• HAP

  • Referenced in 37 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 28 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 26 articles [sw00411]
  • homalg: a meta-package for homological algebra. The central notion of this work is that...
  • SuperLie

  • Referenced in 20 articles [sw14268]
  • highest and lowest), compute Lie (super)algebra homology and cohomology; calculate the Shapovalov determinant...
  • 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...
  • Adinkras

  • Referenced in 9 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...
  • OreMorphisms

  • Referenced in 9 articles [sw11235]
  • OreMorphisms: a homological algebraic package for factoring and decomposing linear functional systems. The purpose...
  • CHomP

  • Referenced in 43 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...
  • Eirene

  • Referenced in 6 articles [sw26097]
  • novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing...
  • Kenzo

  • Referenced in 60 articles [sw04861]
  • ideas of the second author about Effective Homology, mainly around the Serre and Eilenberg-Moore ... should be called the Fundamental Theorem of Algebraic Topology. The first version of the program...
  • OreAlgebraicAnalysis

  • Referenced in 1 article [sw15153]
  • viewpoint, using D-module theory and homological algebra techniques. The different types of systems ... finitely presented left modules over Ore algebras, (2) algorithms for deciding module-theoretic properties, such ... projectiveness, freeness, and (3) algorithms from homological algebra, such as computation of free resolutions...
  • BIGEBRA

  • Referenced in 17 articles [sw00078]
  • BIGEBRA package for Maple. Hopf algebraic structures will replace groups and group representations ... paradigm in forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted ... invariant theory, e.g., the Graßmann-Cayley bracket algebra, are all covered by the Hopf algebraic...
  • 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 13 articles [sw16729]
  • important role in setting up our functorial algebraic “VFC package”. We illustrate the methods ... Gromov-Witten invariants and Hamiltonian Floer homology over ℚ for general symplectic manifolds. Our framework...
  • cellularSheaves

  • Referenced in 3 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...
  • 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 K-algebra...
  • AXIOM

  • Referenced in 169 articles [sw00063]
  • Axiom is a general purpose Computer Algebra system...
  • cdd

  • Referenced in 109 articles [sw00114]
  • The program cdd+ (cdd, respectively) is a C...