gfanFanCommonRefinement -- find the common refinement of two polyhedral fans

Synopsis

Usage:

P = gfanFanCommonRefinement(F,G)
Inputs:
- F, an instance of the type Fan,
- G, an instance of the type Fan,
Optional inputs:
- i1
- i2
Outputs:
- P, an instance of the type Fan, the common refinement of F and G

Description

This method takes two Fans and finds their common refinement.

In the following, F is the fan with two cones partitions the plane along the line $y=x$ while G has two cones that partition the plane along $y = x/2$. The common refinement of these two fans is the fan of the four cones between these two lines.

i1 : QQ[x,y];

i2 : F = gfanToPolyhedralFan gfan {x+y}

o2 = F

o2 : Fan

i3 : G = gfanToPolyhedralFan gfan {x+y^2}

o3 = G

o3 : Fan

i4 : gfanFanCommonRefinement(F,G)

o4 = Fan{...1...}

o4 : Fan

In the next example we take two half planes which overlap in the first quadrant. Their common refinement is simply their intersection.

i5 : QQ[x,y];

gfan Documentation

This program takes two polyhedral fans and computes their common refinement.
Options:
-i1 value:
 Specify the name of the first input file.
-i2 value:
 Specify the name of the second input file.
--stable:
 Compute the stable intersection.

Ways to use gfanFanCommonRefinement :

gfanFanCommonRefinement(Fan,Fan)

For the programmer

The object gfanFanCommonRefinement is a method function with options.