# tutteEvaluate -- evaluate Tutte polynomial

## Synopsis

• Usage:
tutteEvaluate(M, a, b)
• Inputs:
• M,
• a,
• b,
• Outputs:
• , the evaluation of the Tutte polynomial of M at (a, b)

## 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

## Ways to use tutteEvaluate :

• "tutteEvaluate(Matroid,Thing,Thing)"

## For the programmer

The object tutteEvaluate is .