# complex -- Make a complex.

## Synopsis

• Usage:
complex(R,facelist)
complex(R,facelist,facetlist)
complex(R,facelist,Rdual)
complex(R,facelist,facetlist,Rdual)
• Inputs:
• R, ,
• facelist, a list, of the faces, sorted by dimension
• facetlist, a list, of the facets, sorted by dimension
• Rdual, ,
• Outputs:
• ,

## Description

Make a complex from a list of faces and/or facets.

This is mostly used internally but may be occasionally useful for the end user.

 i1 : R=QQ[x_0..x_5] o1 = R o1 : PolynomialRing i2 : C=boundaryCyclicPolytope(3,R) o2 = 2: x x x x x x x x x x x x x x x x x x x x x x x x 0 1 2 0 2 3 0 3 4 0 1 5 1 2 5 2 3 5 0 4 5 3 4 5 o2 : complex of dim 2 embedded in dim 5 (printing facets) equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1 i3 : fC=fc C o3 = {{{}}, {x , x , x , x , x , x }, {x x , x x , x x , x x , x x , x x , 0 1 2 3 4 5 0 1 0 2 1 2 0 3 2 3 0 4 ------------------------------------------------------------------------ x x , x x , x x , x x , x x , x x }, {x x x , x x x , x x x , x x x , 3 4 0 5 1 5 2 5 3 5 4 5 0 1 2 0 2 3 0 3 4 0 1 5 ------------------------------------------------------------------------ x x x , x x x , x x x , x x x }, {}, {}, {}} 1 2 5 2 3 5 0 4 5 3 4 5 o3 : List i4 : C1=complex(R,fC) o4 = 2: x x x x x x x x x x x x x x x x x x x x x x x x 0 1 2 0 2 3 0 3 4 0 1 5 1 2 5 2 3 5 0 4 5 3 4 5 o4 : complex of dim 2 embedded in dim 5 (printing facets) equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1 i5 : C==C1 o5 = true

## Caveat

If both the list of faces and facets is specified there is no consistency check.

• Face -- The class of all faces of complexes or co-complexes.
• complexFromFacets -- Make a complex from its facets.

## Ways to use complex :

• "complex(PolynomialRing,List)"
• "complex(PolynomialRing,List,List)"
• "complex(PolynomialRing,List,List,PolynomialRing)"
• "complex(PolynomialRing,List,PolynomialRing)"

## For the programmer

The object complex is .