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Matroids :: representationOf

representationOf -- represents a realizable/graphic matroid

Synopsis

Description

Given a realizable matroid whose ground set elements are vectors, returns the matrix with those column vectors. If the matroid is graphical, then the graph with edge set equal to the ground set is returned (without loops or parallel edges, since the Graphs package does not support these).

i1 : A = random(ZZ^3,ZZ^5)

o1 = | 8 7 3 8 8 |
     | 1 8 7 5 5 |
     | 3 3 8 7 2 |

              3        5
o1 : Matrix ZZ  <--- ZZ
i2 : M = matroid A

o2 = a matroid of rank 3 on 5 elements

o2 : Matroid
i3 : A == representationOf M

o3 = true
i4 : K4 = completeGraph 4

o4 = Graph{0 => {1, 2, 3}}
           1 => {0, 2, 3}
           2 => {0, 1, 3}
           3 => {0, 1, 2}

o4 : Graph
i5 : M4 = matroid K4

o5 = a matroid of rank 3 on 6 elements

o5 : Matroid
i6 : representationOf M4 === K4

o6 = true

See also

Ways to use representationOf :

For the programmer

The object representationOf is a method function.