In Macaulay2, every
simplicial complex is equipped with a polynomial ring, and the resulting matrix of facets
is defined over this ring.
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
|
The following
faces generate a simplicial complex
consisting of a triangle (on vertices
a,b,c), two edges connecting
c to
d and
b to
d, and an isolated vertex
e.
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
|
There are four facets of
D.
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.