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SimplicialComplexes :: ring(SimplicialComplex)

ring(SimplicialComplex)

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 : 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

See also