# ring(SimplicialComplex)

## Synopsis

• Function: ring
• Usage:
R = ring D
• Inputs:
• Outputs:
• R, a ring, the polynomial ring used to define D

## Description

The vertices of every simplicial complex are variables in the polynomial ring R, and subsets of vertices, such as faces, are represented as squarefree monomials in R.
 i1 : R = QQ[a..d]; i2 : D = simplicialComplex monomialIdeal(a*b*c*d); i3 : ring D o3 = R o3 : PolynomialRing i4 : coefficientRing D o4 = QQ o4 : Ring i5 : S = ZZ[w..z]; i6 : E = simplicialComplex monomialIdeal(w*x*y*z); i7 : ring E o7 = S o7 : PolynomialRing i8 : coefficientRing E o8 = ZZ o8 : Ring

There is a bijection between simplicial complexes and squarefree monomial ideals. This package exploits this correspondence by using commutative algebra routines to perform most of the necessary computations.

## Caveat

Some operations depend on the choice of ring, or its coefficient ring