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ChainComplexMap -- the class of all maps between chain complexes

The type ChainComplexMap is a member of the class Type. Each object of class ChainComplexMap is called a chain complex map. Each chain complex map is also a member of class MutableHashTable.

More general types (whose methods may also apply) :

  • MutableHashTable -- the class of all mutable hash tables
  • HashTable -- the class of all hash tables

    • The usual algebraic operations are available: addition, subtraction, scalar multiplication, and composition. The identity map from a chain complex to itself can be produced with id. An attempt to add (subtract, or compare) a ring element to a chain complex will result in the ring element being multiplied by the appropriate identity map.

    Functions and methods returning a a chain complex map :

  • - ChainComplexMap
  • ChainComplex ** ChainComplexMap -- tensor product
  • ChainComplex ^ Array
  • ChainComplex _ Array
  • chainComplex Matrix -- make a small chain complex
  • ChainComplexMap * ChainComplexMap
  • ChainComplexMap ** ChainComplex -- tensor product
  • ChainComplexMap ** ChainComplexMap -- tensor product
  • ChainComplexMap ** Module
  • ChainComplexMap + ChainComplexMap
  • ChainComplexMap ++ ChainComplexMap
  • ChainComplexMap - ChainComplexMap
  • ChainComplexMap ^ Array
  • ChainComplexMap ^ ZZ
  • ChainComplexMap _ Array
  • dual ChainComplexMap -- dual of a chain complex
  • extend(ChainComplex,ChainComplex,Matrix)
  • Hom(ChainComplexMap,Module)
  • Hom(Module,ChainComplexMap)
  • map(ChainComplex,ChainComplex)
  • map(ChainComplex,ChainComplex,ChainComplexMap)
  • map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
  • Module ** ChainComplexMap
  • nullhomotopy ChainComplexMap
  • prune ChainComplexMap
  • resolution Matrix -- make a projective resolution
  • tensorAssociativity(ChainComplex,ChainComplex,ChainComplex)
  • transpose ChainComplexMap

    • Methods for using a chain complex map :

  • ChainComplexMap + RingElement
  • ChainComplexMap + ZZ
  • ChainComplexMap - RingElement
  • ChainComplexMap == ChainComplexMap
  • ChainComplexMap == RingElement
  • ChainComplexMap == ZZ
  • ChainComplexMap _ ZZ -- get component
  • coimage ChainComplexMap
  • cokernel ChainComplexMap
  • complete ChainComplexMap
  • components ChainComplexMap
  • cone ChainComplexMap
  • degree ChainComplexMap
  • HH ChainComplexMap
  • HH^ZZ ChainComplexMap -- cohomology of a chain complex map
  • HH_ZZ ChainComplexMap -- homology of a chain complex map
  • homology(Nothing,ChainComplexMap)
  • image ChainComplexMap
  • isHomogeneous ChainComplexMap
  • kernel ChainComplexMap
  • net ChainComplexMap
  • ring ChainComplexMap
  • RingElement * ChainComplexMap
  • RingElement + ChainComplexMap
  • RingElement - ChainComplexMap
  • RingElement == ChainComplexMap
  • sum ChainComplexMap -- direct sum of the components of a chain map
  • ZZ * ChainComplexMap
  • ZZ + ChainComplexMap
  • ZZ == ChainComplexMap

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