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 |, | 1 |, | 0 |} | -1 | | -1 | | 1 | | 1 | | 0 | | 1 | | 1 | | 1 | | 1 | | 1 | o3 : List |
The object ccRefinement is a method function.