getRepresentation -- retrieves stored representation

Synopsis

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

Description

For a matroid created from a matrix, this function provides a user-friendly way to access the original matrix. Similarly, for a matroid created from a (simple) graph, this function returns the graph used to create the matroid.

Note that some constructions applied to a matroid M (such as taking dual, or minors) will automatically compute an induced representation (if a representation of M exists), which can be viewed with this function.

 i1 : A = random(QQ^3,QQ^5) o1 = | 9/2 1/2 3/2 7/9 7/10 | | 1/2 1 3/4 7/10 7/3 | | 9/4 3/4 7/4 1/2 7 | 3 5 o1 : Matrix QQ <--- QQ i2 : M = matroid A o2 = a "matroid" of rank 3 on 5 elements o2 : Matroid i3 : A == getRepresentation 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 : getRepresentation M4 === K4 o6 = true i7 : N = M / set{0} o7 = a "matroid" of rank 2 on 4 elements o7 : Matroid i8 : getRepresentation N o8 = | 11925/8863 7515/17726 1 0 | | 3270/62041 1270/8863 0 1 | 2 4 o8 : Matrix QQ <--- QQ