faces -- the i-faces of a simplicial complex

i1 : loadPackage "SimplicialComplexes";

i2 : R = ZZ[a..f]

o2 = R

o2 : PolynomialRing

i3 : D = simplicialComplex monomialIdeal(a*b*c,a*b*f,a*c*e,a*d*e,a*d*f,
                                                   b*c*d,b*d*e,b*e*f,c*d*f,c*e*f)

o3 = | def aef bdf bcf acf cde bce abe acd abd |

o3 : SimplicialComplex

i4 : faces(-1,D)

o4 = | 1 |

             1       1
o4 : Matrix R  <--- R

i5 : faces(0,D)

o5 = | a b c d e f |

             1       6
o5 : Matrix R  <--- R

i6 : faces(1,D)

o6 = | ab ac ad ae af bc bd be bf cd ce cf de df ef |

             1       15
o6 : Matrix R  <--- R

i7 : faces(2,D)

o7 = | abd abe acd acf aef bce bcf bdf cde def |

             1       10
o7 : Matrix R  <--- R

i8 : fVector D

o8 = HashTable{-1 => 1}
               0 => 6
               1 => 15
               2 => 10

o8 : HashTable