FILES

    bruteforce.py
        Used when generating polynomials with Galois groups that are proper
        sub-groups of Sn TO USE

    db.py
        Contains DB class which can be used to store data

    plots.py
        Functions used for producing plots

    polynomial.py
        Functions related to polynomials
    

TO USE

    The scripts here are to be used with Sage. (http://www.sagemath.org)
    There are several ways to do this:

    Within sage: (assuming you are running sage in the directory with scripts)
        (1) sage: load polynomial.py 
        (2) sage: attach polynomial.py
            # This reloads the file when the file is changed (useful when debugging)
        (3) sage: from polynomial import *

    Above methods make all the functions in polynomial.py available globally.

        (4) sage: import polynomial

    This will make functions accessible through polynomial.function_name()

    Standalone script:
        #!/usr/env sage -python
        from sage.all import *
        from polynomial import *
        
        #python code
    
    
Examples

    sage: load polynomial.py
    sage: irreducible_polynomial(4) # Returns an irreducible polynomial of degree 4

    # Generating Normalized roots:

    # This sets x as an element of polynomial ring over rationals

    sage: R.<x> = QQ[]  
    sage: f = x^2 + 1

    # OR

    sage: load polynomial.py
    sage: f = make_polynomial([1, 0, 1])

    # If you have TransitiveGroup installed, this should return an id of galois
    # group of f. 
    # You can install this optional sage package by running: 
    #   sage -i database_gap-4.4.10

    sage: f.galois_group() 

    # This gives a list of normalized roots mod p for 10 prime numbers p
    # starting with 2

    sage: roots_modp(f,2,10)