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# tutteEvaluate -- evaluate Tutte polynomial

- Usage:
    `tutteEvaluate(M, a, b)`
- Inputs:
  - M, a matroid,
  - a, a thing,
  - b, a thing,
- Outputs:
  - a thing, 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

## See also

- tuttePolynomial(Matroid) -- Tutte polynomial of a matroid

## Ways to use tutteEvaluate:

- `tutteEvaluate(Matroid,Thing,Thing)`

## For the programmer

The object tutteEvaluate is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Matroids/doc-Matroids.m2:2597:0.