Singular

I have the following problem: Given a matrix A defined ring r = 0, (x, y, z), dp; that has its VAPs in an extension of the base of coefientes. How can I get the diagonalization of A? And this matrix diagonal and the basis of eigenvectors?

If I understand the question correct, the following should work:
Load the libraries absfact.lib and linalg.lib,
compute the charcteristic polynomial p with e.g. charpoly,
Use the command to absFactorize to find the splitting field of p,
create a ring over the splitting field and map your matrix to this ring,
then use linear algebra from linalg.lib, e.g. jordanmatrix.

Hope this helps