## Synopsis

• Usage:
• Inputs:
• C, ,
• facelist, a list, whose i-th entry is a list of the faces of C of dimension i-1
• facetlist, a list, whose i-th entry is a list of the facets of C of dimension i-1
• Outputs:
• C, ,

## Description

Adds to a complex the face data and facet data (computed if not specified), i.e., C.fc, C.facets, C.dim, C.fvector, C.isEquidimensional, C.isSimp are updated.

This allows us to add the face data later to a complex generated previously by newEmptyComplex.

Note that the input C is modified by this method.

This function is mainly used internally, but may occasionally be useful to the user and is hence exported.

 i1 : R=QQ[x_0..x_4] o1 = R o1 : PolynomialRing i2 : addCokerGrading(R) o2 = | -1 -1 -1 -1 | | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | 5 4 o2 : Matrix ZZ <--- ZZ 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 (x x , x x , x x , x x , x x ) 0 1 1 2 2 3 3 4 0 4 o3 : Ideal of R i4 : C=idealToComplex(I) o4 = 1: x x x x x x x x x x 0 2 0 3 1 3 1 4 2 4 o4 : complex of dim 1 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1 i5 : Cl=newEmptyComplex(R) o5 = empty complex o5 : complex of dim -1 embedded in dim 4 (printing facets) equidimensional, simplicial i6 : addFaceDataToComplex(Cl,fc C) o6 = 1: x x x x x x x x x x 0 2 0 3 1 3 1 4 2 4 o6 : complex of dim 1 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1 i7 : Cl==C o7 = true

## Caveat

If both facelist and facetlist are specified this function does not make any consistency check.

• newEmptyComplex -- Generates an empty complex.
• dim -- compute the Krull dimension
• fvector -- The F-vector of a complex.
• fc -- The faces of a complex.
• isSimp -- Check whether a complex or co-complex is simplicial.
• isEquidimensional -- Check whether a complex or co-complex is equidimensional.