Working with Galois Groups in Magma

These notes complement the lectures and aim to give you practical experience in working with Galois groups in Magma. They are aimed at people for whom working with Magma is something of a struggle. I myself am still in this category, although perhaps starting to leave it, having written these notes . . . . Given the aims, the exercises corresponding to the first two lectures are intended to be easy. They are commonly just running programs and they never present obstructions to continuing. The point is to increase the comfort level of beginners to Magma. Another way I keep the computational context simple is that I center everything on a single datatype, polynomials in Z[x]. If you are truly a rank beginner, I recommend typing in the displayed code as an aid to understanding it. Some of the most basic Magma constructions are used repeatedly. If you are past this level and would learn nothing by your own typing, all the displayed code is available in the file exercisesmagma. If you are fluent at Magma, a meta-exercise for the first two days is to improve my code! The exercises corresponding to the third lecture are harder and more open-ended. If the material in the first two sections becomes too easy for you at some point, feel free to move ahead.