### Factorization of $f \in \mathbb{Q}[X]$ in field extension $\mathbb{Q}(\alpha)$.

I'm given an irreducible polynomial $f \in \mathbb{Q}[X]$ 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 $\alpha_1$ of $f$ and studies the factorization of $f$ in the field extension $\mathbb{Q}(\alpha_1)$.

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.