# cones -- computes all cones of a fan of a certain dimension

## Synopsis

• Usage:
L = cones(d,F)
• Inputs:
• d, an integer, between 0 and the dimension of the fan
• F, an instance of the type Fan
• Outputs:

## Description

cones computes the List of all Cones in F of dimension d.

 i1 : F = normalFan hypercube 3 o1 = {ambient dimension => 3 } number of generating cones => 8 number of rays => 6 top dimension of the cones => 3 o1 : Fan i2 : L = cones(2,F) o2 = {{ambient dimension => 3 }, {ambient dimension => 3 dimension of lineality space => 0 dimension of lineality space => dimension of the cone => 2 dimension of the cone => 2 number of facets => 2 number of facets => 2 number of rays => 2 number of rays => 2 ------------------------------------------------------------------------ }, {ambient dimension => 3 }, {ambient dimension => 3 0 dimension of lineality space => 0 dimension of lineality space dimension of the cone => 2 dimension of the cone => 2 number of facets => 2 number of facets => 2 number of rays => 2 number of rays => 2 ------------------------------------------------------------------------ }, {ambient dimension => 3 }, => 0 dimension of lineality space => 0 dimension of the cone => 2 number of facets => 2 number of rays => 2 ------------------------------------------------------------------------ {ambient dimension => 3 }, {ambient dimension => 3 dimension of lineality space => 0 dimension of lineality space => dimension of the cone => 2 dimension of the cone => 2 number of facets => 2 number of facets => 2 number of rays => 2 number of rays => 2 ------------------------------------------------------------------------ }, {ambient dimension => 3 }, {ambient dimension => 3 0 dimension of lineality space => 0 dimension of lineality space dimension of the cone => 2 dimension of the cone => 2 number of facets => 2 number of facets => 2 number of rays => 2 number of rays => 2 ------------------------------------------------------------------------ }, {ambient dimension => 3 }, => 0 dimension of lineality space => 0 dimension of the cone => 2 number of facets => 2 number of rays => 2 ------------------------------------------------------------------------ {ambient dimension => 3 }, {ambient dimension => 3 dimension of lineality space => 0 dimension of lineality space => dimension of the cone => 2 dimension of the cone => 2 number of facets => 2 number of facets => 2 number of rays => 2 number of rays => 2 ------------------------------------------------------------------------ }} 0 o2 : List

To actually see the cones of the fan we can look at their rays, for example:

 i3 : apply(L,rays) o3 = {| 0 0 |, | -1 0 |, | -1 0 |, | 0 0 |, | 1 0 |, | 1 0 |, | 1 0 |, | -1 0 | | 0 0 | | 0 -1 | | 1 0 | | 0 0 | | 0 1 | | 0 -1 | | 0 -1 | | 0 -1 | | 0 0 | | 0 -1 | | 0 -1 | | 0 0 | | 0 0 | ------------------------------------------------------------------------ | -1 0 |, | 0 0 |, | -1 0 |, | 1 0 |, | 0 0 |} | 0 1 | | -1 0 | | 0 0 | | 0 0 | | 1 0 | | 0 0 | | 0 1 | | 0 1 | | 0 1 | | 0 1 | o3 : List

## Ways to use cones :

• "cones(ZZ,Fan)"

## For the programmer

The object cones is .