Provides a user-friendly method to evaluate the Tutte polynomial at given values (i.e. calls substitute with the correct variables in the ring of the Tutte polynomial). For example, if M has Tutte polynomial T, then T(1,1) is the number of bases of M.
i1 : M = uniformMatroid(2, 4) o1 = a matroid of rank 2 on 4 elements o1 : Matroid |
i2 : tutteEvaluate(M, 1, 1) o2 = 6 |
If M = M(G) is the graphic matroid of a graph G, then T(2, 1) counts the number of spanning forests of G, and T(2, 0) counts the number of acyclic orientations of G.
i3 : M = matroid completeGraph 5 o3 = a matroid of rank 4 on 10 elements o3 : Matroid |
i4 : tutteEvaluate(M, 2, 1) o4 = 291 |
i5 : tutteEvaluate(M, 2, 0) o5 = 120 |
The object tutteEvaluate is a method function.