Square‑Free Factorization in ℤ[x]

This script computes the square‑free factorization of a polynomial with integer coefficients

f(x) = h_1(x) h_2(x)^2 ... h_k(x)^k,

where each h_i(x) is square‑free.

Polynomial arithmetic (addition, subtraction, multiplication, division, gcd) is implemented manually via python lists in ℤ[x].
Division and GCD are computed in ℚ[x] using exact rational arithmetic (fractions.Fraction), then normalized back to ℤ[x].

Usage

Run from terminal

python3 factorize.py <coefficients>

Coefficients are given from lowest degree to highest.

Example for
f(x) = x^3 - 5x^2 + 2

python3 factorize.py 2 0 -5 1

Requirements

Uses only Python standard library modules:

• argparse
• fractions
• math
• functools