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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)
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Python scripts dependent on Sage for number theory research
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