oalg-abg-1.0.0.0: Finitely generated abelian groups.
Copyright(c) Erich Gut
LicenseBSD3
Maintainerzerich.gut@gmail.com
Safe HaskellSafe-Inferred
LanguageHaskell2010

OAlg.AbelianGroup.KernelsAndCokernels

Description

Kernels and Cokernels for homomorphisms between finitely generated abelian groups.

Synopsis

Kernels

abhKernels :: Kernels N1 AbHom Source #

kernels for AbHom.

Cokernels

abhCokernels :: Cokernels N1 AbHom Source #

cokernels for AbHom.

Smith Normal

isoSmithNormal :: AbGroup -> Inv AbHom Source #

isomorphism to its smith normal group.

Properties Let g be in AbGroup, then holds:

  1. start (isoSmithNormal g) == g.
  2. end (isoSmithNormal g) is smith normal (see definition AbGroup).

Adjunction

abhSliceFreeAdjunction :: Attestable k => Free k AbHom -> Adjunction (SliceCokernelKernel (Free k) AbHom) (SliceFactor From (Free k) AbHom) (SliceFactor To (Free k) AbHom) Source #

the cokernel-kernel adjunction for a given Free k.

Orphan instances

Attestable k => SliceCokernelTo (Free k) AbHom Source # 
Instance details

Methods

sliceCokernelTo :: Slice 'To (Free k) AbHom -> Cokernel N1 AbHom #

Attestable k => SliceKernelFrom (Free k) AbHom Source # 
Instance details

Methods

sliceKernelFrom :: Slice 'From (Free k) AbHom -> Kernel N1 AbHom #