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

Synopsis

• Usage:
allFaces S
allFaces(k, S)
• Inputs:
• k, an integer, the highest dimension to return ($dim S$ by default)
• 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