# Eigenvalues of matrix with entries in polynomial ring

Hi!

I just wrote some code on the sage-combinat queue which computes a matrix with entries in a polynomial ring R = PolynomialRing(QQ, 'x', n)

```
sage: P = Poset(([1,2,3,4], [[1,3],[1,4],[2,3]]), linear_extension = True)
sage: L = P.linear_extensions()
sage: M = L.markov_chain_transition_matrix(labeling = 'source')
sage: M
[-x0 - x1 - x2 x3 x0 + x3 0 0]
[ x1 + x2 -x0 - x1 - x3 0 x1 0]
[ 0 x1 -x0 - x3 0 x1]
[ 0 x0 0 -x0 - x1 - x2 x0 + x3]
[ x0 0 0 x0 + x2 -x0 - x1 - x3]
sage: M.eigenvalues()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
/Applications/sage-5.0.beta7/devel/sage-combinat/sage/combinat/posets/<ipython console> in <module>()
/Applications/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.eigenvalues (sage/matrix/matrix2.c:26415)()
/Applications/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.fcp (sage/matrix/matrix2.c:11089)()
/Applications/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_element.so in sage.rings.polynomial.polynomial_element.Polynomial.factor (sage/rings/polynomial/polynomial_element.c:22655)()
NotImplementedError:
```

Is it possible to compute this some other way or is this just not yet implemented (which would surprise me!).

Thanks,

Anne

Edit (originally posted as an answer by the original poster of the question)

Here is an easier example with the question:

```
sage: R = PolynomialRing(QQ, 'x', 2)
sage: x = R.gens()
sage: M = matrix([[x[0],x[1]],[x[1],x[0]]])
sage: M.eigenvalues()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
/Applications/sage-5.0.beta7/devel/sage-combinat/sage/combinat/posets/<ipython console> in <module>()
/Applications/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/matrix /matrix2.so in sage.matrix.matrix2.Matrix.eigenvalues (sage/matrix/matrix2.c:26415)()
/Applications/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.fcp (sage/matrix/matrix2.c:11089)()
/Applications/sage-5.0.beta7/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_element.so in sage.rings.polynomial.polynomial_element.Polynomial.factor (sage/rings/polynomial/polynomial_element.c:22655)()
NotImplementedError:
```

Just for future reference, this site uses markdown for markup, so indenting everything four spaces makes it look like code (or highlighting and using the "code" button).