ChainComplex -- the class of all chain complexes

Functions and methods returning a chain complex:

• 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
• ChainComplex ++ ChainComplex -- direct sum
• ChainComplex Array -- degree shift
• coimage(ChainComplexMap) (missing documentation)
• cokernel(ChainComplexMap) (missing documentation)
• complete(ChainComplex) -- complete the internal parts
• cone(ChainComplexMap)
• dual(ChainComplex) -- dual
• GradedModule ** ChainComplex -- tensor product
• Hom(ChainComplex,Module) -- see Hom(Module,ChainComplex) -- the Hom functor
• Hom(Module,ChainComplex) -- the Hom functor
• image(ChainComplexMap) (missing documentation)
• kernel(ChainComplexMap) -- kernel of a chain complex map
• koszul(Matrix) -- the Koszul complex
• minimalPresentation(ChainComplex) (missing documentation)
• Module Array -- make a chain complex from a module
• new ChainComplex -- make a new chain complex from scratch
• new ChainComplex from Resolution (missing documentation)
• prune(ChainComplex) (missing documentation)
• resolution(Ideal) -- compute a projective resolution of (the quotient ring corresponding to) an ideal
• resolution(Module) -- compute a free resolution of a module
• Ring ^ BettiTally -- construct a chain complex with prescribed Betti table
• RingMap ChainComplex (missing documentation)

Methods that use a chain complex:

• betti(ChainComplex) -- see betti(GradedModule) -- Betti diagram showing the of degrees in a graded module or chain complex
• ChainComplex ** ChainComplexMap -- tensor product
• ChainComplex == ChainComplex (missing documentation)
• ChainComplex == ZZ (missing documentation)
• ChainComplex ^ Array -- projection onto summand
• ChainComplex ^ ZZ -- access member, cohomological degree
• ChainComplex _ Array -- inclusion from summand
• ChainComplex _ ZZ -- component
• ChainComplex _ ZZ = Thing -- install component of chain complex
• ChainComplexMap ** ChainComplex -- tensor product
• components(ChainComplex)
• directSum(ChainComplex) (missing documentation)
• extend(ChainComplex,ChainComplex,Matrix)
• formation(ChainComplex) (missing documentation)
• gradedModule(ChainComplex) -- see gradedModule(List) -- 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) (missing documentation)
• isDirectSum(ChainComplex) (missing documentation)
• isHomogeneous(ChainComplex) (missing documentation)
• 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
• mathML(ChainComplex) (missing documentation)
• net(ChainComplex) (missing documentation)
• poincare(ChainComplex) -- assemble degrees of a chain complex into a polynomial
• poincareN(ChainComplex) -- assemble degrees into polynomial
• regularity(ChainComplex) -- compute the Castelnuovo-Mumford regularity
• ring(ChainComplex) (missing documentation)
• status(ChainComplex) -- status of a resolution computation
• sum(ChainComplex) -- direct sum of the components of a chain complex
• tensorAssociativity(ChainComplex,ChainComplex,ChainComplex) (missing documentation)
• texMath(ChainComplex) (missing documentation)
• ZZ == ChainComplex (missing documentation)

For the programmer

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

The source of this document is in OldChainComplexes/docs/doc9.m2:152:0.