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ring(SimplicialComplex) -- get the associated ring of an object

Synopsis

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 : loadPackage "SimplicialComplexes";
i2 : R = QQ[a..d];
i3 : D = simplicialComplex monomialIdeal(a*b*c*d);
i4 : ring D

o4 = R

o4 : PolynomialRing
i5 : coefficientRing D

o5 = QQ

o5 : Ring
i6 : S = ZZ[w..z];
i7 : E = simplicialComplex monomialIdeal(w*x*y*z);
i8 : ring E

o8 = S

o8 : PolynomialRing
i9 : coefficientRing E

o9 = ZZ

o9 : 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

See also