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

Synopsis

• Usage:

  F = ccRefinement R

• Inputs:
  • R, a matrix
• Outputs:
  • F, an instance of the type 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 = F

o2 : Fan

i3 : rays F

o3 = | 0 -1 1  -1 1 |
     | 0 -1 -1 1  1 |
     | 1 1  1  1  1 |

              3        5
o3 : Matrix ZZ  <--- ZZ