Eigenvalues of matrix with entries in polynomial ring

edit

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: