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";
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i2 : R = QQ[a..d];
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i3 : D = simplicialComplex monomialIdeal(a*b*c*d);
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i4 : ring D
o4 = R
o4 : PolynomialRing
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i5 : coefficientRing D
o5 = QQ
o5 : Ring
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i6 : S = ZZ[w..z];
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i7 : E = simplicialComplex monomialIdeal(w*x*y*z);
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i8 : ring E
o8 = S
o8 : PolynomialRing
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i9 : coefficientRing E
o9 = ZZ
o9 : Ring
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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.