imageFan -- computes the fan of the image

Usage:

F = imageFan(M,C)
Inputs:
- M, a matrix
- C, a convex rational cone
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 a method function.

The source of this document is in OldPolyhedra.m2:7214:0.