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Chain complexes and homology¶

Sage includes some tools for algebraic topology, and in particular computing homology groups.

  • Chain complexes
    • ChainComplex()
    • ChainComplex_class
    • Chain_class
  • Chains and cochains
    • CellComplexReference
    • Chains
    • Cochains
  • Morphisms of chain complexes
    • ChainComplexMorphism
    • is_ChainComplexMorphism()
  • Chain homotopies and chain contractions
    • ChainContraction
    • ChainHomotopy
  • Homspaces between chain complexes
    • ChainComplexHomspace
    • is_ChainComplexHomspace()
  • Koszul Complexes
    • KoszulComplex
  • Hochschild Complexes
    • HochschildComplex
  • Homology Groups
    • HomologyGroup()
    • HomologyGroup_class
  • Homology and cohomology with a basis
    • CohomologyRing
    • HomologyVectorSpaceWithBasis
    • sum_indices()
  • Algebraic topological model for a cell complex
    • algebraic_topological_model()
    • algebraic_topological_model_delta_complex()
  • Induced morphisms on homology
    • InducedHomologyMorphism
  • Utility Functions for Matrices
    • dhsw_snf()
  • Interface to CHomP
    • CHomP
    • have_chomp()
    • homchain()
    • homcubes()
    • homsimpl()
    • process_generators_chain()
    • process_generators_cubical()
    • process_generators_simplicial()

Indices and Tables¶

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