Macaulay2 » Documentation
Packages » OldPolyhedra :: imageFan
next | previous | forward | backward | up | index | toc

# 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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldPolyhedra.m2:7214:0.