next | previous | forward | backward | up | top | index | toc | Macaulay2 website
SimplicialComplexes :: dim(SimplicialComplex)

dim(SimplicialComplex) -- dimension of a simplicial complex

Synopsis

Description

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];
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
i3 : dim D

o3 = 3
The void complex has dimension minus infinity, while the irrelevant complex has dimension -1.
i4 : void = simplicialComplex monomialIdeal 1_R;
i5 : dim void

o5 = -infinity

o5 : InfiniteNumber
i6 : irrelevant = simplicialComplex {1_R};
i7 : dim irrelevant

o7 = -1

See also