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LabeledModuleMap -- the class of maps between LabeledModules

Description

A map between two labeled modules remembers the labeled module structure of the source of target. Some, but not all methods available for maps have been extended to this class. In these cases, one should apply the method to the underlying matrix. See rank(LabeledModuleMap) (missing documentation) .

Functions and methods returning a map of labeled modules:

  • cauchyMap -- produces one surjection from the Cauchy decomposition of the exterior power of a tensor product
  • flattenedESTensor(List,Ring) (missing documentation)
  • flattenedGenericTensor(List,Ring) -- see flattenedGenericTensor -- Make a generic tensor of given format
  • LabeledModuleMap * LabeledModuleMap (missing documentation)
  • LabeledModuleMap ** LabeledModuleMap (missing documentation)
  • map(LabeledModule,LabeledModule,LabeledModuleMap) -- creates a new LabeledModuleMap from a given LabeledModuleMap
  • map(LabeledModule,LabeledModule,ZZ) -- creates scalar multiplication by an integer as a LabeledModuleMap
  • minorsMap(LabeledModuleMap,LabeledModule) -- see minorsMap -- creates a map of labeled free modules whose image is the minors of a map of labeled free modules
  • minorsMap(Matrix,LabeledModule) -- see minorsMap -- creates a map of labeled free modules whose image is the minors of a map of labeled free modules
  • pureResES1(List,Ring) (missing documentation)
  • pureResTC1(List,Ring) (missing documentation)
  • symmetricMultiplication -- creates the symmetric multiplication map
  • tensor(LabeledModuleMap,LabeledModuleMap) -- creates the tensor product of two maps of labeled modules, as a map of labeled module
  • tensorComplex1(LabeledModuleMap) -- see tensorComplex1 -- computes the first map of the tensor complex
  • tensorComplex1(LabeledModuleMap,List) -- see tensorComplex1 -- computes the first map of the tensor complex
  • traceMap(LabeledModule) -- see traceMap -- produces the trace map from a ring to a free module tensored with its dual
  • transpose(LabeledModuleMap) (missing documentation)

Methods that use a map of labeled modules:

  • cokernel(LabeledModuleMap) (missing documentation)
  • hyperdeterminant(LabeledModuleMap) -- see hyperdeterminant -- computes the hyperdeterminant of a boundary format tensor
  • hyperdeterminantMatrix(LabeledModuleMap) -- see hyperdeterminantMatrix -- computes a matrix whose determinant equals the hyperdeterminant of a boundary format tensor
  • matrix(LabeledModuleMap) (missing documentation)
  • net(LabeledModuleMap) (missing documentation)
  • rank(LabeledModuleMap) (missing documentation)
  • ring(LabeledModuleMap) (missing documentation)
  • source(LabeledModuleMap) -- the source of a map of a labeled modules
  • target(LabeledModuleMap) -- the target of a map of a labeled modules

For the programmer

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


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/TensorComplexes.m2:1352:0.