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dim(SimplicialComplex) -- dimension of a simplicial complex

Synopsis

Description

i1 : loadPackage "SimplicialComplexes";
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.
i2 : R = ZZ[a..h];
i3 : D = simplicialComplex{a*b*c*d, a*b*e, c*d*f, f*g, g*a, h}

o3 = | h fg ag cdf abe abcd |

o3 : SimplicialComplex
i4 : dim D

o4 = 3
The void complex has dimension minus infinity, while the irrelevant complex has dimension -1.
i5 : void = simplicialComplex monomialIdeal 1_R;
i6 : dim void

o6 = -infinity

o6 : InfiniteNumber
i7 : irrelevant = simplicialComplex {1_R};
i8 : dim irrelevant

o8 = -1

See also