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ccRefinement -- computes the coarsest common refinement of a set of rays

Synopsis

Usage:
F = ccRefinement R
Inputs:
- R, a matrix
Outputs:
- F, an object of class Fan

Description

The coarsest common refinement of a set of rays R is the common refinement of all possible triangulations of the rays.

For example, consider a three dimensional cone with four rays:

i1 : R = matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}}

o1 = | 1 1  -1 -1 |
     | 1 -1 1  -1 |
     | 1 1  1  1  |

              3        4
o1 : Matrix ZZ  <--- ZZ

The coarsest common refinement has a fifth ray and consists of four cones.

i2 : F = ccRefinement R

o2 = {ambient dimension => 3         }
      number of generating cones => 4
      number of rays => 5
      top dimension of the cones => 3

o2 : Fan

i3 : rays F

o3 = {| 1  |, | 1 |, | -1 |, | 0 |, | -1 |}
      | -1 |  | 1 |  | -1 |  | 0 |  | 1  |
      | 1  |  | 1 |  | 1  |  | 1 |  | 1  |

o3 : List

Ways to use `ccRefinement` :

ccRefinement(Matrix)