# GradedModuleMap -- the class of all maps between graded modules

## Functions and methods returning a graded module map :

• "GradedModuleMap * GradedModuleMap" -- see * -- a binary operator, usually used for multiplication
• "RingElement * GradedModuleMap" -- see * -- a binary operator, usually used for multiplication
• "GradedModuleMap + GradedModuleMap" -- see + -- a unary or binary operator, usually used for addition
• "GradedModuleMap + RingElement" -- see + -- a unary or binary operator, usually used for addition
• "RingElement + GradedModuleMap" -- see + -- a unary or binary operator, usually used for addition
• "- GradedModuleMap" -- see - -- a unary or binary operator, usually used for negation or subtraction
• "GradedModuleMap - GradedModuleMap" -- see - -- a unary or binary operator, usually used for negation or subtraction
• "GradedModuleMap - RingElement" -- see - -- a unary or binary operator, usually used for negation or subtraction
• "RingElement - GradedModuleMap" -- see - -- a unary or binary operator, usually used for negation or subtraction
• "GradedModuleMap ^ ZZ" -- see ChainComplexMap ^ ZZ -- iterated composition
• "gradedModuleMap(List)" -- see gradedModuleMap -- make a map of graded modules
• "gradedModuleMap(Matrix)" -- see gradedModuleMap -- make a map of graded modules
• "gradedModuleMap(Sequence)" -- see gradedModuleMap -- make a map of graded modules
• HH ChainComplexMap -- homology of a chain complex map
• "map(GradedModule,GradedModule,Function)" -- see map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
• "GradedModuleMap ++ GradedModuleMap" -- see Matrix ++ Matrix -- direct sum of maps
• "GradedModuleMap ^ Array" -- see Matrix ^ Array -- component of map corresponding to summand of target
• "GradedModuleMap _ Array" -- see Matrix _ Array -- component of map corresponding to summand of source
• "minimalPresentation(GradedModuleMap)" -- see minimalPresentation(Module) -- minimal presentation of a module
• "prune(GradedModuleMap)" -- see minimalPresentation(Module) -- minimal presentation of a module
• "tensorAssociativity(GradedModule,GradedModule,GradedModule)" -- see tensorAssociativity -- associativity isomorphisms for tensor products

## Methods that use a graded module map :

• "GradedModuleMap == GradedModuleMap" -- see == -- equality
• "GradedModuleMap == RingElement" -- see == -- equality
• "GradedModuleMap == ZZ" -- see == -- equality
• "RingElement == GradedModuleMap" -- see == -- equality
• "ZZ == GradedModuleMap" -- see == -- equality
• "GradedModuleMap _ ZZ" -- see ChainComplexMap _ ZZ -- component map
• "coimage(GradedModuleMap)" -- see coimage -- coimage of a map
• "cokernel(GradedModuleMap)" -- see cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
• "components(GradedModuleMap)" -- see components -- list the components of a direct sum
• degree(GradedModuleMap) (missing documentation)
• "formation(GradedModuleMap)" -- see formation -- recover the methods used to make a module
• GradedModuleMap | GradedModuleMap -- a binary operator, often used for horizontal concatenation
• GradedModuleMap || GradedModuleMap -- a binary operator, often used for vertical concatenation
• "image(GradedModuleMap)" -- see image -- image of a map
• "kernel(GradedModuleMap)" -- see kernel(ChainComplexMap) -- kernel of a chain complex map
• "ring(GradedModuleMap)" -- see ring -- get the associated ring of an object
• source(GradedModuleMap) -- find the source of a map of graded modules
• target(GradedModuleMap) -- find the target of a map of graded modules

## For the programmer

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