facets -- the facets of a simplicial complex

Synopsis

• Usage:

  facets D

• Inputs:
  • D, a simplicial complex
• Optional inputs:
  • useFaceClass => ..., default value false, Option to return faces in the class Face
• Outputs:
  • a matrix, with one row, whose entries are squarefree monomials representing the facets (maximal faces) of D

Description

The 3-dimensional sphere has a unique minimal nonface which corresponds to the interior.

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

i2 : sphere = simplicialComplex monomialIdeal(a*b*c*d*e)

o2 = | bcde acde abde abce abcd |

o2 : SimplicialComplex

i3 : facets sphere

o3 = | bcde acde abde abce abcd |

             1       5
o3 : Matrix R  <--- R

i4 : D = simplicialComplex {e, c*d, b*d, a*b*c, a*b, c}

o4 = | e cd bd abc |

o4 : SimplicialComplex

i5 : facets D

o5 = | e cd bd abc |

             1       4
o5 : Matrix R  <--- R

Note that no computatation is performed by this routine; all the computation was done while constructing the simplicial complex.

A simplicial complex is displayed by listing its facets, and so this function is frequently unnecessary.

See also

• SimplicialComplexes -- simplicial complexes
• simplicialComplex -- create a simplicial complex
• faces -- the i-faces of a simplicial complex