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];
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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];
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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.