# CoChainComplex VS¶

- VS: AbelianGroup

Delta Complexes are defined by a sequence of ‘face maps’, These can be represented by a list of matrices. for more documentation see: http://www.euclideanspace.com/prog/scratchpad/mycode/topology/chain/cochain/ Date Created: Jan 2016 Basic Operations: Related packages: Related categories: Related Domains: ChainComplex Also See: AMS Classifications:

- coboundary: (%, NonNegativeInteger, List VS) -> List VS
- calculate coboundary at dimention
`n`

for a given input

- coChainComplex: List Matrix Integer -> %
- constructor
- coerce: % -> OutputForm
- from CoercibleTo OutputForm

- coHomology: % -> List Homology
- calculate homology using SmithNormalForm
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- latex: % -> String
- from SetCategory

- validate: % -> Boolean
`true`

if this is a valid chain complex, that is: 1. maps compose 2. product of adjacent coboundary maps is zero