# CubicalFacet¶

alg_top.spad line 945 [edit on github]

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 PartialOrder

- >: (%, %) -> Boolean
from PartialOrder

- 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

- 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