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
|