representationOf -- represents a realizable/graphic matroid

Synopsis

• Usage:
representationOf M
• Inputs:
• M, ,
• Outputs:
• , a representation of M (either a matrix or a graph)

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