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
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i2 : nonbases M
o2 = {set {1, 2}, set {0, 3}, set {1, 3}, set {2, 3}}
o2 : List
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The object nonbases is a method function.