The following simplicial complex consists of a tetrahedron,
with two triangles attached, two more edges and an isolated
vertex. Since the largest facet has 4 vertices, this
complex has dimension 3.
i1 : R = ZZ[a..h];
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i2 : D = simplicialComplex{a*b*c*d, a*b*e, c*d*f, f*g, g*a, h}
o2 = | h fg ag cdf abe abcd |
o2 : SimplicialComplex
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i3 : dim D
o3 = 3
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The void complex has dimension minus infinity, while the
irrelevant complex has dimension -1.
i4 : void = simplicialComplex monomialIdeal 1_R;
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i5 : dim void
o5 = -infinity
o5 : InfiniteNumber
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i6 : irrelevant = simplicialComplex {1_R};
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i7 : dim irrelevant
o7 = -1
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