image(PosetMap,List) -- the image of a poset map

Function: image
Usage:

image(f, L)
Inputs:
- f, a map of posets,
- L, a list, a subset of vertices source f
Outputs:
- a list,

Description

The image of the map $[3]\rightarrow[10]$ given by $i\mapsto 2i$ is computed below.

i1 : f = map(chain 10, chain 3, {1=>2, 2=>4, 3=>6})

o1 = PosetMap{1 => 2                                            }
              2 => 4
              3 => 6
              source => Relation Matrix: | 1 1 1 |
                                         | 0 1 1 |
                                         | 0 0 1 |
              target => Relation Matrix: | 1 1 1 1 1 1 1 1 1 1 |
                                         | 0 1 1 1 1 1 1 1 1 1 |
                                         | 0 0 1 1 1 1 1 1 1 1 |
                                         | 0 0 0 1 1 1 1 1 1 1 |
                                         | 0 0 0 0 1 1 1 1 1 1 |
                                         | 0 0 0 0 0 1 1 1 1 1 |
                                         | 0 0 0 0 0 0 1 1 1 1 |
                                         | 0 0 0 0 0 0 0 1 1 1 |
                                         | 0 0 0 0 0 0 0 0 1 1 |
                                         | 0 0 0 0 0 0 0 0 0 1 |

o1 : PosetMap

i2 : image f

o2 = {2, 4, 6}

o2 : List

The image of ${1,2}$ under this map is computed below.

i3 : image(f, {1,2})

o3 = {2, 4}

o3 : List

Ways to use this method:

image(PosetMap)
image(PosetMap,List) -- the image of a poset map

The source of this document is in MacaulayPosets.m2:1624:0.