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 = F o1 : Fan i2 : L = cones(2,F) o2 = {{0, 2}, {0, 3}, {0, 4}, {0, 5}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 4}, ------------------------------------------------------------------------ {2, 5}, {3, 4}, {3, 5}} o2 : List

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

 i3 : raysF = rays F o3 = | -1 1 0 0 0 0 | | 0 0 -1 1 0 0 | | 0 0 0 0 -1 1 | 3 6 o3 : Matrix ZZ <--- ZZ i4 : apply(L, c -> raysF_c) o4 = {| -1 0 |, | -1 0 |, | -1 0 |, | -1 0 |, | 1 0 |, | 1 0 |, | 1 0 |, | 0 -1 | | 0 1 | | 0 0 | | 0 0 | | 0 -1 | | 0 1 | | 0 0 | | 0 0 | | 0 0 | | 0 -1 | | 0 1 | | 0 0 | | 0 0 | | 0 -1 | ------------------------------------------------------------------------ | 1 0 |, | 0 0 |, | 0 0 |, | 0 0 |, | 0 0 |} | 0 0 | | -1 0 | | -1 0 | | 1 0 | | 1 0 | | 0 1 | | 0 -1 | | 0 1 | | 0 -1 | | 0 1 | o4 : List

Ways to use cones :

• "cones(ZZ,Fan)"

For the programmer

The object cones is .