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gfanFanCommonRefinement -- find the common refinement of two polyhedral fans

Synopsis

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 :

For the programmer

The object gfanFanCommonRefinement is a method function with options.