# CubicalFacet¶

A single vertex, edge, square, cube… for more documentation see: http://www.euclideanspace.com/prog/scratchpad/mycode/topology/cubical/ Date Created: April 2016 Basic Operations: Related packages: Related categories: FacetCategory Related Domains: Also See: AMS Classifications:

- <: (%, %) -> Boolean
- from PartialOrder
- <=: (%, %) -> Boolean
- from PartialOrder
- =: (%, %) -> Boolean
- from BasicType
- >: (%, %) -> Boolean
- from PartialOrder
- >=: (%, %) -> Boolean
- from PartialOrder
- ~=: (%, %) -> Boolean
- from BasicType

- allSubsets: (%, NonNegativeInteger) -> List %
`allSubsets of`

a given facet returned in reverse order subsets returned are not oriented

- allSubsets: (%, NonNegativeInteger, NonNegativeInteger) -> List %
`allSubsets of`

a given length returned in reverse order subsets returned are not oriented

- boundary: % -> List %
- construct the boundary. This is like hollowing out the facet.
- coerce: % -> OutputForm
- from CoercibleTo OutputForm

- cubicalFacet: (Integer, CubicalFacet) -> %
- Copy constructor which can change mul

- cubicalFacet: (Integer, List Segment Integer) -> %
- Constructor for cubical facet intervals are always stored in low..high order orientation is calculated by the number of intervals that have to be flipped to put it in order.
- empty?: % -> Boolean
- from FacetCategory

- getIntervals: % -> List Segment Integer
- returns intervals in face one for each dimension
- getMult: % -> Integer
- from FacetCategory
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- latex: % -> String
- from SetCategory
- max: (%, %) -> %
- from OrderedSet
- min: (%, %) -> %
- from OrderedSet
- order: % -> NonNegativeInteger
- from FacetCategory

- position: (%, List %) -> Integer
- return index of
`e`

in`lst`

. Index will be negative if`e`

has negative multiplier.

- product: (%, %) -> %
- This function returns the product of two cubical facets. Unlike the simplex case, the product is a sinle facet

- sameFace?: (%, %) -> Boolean
`true`

if this is the same face although the orientation may be different.

- setMult: (%, Integer) -> %
- sets multiplier of face
- smaller?: (%, %) -> Boolean
- from Comparable