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allFaces -- returns all faces of a simplicial complex, up to a given dimension

Usage:

allFaces S

allFaces(k, S)
Inputs:
- k, an integer, the highest dimension to return ($dim S$ by default)
- S, an abstract simplicial complex,
Outputs:
- L, a list, the list of all faces of $S$ (excluding the $(-1)$-dimensional face \{\}) up to dimension $k$

Description

i1 : R = QQ[a..e];

i2 : S = simplicialComplex {a*b*c*d*e};

i3 : allFaces S

o3 = {a, b, c, d, e, a*b, a*c, a*d, a*e, b*c, b*d, b*e, c*d, c*e, d*e, a*b*c,
     ------------------------------------------------------------------------
     a*b*d, a*b*e, a*c*d, a*c*e, a*d*e, b*c*d, b*c*e, b*d*e, c*d*e, a*b*c*d,
     ------------------------------------------------------------------------
     a*b*c*e, a*b*d*e, a*c*d*e, b*c*d*e, a*b*c*d*e}

o3 : List

i4 : allFaces(2, S)

o4 = {a, b, c, d, e, a*b, a*c, a*d, a*e, b*c, b*d, b*e, c*d, c*e, d*e, a*b*c,
     ------------------------------------------------------------------------
     a*b*d, a*b*e, a*c*d, a*c*e, a*d*e, b*c*d, b*c*e, b*d*e, c*d*e}

o4 : List

See also

faces -- computes all faces of a certain codimension of a Cone or Polyhedron
facets -- Giving the facet inequalities of a cone or polyhedron.

Ways to use allFaces:

allFaces(SimplicialComplex)
allFaces(ZZ,SimplicialComplex)

For the programmer

The object allFaces is a method function.

The source of this document is in SimplicialDecomposability.m2:500:0.