GradedModule -- the class of all graded modules

Types of graded module:

• ChainComplex -- the class of all chain complexes

Functions and methods returning a graded module:

• ambient(GradedModule) (missing documentation)
• GradedModule ++ GradedModule -- see ChainComplex ++ ChainComplex -- direct sum
• coimage(GradedModuleMap) (missing documentation)
• cokernel(GradedModuleMap) (missing documentation)
• cover(GradedModule) (missing documentation)
• directSum(GradedModule) (missing documentation)
• GradedModule ** GradedModule -- a binary operator, usually used for tensor product or Cartesian product
• GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product
• Module ** GradedModule -- see GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product
• GradedModule ++ Module (missing documentation)
• GradedModule Array -- degree shift
• gradedModule(ChainComplex) -- see gradedModule(List) -- make a graded module
• gradedModule(List) -- make a graded module
• gradedModule(Module) -- see gradedModule(List) -- make a graded module
• gradedModule(Sequence) -- see gradedModule(List) -- make a graded module
• HH ChainComplex -- homology of a chain complex
• image(GradedModuleMap) (missing documentation)
• kernel(GradedModuleMap) -- see kernel(ChainComplexMap) -- kernel of a chain complex map
• minimalPresentation(GradedModule) (missing documentation)
• Module ++ GradedModule (missing documentation)
• prune(GradedModule) (missing documentation)
• source(GradedModuleMap) -- find the source of a map of graded modules
• super(GradedModule) (missing documentation)
• target(GradedModuleMap) -- find the target of a map of graded modules

Methods that use a graded module:

• betti(GradedModule) -- Betti diagram showing the of degrees in a graded module or chain complex
• ChainComplex ** GradedModule -- tensor product
• GradedModule _ ZZ -- see ChainComplex _ ZZ -- component
• chainComplex(GradedModule) -- make a chain complex from a graded module
• complete(GradedModule)
• components(GradedModule) (missing documentation)
• formation(GradedModule) (missing documentation)
• GradedModule ** ChainComplex -- tensor product
• GradedModule == GradedModule (missing documentation)
• isDirectSum(GradedModule) (missing documentation)
• length(GradedModule) -- length of a graded module
• map(GradedModule,GradedModule,Function) -- see map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
• mathML(GradedModule) (missing documentation)
• max(GradedModule) -- get the maximum element in a list or sequence
• min(GradedModule) -- get the minimum element in a list or sequence
• net(GradedModule) (missing documentation)
• rank(GradedModule) (missing documentation)
• ring(GradedModule) (missing documentation)
• tensorAssociativity(GradedModule,GradedModule,GradedModule) (missing documentation)
• texMath(GradedModule) (missing documentation)

For the programmer

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

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/OldChainComplexes/docs/doc9.m2:45:0.