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| """Benchmarks for polynomials over Galois fields. """ | |
| from sympy.polys.galoistools import gf_from_dict, gf_factor_sqf | |
| from sympy.polys.domains import ZZ | |
| from sympy.core.numbers import pi | |
| from sympy.ntheory.generate import nextprime | |
| def gathen_poly(n, p, K): | |
| return gf_from_dict({n: K.one, 1: K.one, 0: K.one}, p, K) | |
| def shoup_poly(n, p, K): | |
| f = [K.one] * (n + 1) | |
| for i in range(1, n + 1): | |
| f[i] = (f[i - 1]**2 + K.one) % p | |
| return f | |
| def genprime(n, K): | |
| return K(nextprime(int((2**n * pi).evalf()))) | |
| p_10 = genprime(10, ZZ) | |
| f_10 = gathen_poly(10, p_10, ZZ) | |
| p_20 = genprime(20, ZZ) | |
| f_20 = gathen_poly(20, p_20, ZZ) | |
| def timeit_gathen_poly_f10_zassenhaus(): | |
| gf_factor_sqf(f_10, p_10, ZZ, method='zassenhaus') | |
| def timeit_gathen_poly_f10_shoup(): | |
| gf_factor_sqf(f_10, p_10, ZZ, method='shoup') | |
| def timeit_gathen_poly_f20_zassenhaus(): | |
| gf_factor_sqf(f_20, p_20, ZZ, method='zassenhaus') | |
| def timeit_gathen_poly_f20_shoup(): | |
| gf_factor_sqf(f_20, p_20, ZZ, method='shoup') | |
| P_08 = genprime(8, ZZ) | |
| F_10 = shoup_poly(10, P_08, ZZ) | |
| P_18 = genprime(18, ZZ) | |
| F_20 = shoup_poly(20, P_18, ZZ) | |
| def timeit_shoup_poly_F10_zassenhaus(): | |
| gf_factor_sqf(F_10, P_08, ZZ, method='zassenhaus') | |
| def timeit_shoup_poly_F10_shoup(): | |
| gf_factor_sqf(F_10, P_08, ZZ, method='shoup') | |
| def timeit_shoup_poly_F20_zassenhaus(): | |
| gf_factor_sqf(F_20, P_18, ZZ, method='zassenhaus') | |
| def timeit_shoup_poly_F20_shoup(): | |
| gf_factor_sqf(F_20, P_18, ZZ, method='shoup') | |