# dimension -- The dimension of a simplicial complex or a face of a simplicial complex.

## Synopsis

• Usage:
dimension(D)
dimension(F)
• Inputs:
• D, an object of class Complex
• F, an object of class Face
• Outputs:

## Description

Returns the dimension of a simplicial Complex or of a Face of a simplicial complex.

 `i1 : K=QQ;` `i2 : R=K[x_0..x_4];` ```i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0); o3 : Ideal of R``` ```i4 : D=idealToComplex I o4 = {x x , x x , x x , x x , x x } 2 4 0 3 0 2 1 3 1 4 o4 : complex with 5 facets on the vertices x x x x x 0 1 2 3 4``` ```i5 : dimension D o5 = 1``` ```i6 : fc=facets D o6 = {x x , x x , x x , x x , x x } 2 4 0 3 0 2 1 3 1 4 o6 : List``` ```i7 : dimension fc#0 o7 = 1```

## See also

• Complex -- The class of all simplicial complexes.
• Face -- The class of faces of simplicial complexes.
• facets -- The facets of a simplicial complex.
• faces -- Returns the faces of a complex
• idealToComplex -- Compute the Stanley-Reisner complex.

## Ways to use dimension :

• dimension(Complex)
• dimension(Face)