GradedModule -- the class of all graded modules
Description
A new graded module can be made with 'M = new GradedModule'. The i-th module can be installed with a statement like M#i=N, and can be retrieved with an expression like M_i. The ground ring should be installed with a statement like M.ring = R.
Types of graded module :
Functions and methods returning a graded module :
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ambient(GradedModule) (missing documentation)
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GradedModule ++ GradedModule, see ChainComplex ++ ChainComplex -- direct sum
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coimage(GradedModuleMap), see coimage -- coimage of a map
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cokernel(GradedModuleMap), see cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
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cover(GradedModule), see cover(Module) -- get the covering free module
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directSum(GradedModule), see directSum -- direct sum of modules or maps
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gradedModule(ChainComplex), see gradedModule -- make a graded module
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gradedModule(List), see gradedModule -- make a graded module
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gradedModule(Module), see gradedModule -- make a graded module
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gradedModule(Sequence), see gradedModule -- make a graded module
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GradedModule ** GradedModule -- a binary operator, usually used for tensor product or Cartesian product
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GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product
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Module ** GradedModule, see GradedModule ** Module -- a binary operator, usually used for tensor product or Cartesian product
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GradedModule Array -- degree shift
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HH ChainComplex -- homology of a chain complex
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Hom(GradedModule,GradedModule) (missing documentation)
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image(GradedModuleMap), see image -- image of a map
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kernel(GradedModuleMap), see kernel(ChainComplexMap) -- kernel of a chain complex map
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minimalPresentation(GradedModule), see minimalPresentation(Module) -- minimal presentation of a module
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prune(GradedModule), see minimalPresentation(Module) -- minimal presentation of a module
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GradedModule ++ Module, see Module ++ Module -- direct sum of modules
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Module ++ GradedModule, see Module ++ Module -- direct sum of modules
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source(GradedModuleMap) -- find the source of a map of graded modules
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super(GradedModule), see super -- get the ambient module
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target(GradedModuleMap) -- find the target of a map of graded modules
Methods that use a graded module :
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GradedModule == GradedModule, see == -- equality
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betti(GradedModule) -- display of degrees in a graded module
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ChainComplex ** GradedModule -- tensor product
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GradedModule _ ZZ, see ChainComplex _ ZZ -- component
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chainComplex(GradedModule) -- make a chain complex from a graded module
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complete(GradedModule), see complete
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components(GradedModule), see components -- list the components of a direct sum
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GradedModule ** ChainComplex -- tensor product
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heft(GradedModule), see heft -- heft vector of ring, module, graded module, or resolution
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isDirectSum(GradedModule), see isDirectSum -- whether something is a direct sum
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length(GradedModule) -- length of a graded module
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map(GradedModule,GradedModule,Function), see map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
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max(GradedModule)
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min(GradedModule)
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rank(GradedModule), see rank -- compute the rank
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ring(GradedModule), see ring -- get the associated ring of an object
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tensorAssociativity(GradedModule,GradedModule,GradedModule), see tensorAssociativity -- associativity isomorphisms for tensor products