ChainComplex -- the class of all chain complexes

Functions and methods returning a chain complex :

• "Ring ^ BettiTally" -- see BettiTally -- the class of all Betti tallies
• chainComplex -- make a chain complex
• ChainComplex ** ChainComplex -- tensor product
• "ChainComplex ** Module" -- see ChainComplex ** ChainComplex -- tensor product
• "Module ** ChainComplex" -- see ChainComplex ** ChainComplex -- tensor product
• ChainComplex ** GradedModule -- tensor product
• ChainComplex ** Ring -- a binary operator, usually used for tensor product or Cartesian product
• ChainComplex ++ ChainComplex -- direct sum
• ChainComplex Array -- degree shift
• "coimage(ChainComplexMap)" -- see coimage -- coimage of a map
• "cokernel(ChainComplexMap)" -- see cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
• complete(ChainComplex) -- complete the internal parts
• cone(ChainComplexMap) -- mapping cone of a chain map
• dual(ChainComplex) -- dual
• "eagonNorthcott" -- see eagonNorthcott(Matrix) -- Eagon-Northcott complex of a matrix of linear forms
• GradedModule ** ChainComplex -- tensor product
• "Hom(ChainComplex,Module)" -- see Hom(Module,ChainComplex)
• Hom(Module,ChainComplex)
• "image(ChainComplexMap)" -- see image -- image of a map
• kernel(ChainComplexMap) -- kernel of a chain complex map
• koszul(Matrix) -- the Koszul complex
• "minimalPresentation(ChainComplex)" -- see minimalPresentation(Module) -- minimal presentation of a module
• "prune(ChainComplex)" -- see minimalPresentation(Module) -- minimal presentation of a module
• Module Array -- make a chain complex from a module
• new ChainComplex -- make a new chain complex from scratch
• new ChainComplex from Resolution (missing documentation)
• resolution(Ideal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal
• "resolution(MonomialIdeal)" -- see resolution(Ideal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal
• resolution(Module) -- compute a free resolution of a module
• "RingMap ChainComplex" -- see RingMap RingElement -- apply a ring map

Methods that use a chain complex :

• "ChainComplex == ChainComplex" -- see == -- equality
• "ChainComplex == ZZ" -- see == -- equality
• "ZZ == ChainComplex" -- see == -- equality
• "betti(ChainComplex)" -- see betti -- display or modify a Betti diagram
• ChainComplex ** ChainComplexMap -- tensor product
• ChainComplex ^ ZZ -- access member, cohomological degree
• ChainComplex _ ZZ -- component
• ChainComplex _ ZZ = Thing -- install component of chain complex
• ChainComplexMap ** ChainComplex -- tensor product
• components(ChainComplex) -- list the components of a direct sum
• "directSum(ChainComplex)" -- see directSum -- direct sum of modules or maps
• extend(ChainComplex,ChainComplex,Matrix) -- extend a module map to a chain map, if possible
• "formation(ChainComplex)" -- see formation -- recover the methods used to make a module
• "gradedModule(ChainComplex)" -- see gradedModule -- make a graded module
• HH ChainComplex -- homology of a chain complex
• HH^ZZ ChainComplex -- cohomology of a chain complex
• HH_ZZ ChainComplex -- homology of a chain complex
• "inducedMap(ChainComplex,ChainComplex)" -- see inducedMap(Module,Module) -- compute the map induced by the identity
• "isDirectSum(ChainComplex)" -- see isDirectSum -- whether something is a direct sum
• "isHomogeneous(ChainComplex)" -- see isHomogeneous -- whether something is homogeneous (graded)
• length(ChainComplex) -- length of a chain complex or graded module
• map(ChainComplex,ChainComplex,ChainComplexMap) (missing documentation)
• map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
• "ChainComplex ^ Array" -- see Module ^ Array -- projection onto summand
• "ChainComplex _ Array" -- see Module _ Array -- inclusion from summand
• poincare(ChainComplex) -- assemble degrees of a chain complex into a polynomial
• "poincareN(ChainComplex)" -- see poincareN -- assemble degrees into polynomial
• "regularity(ChainComplex)" -- see regularity -- compute the Castelnuovo-Mumford regularity
• "ring(ChainComplex)" -- see ring -- get the associated ring of an object
• "status(ChainComplex)" -- see status -- status of a resolution computation
• sum(ChainComplex) -- direct sum of the components of a chain complex
• "tensorAssociativity(ChainComplex,ChainComplex,ChainComplex)" -- see tensorAssociativity -- associativity isomorphisms for tensor products

For the programmer

The object ChainComplex is a type, with ancestor classes GradedModule < MutableHashTable < HashTable < Thing.