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:
- L, a list

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 a method function.