ChainComplex -- the class of all chain complexes

Functions and methods returning a chain complex :

• ChainComplex ** Module, see ** -- a binary operator, usually used for tensor product or Cartesian product
• ChainComplex ** Ring, see ** -- a binary operator, usually used for tensor product or Cartesian product
• Module ** ChainComplex, see ** -- a binary operator, usually used for tensor product or Cartesian product
• chainComplex -- make a chain complex
• ChainComplex ** ChainComplex -- tensor product
• ChainComplex ** GradedModule -- tensor product
• ChainComplex ++ ChainComplex -- direct sum
• ChainComplex Array -- degree shift
• chainComplex(GradedModule) -- make a chain complex from a graded module
• 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
• minimalPresentation(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
• 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 projective resolution of a module
• RingMap ChainComplex, see RingMap RingElement -- apply a ring map

Methods that use a chain complex :

• ChainComplex == ChainComplex, see == -- equality
• betti(ChainComplex) -- display of degrees in a chain complex
• ChainComplex ** ChainComplexMap -- tensor product
• ChainComplex ^ ZZ -- access member, cohomological degree
• ChainComplex _ ZZ -- component
• ChainComplex _ ZZ = Thing -- missing documentation
• 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
• 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)
• map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
• max(ChainComplex) -- maximum index in a chain complex
• min(ChainComplex) -- minimum index in a chain complex
• ChainComplex ^ Array, see Module ^ Array -- projection onto summand
• ChainComplex _ Array, see Module _ Array -- get inclusion map into direct sum
• 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.