rank M
The rank of a matroid is the common size of a(ny) basis of M. This is a basic numerical invariant of a matroid.
i1 : M = matroid({a,b,c,d},{{a,b},{a,c}}) o1 = a "matroid" of rank 2 on 4 elements o1 : Matroid
i2 : rank M o2 = 2