Making simplicial modules -- information about the basic constructors

Basic constructors

• simplicialModule(HashTable,HashTable,HashTable,ZZ) -- make a simplicial module
• simplicialModule(Module,ZZ) -- make a simplicial module associated to a complex concentrated in degree 0
• SimplicialModule Array -- shift a simplicial module or simplicial module map
• isWellDefined(SimplicialModule) -- whether a simplicial module is well-defined

Important computations creating new simplicial modules

• simplicialModule(Complex) -- compute the image of a non-negatively graded complex under the Dold-Kan correspondence
• simplicialTensor(Complex,Complex) -- compute the simplicial tensor product and cache direct sum indices for easy access

More advanced constructors

• SimplicialModule ++ SimplicialModule -- direct sum of simplicial modules
• SimplicialModule ** SimplicialModule -- tensor product of simplicial modules
• RingMap SimplicialModule -- apply a ring map to a simplicial module
• RingMap ** SimplicialModule -- tensor a simplicial module along a ring map
• minimalPresentation(SimplicialModule) -- minimal presentation of all terms in a simplicial module
• truncate(List,SimplicialModule) -- truncation of a simplicial module at a specified degree or set of degrees

Extracting simplicial modules from simplicial maps

• source(SimplicialModuleMap) -- get the source of a map of simplicial modules
• target(SimplicialModuleMap) -- get the target of a map of simplicial modules
• kernel(SimplicialModuleMap) -- make the kernel of a map of simplicial modules
• cokernel(SimplicialModuleMap) -- make the cokernel of a map of simplicial modules
• image(SimplicialModuleMap) -- make the image of a map of simplicial modules
• coimage(SimplicialModuleMap) -- make the coimage of a map of simplicial modules