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

## Synopsis

• Usage:
F = ccRefinement R
• Inputs:
• R,
• 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

## Ways to use ccRefinement :

• "ccRefinement(Matrix)"

## For the programmer

The object ccRefinement is .