facets Delta
In this package, an abstract simplicial complex $\Delta$ is identified with a squarefree monomial ideal in a polynomial ring. The vertices of $\Delta$ correspond to a subset of the variables in the polynomial ring, and each face is identified as the product of the variables corresponding to the vertices of that face. This method function returns a list whose entries are the squarefree monomials representing the maximal faces of $\Delta$.
The order of the facets is determined by the monomial order on the underlying polynomial ring. The facets of an abstract simplicial complex are used when outputting or printing; see net(SimplicialComplex).




The abstract simplicial complex from Example 1.8 of MillerSturmfels' Combinatorial Commutative Algebra consists of a triangle (on vertices $a$, $b$, $c$), two edges (connecting $c$ to $d$ and $b$ to $d$), and an isolated vertex (namely $e$). It has six minimal nonfaces.



The irrelevant complex has the empty set as a facet whereas the void complex has no facets.





The list of facets is part of the defining data of an abstract simplicial complex. While this method function does no computation, it allows us access to this data.
