Factorization of f∈Q[X] in field extension Q(α).
I'm given an irreducible polynomial f∈Q[X] of degree 5 and I want to determine its Galois group without using the predefined functions of sage. The method I want to follow takes a root α1 of f and studies the factorization of f in the field extension Q(α1).
I believe this is possible with other software. How can I do it with sage?
Edit
Apparently, Abstract Algebra: An Interactive Approach, Second Edition but they use InitDomain function which is not recognized by my notebook...Maybe this code notebook.
Apparently the book gives a CD where an interface between sage and gap is not public...done. So probably the solution requires using gap commands.