 articles
[sw04871]
 Computing simplicial homology based on efficient Smith normal form algorithms Geometric properties of topological spaces ... conveniently expressed by algebraic invariants of the space. This paper focuses on methods ... computer calculation of the homology of finite simplicial complexes and its applications. The calculation ... example with calculations of Lie algebra homology...

homalg
 Referenced in 30 articles
[sw00411]
 homalg: a metapackage for homological algebra. The central notion of this work is that...

Adinkras
 Referenced in 27 articles
[sw09383]
 shown connections with coding theory and Clifford algebras. Furthermore, adinkras offer many natural and accessible ... make new connections to other fields (homological algebra, poset theory, and polytopes), and solve some...

SuperLie
 Referenced in 25 articles
[sw14268]
 highest and lowest), compute Lie (super)algebra homology and cohomology; calculate the Shapovalov determinant...

OreMorphisms
 Referenced in 12 articles
[sw11235]
 OreMorphisms: a homological algebraic package for factoring and decomposing linear functional systems. The purpose...

Eirene
 Referenced in 11 articles
[sw26097]
 novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing...

PurityFiltration
 Referenced in 10 articles
[sw07656]
 means of elementary methods of homological algebra. Our approach avoids using sophisticated methods such...

conley
 Referenced in 10 articles
[sw00154]
 conley is based on our abstract homological algebra package homalg. We emphasize that the notion...

CHomP
 Referenced in 51 articles
[sw09358]
 CHomP, Computational homology project. Much of the fascination and challenge of studying nonlinear systems arises ... important that these techniques be computationally efficient. Algebraic Topology is the classical mathematical tool ... nonlinear spaces and functions, within which homology is perhaps the most computable subset. In particular ... large datasets can be reduced to compact algebraic expressions that provide insight into underlying geometric...

pAQFT
 Referenced in 7 articles
[sw11711]
 local symmetries in the framework of perturbative algebraic quantum field theory (pAQFT). Our main result ... invariance and, using the language of homological algebra, we compare different approaches to quantization...

OreAlgebraicAnalysis
 Referenced in 4 articles
[sw15153]
 viewpoint, using Dmodule theory and homological algebra techniques. The different types of systems ... finitely presented left modules over Ore algebras, (2) algorithms for deciding moduletheoretic properties, such ... projectiveness, freeness, and (3) algorithms from homological algebra, such as computation of free resolutions...

EAT
 Referenced in 17 articles
[sw09167]
 symbolic software for effective homology computation. Kenzo: EAT (= Effective Algebraic Topology), the previous program. Before ... goal was the computation of the first homology groups of some loop spaces, for which...

BIGEBRA
 Referenced in 21 articles
[sw00078]
 BIGEBRA package for Maple. Hopf algebraic structures will replace groups and group representations ... paradigm in forthcoming times. Ktheory, cohomology, entanglement, statistics, representation categories, quantized or twisted ... invariant theory, e.g., the GraßmannCayley bracket algebra, are all covered by the Hopf algebraic...

Kenzo
 Referenced in 65 articles
[sw04861]
 ideas of the second author about Effective Homology, mainly around the Serre and EilenbergMoore ... should be called the Fundamental Theorem of Algebraic Topology. The first version of the program...

RedHom
 Referenced in 12 articles
[sw08776]
 homology of sets. The library implements algorithms based on geometric and algebraic reduction methods: acyclic ... used to compute Betti numbers, torsion coefficients, homology generators, persistence intervals and maps induced...

VFC package
 Referenced in 20 articles
[sw16729]
 important role in setting up our functorial algebraic “VFC package”. We illustrate the methods ... GromovWitten invariants and Hamiltonian Floer homology over ℚ for general symplectic manifolds. Our framework...

cellularSheaves
 Referenced in 4 articles
[sw25131]
 well as cosheaves, and their (co)homologies. As motivation, we summarize some results from toric ... linking cellular sheaf cohomologies to cohomologies of algebraic varieties. We then give an overview...

RiemannSurface
 Referenced in 1 article
[sw41771]
 plane algebraic curve over a subfield of the complex numbers. A homology basis is derived...

purityfiltration.lib
 Referenced in 1 article
[sw10991]
 Purity Filtration of Modules over (Non)commutative Algebras. Purity is a notion with several meanings ... homological grade number j_A(M) of a module M over an Kalgebra...