OrientedFacetΒΆ

alg_top.spad line 261

A single vertex, edge, triangle... for more documentation see: http://www.euclideanspace.com/prog/scratchpad/mycode/topology/simplex/ Date Created: March 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
addVertex: (%, NonNegativeInteger) -> %
used by cone. Adds a vertex to face.
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
boolWordPermute: (List List Boolean, NonNegativeInteger, NonNegativeInteger) -> List List Boolean
recursive part of boolWordPermute
boolWordPermute: (NonNegativeInteger, NonNegativeInteger) -> List List Boolean
boolean word permutation find all permutations of numZeros and numOnes used by product to calculate all paths through lattice
boundary: % -> List %
construct the boundary. This is like hollowing out the facet.
coerce: % -> OutputForm
from CoercibleTo OutputForm
empty?: % -> Boolean
from FacetCategory
getIndexes: % -> List NonNegativeInteger
returns indexes in face
getIndexesSigned: % -> List Integer
returns indexes in face with sign to give orientation
getMult: % -> Integer
from FacetCategory
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
isSubsetOf?: (%, %) -> Boolean
returns true if face ‘a’ is contained in face 'b'. true subset only : returns false if a=b
join: (%, %) -> %
used by simplicalJoin. Returns join (union) of ‘a’ and 'b'. That is: returns a facet containing indexes in both ‘a’ and 'b'.
latex: % -> String
from SetCategory
max: (%, %) -> %
from OrderedSet
maxIndex: % -> NonNegativeInteger
returns maximum index
min: (%, %) -> %
from OrderedSet
minIndex: % -> NonNegativeInteger
returns minimum index
order: % -> NonNegativeInteger
from FacetCategory
orientedFacet: (Integer, List NonNegativeInteger) -> %
Constructor for oriented facet oriented facet is always stored in vertex order orientation is calculated by the number of edges that have to be flipped to put it in order.
orientedFacet: (Integer, OrientedFacet) -> %
Copy constructor which can change mul
orientedFacetIfCan: List % -> Union(%, failed)
Constructor for oriented face from its boundary. This is like filling-in the boundary, in that sense it is the inverse of ‘boundary’. May fail, for instance in ‘implied’ loops, where both ends of an edge are the same point. Also similar cases for higher order facets.
orientedFacetSigned: List Integer -> %
Constructor for oriented face which removes duplicates If the face is positive then we expect the sequence to be: + - + - ...
orientedFacetUnsigned: List Integer -> %
Constructor for oriented face which removes duplicates and ignores orientation
position: (%, List %) -> Integer
return index of e in lst. Index will be negative if e has negative multiplier.
product: (%, %) -> List ProductFacet
This function returns the product of two facets. For more detailed explanation of simplex product code see: url{http://www.euclideanspace.com/prog/scratchpad/mycode/topology/simplex/product/} Also see Hatcher [9]. page 277 - The simplical cross product. page 278 - The cohomology cross product. Returns list, each entry is a ‘lattice path’ from (0, 0) to (x, y) where x is number of entries in sa and y is number of entries in sb.
refactorIndexes: (%, NonNegativeInteger) -> %
adds 'n' to each index. Used to refactor simplexes so that they don't overlap.
reindex: % -> %
re-index so that indexes start at 1 and are then consecutive.
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
subtract: (%, %) -> %
used by link. Returns face ‘a’ minus the vertices in face 'b'.

BasicType

CoercibleTo OutputForm

Comparable

FacetCategory

OrderedSet

PartialOrder

SetCategory