SimplicialModules : Table of Contents

• SimplicialModules -- A package for creating and computing objects in the category of Simplicial R-Modules
• arithmetic with simplicial module maps -- perform arithmetic operations on simplicial module maps
• Basic invariants and properties -- information about accessing basic features
• coimage(SimplicialModuleMap) -- make the coimage of a map of simplicial modules
• cokernel(SimplicialModuleMap) -- make the cokernel of a map of simplicial modules
• components(SimplicialModule) -- list the components of a direct sum
• components(SimplicialModuleMap) -- list the components of a direct sum
• degree(SimplicialModuleMap) -- get the degree of a map of simplicial modules
• directSum(SimplicialModule) -- direct sum of simplicial modules
• exteriorInclusion -- computes the image of the 2nd exterior power into the tensor product
• extPower -- compute the Dold-Puppe extension of the exterior power functor to simplicial modules
• extPower(...,Degeneracy=>...) -- whether to compute degeneracy maps
• extPower(...,TopDegree=>...) -- top degree for the construction
• face/degeneracy maps of a simplicial module -- access the face and degeneracy maps of a simplicial module
• forgetComplex(...,RememberSummands=>...) -- whether to remember direct sum structure
• forgetComplex(SimplicialModule) -- forget the underlying complex data of a simplicial module obtained as a Dold-Kan image
• forgetDegeneracy(SimplicialModule) -- forget the data of degeneracy maps of a simplicial object
• id _ SimplicialModule -- the identity map of a simplicial module
• image(SimplicialModuleMap) -- make the image of a map of simplicial modules
• inducedMap(...,Degree=>...) -- specify the degree of an induced map of simplicial modules
• inducedMap(SimplicialModule,SimplicialModule) -- make the map of simplicial modules induced at each term by the identity map
• isCommutative(SimplicialModuleMap) -- whether a simplicial module map commutes with the face/degeneracy maps
• isHomogeneous(SimplicialModuleMap) -- whether a map of simplicial modules is homogeneous
• isShortExactSequence(SimplicialModuleMap,SimplicialModuleMap) -- whether a pair of simplicial module maps forms a short exact sequence
• isSimplicialModule(SimplicialModule) -- check if the simplicial identities hold for a simplicial object with degeneracy map keys
• isSimplicialMorphism(SimplicialModuleMap) -- whether a simplicial module map is a morphism of simplicial modules
• isWellDefined(SimplicialModule) -- whether a simplicial module is well-defined
• isWellDefined(SimplicialModuleMap) -- whether a map of simplicial modules is well-defined
• kernel(SimplicialModuleMap) -- make the kernel of a map of simplicial modules
• Making maps between simplicial modules -- information about the basic constructors
• Making simplicial modules -- information about the basic constructors
• map(...,Degree=>...) -- specify the degree of a map of simplicial modules
• map(...,DegreeLift=>...) -- unused option for maps of simplicial modules
• map(...,DegreeMap=>...) -- unused option for maps of simplicial modules
• map(SimplicialModule,SimplicialModule,HashTable) -- make a map of simplicial modules
• map(SimplicialModule,SimplicialModule,SimplicialModuleMap) -- make a new map of simplicial modules, induced from an existing one
• map(SimplicialModule,SimplicialModule,ZZ) -- make the zero map or identity between simplicial modules
• minimalPresentation(...,Exclude=>...) -- exclude option for minimal presentation
• minimalPresentation(SimplicialModule) -- minimal presentation of all terms in a simplicial module
• naiveNorm(SimplicialModule,ZZ) -- compute the naive normalization of a simplicial object
• normalize(SimplicialModule,ZZ) -- normalization functor from simplicial modules to nonnegatively-graded chain complexes
• randomSimplicialMap(SimplicialModule,SimplicialModule) -- a random map of simplicial modules
• ring(SimplicialModule) -- access the ring of a simplicial module or a simplicial module map
• RingMap ** SimplicialModule -- tensor a simplicial module along a ring map
• RingMap ** SimplicialModuleMap -- tensor a map of simplicial modules along a ring map
• RingMap SimplicialModule -- apply a ring map to a simplicial module
• RingMap SimplicialModuleMap -- apply a ring map to a map of simplicial modules
• schurMap -- construct the Dold-Puppe extension of the Schur functor
• schurMap(...,Degeneracy=>...) -- whether to compute degeneracy maps
• schurMap(...,TopDegree=>...) -- top degree for the construction
• SimplicialModule -- the class of all simplicial modules
• simplicialModule -- make a simplicial module
• SimplicialModule ** Matrix -- create the tensor product of a simplicial module and a map of modules
• SimplicialModule ** SimplicialModule -- tensor product of simplicial modules
• SimplicialModule == SimplicialModule -- whether two simplicial modules are equal
• SimplicialModule _ Array -- the canonical inclusion or projection map of a direct sum
• SimplicialModule _ ZZ -- access individual objects of a simplicial module
• SimplicialModule Array -- shift a simplicial module or simplicial module map
• simplicialModule(...,Degeneracy=>...) -- whether to compute degeneracy maps
• simplicialModule(Module,ZZ) -- make a simplicial module associated to a complex concentrated in degree 0
• SimplicialModuleMap -- the class of all maps between simplicial modules
• SimplicialModuleMap * SimplicialModuleMap -- composition of homomorphisms of simplicial modules
• SimplicialModuleMap ** SimplicialModuleMap -- the map of simplicial modules between tensor simplicial modules
• SimplicialModuleMap ++ SimplicialModuleMap -- direct sum of simplicial module maps
• SimplicialModuleMap == SimplicialModuleMap -- whether two simplicial module maps are equal
• SimplicialModuleMap ^ Array -- the composition with the canonical inclusion or projection map
• SimplicialModuleMap ^ ZZ -- the n-fold composition
• SimplicialModuleMap _ ZZ -- access individual matrices in a simplicial module map
• SimplicialModuleMap | SimplicialModuleMap -- join or concatenate maps horizontally
• SimplicialModuleMap || SimplicialModuleMap -- join or concatenate maps vertically
• simplicialTensor -- compute the simplicial tensor product and cache direct sum indices for easy access
• simplicialTensor(...,Degeneracy=>...) -- whether to compute degeneracy maps
• simplicialTensor(...,TopDegree=>...) -- top degree for the construction
• source(SimplicialModuleMap) -- get the source of a map of simplicial modules
• symmetricQuotient -- computes the image of the surjection from the simplicial tensor product onto the second symmetric power of a simplicial module
• target(SimplicialModuleMap) -- get the target of a map of simplicial modules
• tensorLES -- computes the long exact sequence of homology induced by the canonical short exact sequence of complexes
• tensorwithComponents -- compute the tensor product of direct summands, caching the components for easy access
• The Dold-Kan Correspondence in Macaulay2 -- compute the image of a non-negatively graded complex under the Dold-Kan correspondence
• topDegree -- top degree of a simplicial module
• truncate(List,SimplicialModule) -- truncation of a simplicial module at a specified degree or set of degrees
• truncate(List,SimplicialModuleMap) -- truncation of a simplicial module map at a specified degree or set of degrees