Computing Galois groups

Hi,

I am trying to compute some Galois groups with Axiom.

A way is to go after the example given in section 8.13 of the manual 
which follows closely and implements the original definition by Galois 
of the Galois group.

I am trying a different way: I would like to exploit a theorem by 
Kronecker which provides an easy algorithm to compute the Galois group 
of a given polynomial.

I wrote the function which implements the algorithm and it works... 
sometimes. :(

Which means that I have some problems.

My question is: is there anybody that is willing to help me to fix it if 
I post the code?

The code is not very long (about 40-50 lines) but it needs to be 
explained, so I am asking before to make the effort.

TIA

Fabio