# imageFan -- computes the fan of the image

## Synopsis

• Usage:
F = imageFan(M,C)
• Inputs:
• M,
• Outputs:
• F, an instance of the type Fan

## Description

M must be a matrix from the ambient space of the Cone C to some target space. The imageFan is the common refinement of the images of all faces of C.

 i1 : C = posHull matrix {{2,1,-1,-3},{1,1,1,1},{0,1,-1,0}} o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of the cone => 3 number of facets => 4 number of rays => 4 o1 : Cone i2 : M = matrix {{1,0,0},{0,1,0}} o2 = | 1 0 0 | | 0 1 0 | 2 3 o2 : Matrix ZZ <--- ZZ i3 : F = imageFan(M,C) o3 = {ambient dimension => 2 } number of generating cones => 3 number of rays => 4 top dimension of the cones => 2 o3 : Fan i4 : rays F o4 = {| -3 |, | -1 |, | 1 |, | 2 |} | 1 | | 1 | | 1 | | 1 | o4 : List

## Ways to use imageFan :

• "imageFan(Matrix,Cone)"

## For the programmer

The object imageFan is .