ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 30 Dec 2017 12:14:54 -0600Factorization of $f \in \mathbb{Q}[X]$ in field extension $\mathbb{Q}(\alpha)$.http://ask.sagemath.org/question/40374/factorization-of-f-in-mathbbqx-in-field-extension-mathbbqalpha/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.
Apparently the book gives a CD where an interface between sage and gap is done. So probably the solution requires using gap commands.Rodrigo RayaSat, 30 Dec 2017 12:14:54 -0600http://ask.sagemath.org/question/40374/