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Matroids :: tutteEvaluate

tutteEvaluate -- evaluate Tutte polynomial

Synopsis

Description

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

See also

Ways to use tutteEvaluate :

For the programmer

The object tutteEvaluate is a method function.