FiniteSimplicialSet

org.appliedtopology.tda4j.cells.FiniteSimplicialSet
See theFiniteSimplicialSet companion object
class FiniteSimplicialSet[G](val generatorsByDim: IndexedSeq[Set[G]], val faces: G => IndexedSeq[SSetElement[G]])(using val ord: Ordering[G])

A finite simplicial set presented by generators (non-degenerate simplices) and, for each generator, its primitive face data -- from which everything else (arbitrary d_i/s_j, the OrderedCell instance feeding the homology engines) is inferred via faceOf/insertOuter (SSetElement.scala).

faces(g), for g of dimension n, must supply exactly n+1 already-normalized SSetElements of dimension n-1 each (empty for n = 0) -- validate() checks this contract plus the simplicial identities at runtime, since it's easy to get a hand-written presentation subtly wrong with no crash, just silently wrong homology.

Attributes

Companion
object
Experimental
true
Graph
Supertypes
class Object
trait Matchable
class Any

Members list

Value members

Concrete methods

def dOp(i: Int, elt: SSetElement[G]): SSetElement[G]
def dimOf(g: G): Int
def sOp(j: Int, elt: SSetElement[G]): SSetElement[G]
def validate(): Seq[String]

Concrete fields

val faces: G => IndexedSeq[SSetElement[G]]
val generatorsByDim: IndexedSeq[Set[G]]

Givens

Givens

given cellInstance: is[G, OrderedCell]
given ord: Ordering[G]