I'm just becoming interested in the use of programming in Mathematics (specifically group theory/number theory). Now, I was wondering whether there were any particular scripts (raw scripts) that were available in determining the Galois Group of certain polynomials. In fact, I was wondering whether there were particular scripts that could determine the suitable polynomials over Q associated with M11 (the simplest Mathieu group).
I am not looking for particular packages (e.g GAP/Sage), but rather the raw script for these packages such that if you were to put in M11 you could output an associated polynomial (whether over Q or as a polynomial in integers) and the specific method involved. The reason for this question is I would like to see the number of specific scripts that are available for determining M11 as a Galois group and the computational efficiency with respect to the different scripts. Eventually I would like to apply the scripts further to other finite groups and modify them but to see the skeleton for M11 would be tremendously helpful.
Thank you for your help!