# nonbases -- nonbases of matroid

## Synopsis

• Usage:
nonbases M
• Inputs:
• M, ,
• Outputs:
• a list, of nonbases

## Description

In any matroid, all basis elements have the same cardinality r (which is the rank of the matroid). The nonbases of a matroid are the subsets of the ground set of cardinality r that are dependent.

Just as with bases and circuits, nonbases are stored via their indices (rather than the elements of the ground set themselves).

 i1 : M = matroid({a,b,c,d},{{a,b},{a,c}}) o1 = a matroid of rank 2 on 4 elements o1 : Matroid i2 : nonbases M o2 = {set {1, 2}, set {0, 3}, set {1, 3}, set {2, 3}} o2 : List