"""
A performant numpy extension for Galois fields.
"""
from .version import __version__
from .algorithm import prev_prime, next_prime, factors, prime_factors, is_prime, euclidean_algorithm, extended_euclidean_algorithm, \
chinese_remainder_theorem, euler_totient, carmichael, modular_exp, primitive_roots, primitive_root, \
min_poly
from .conway import conway_polynomial
from .gf import GFBase
from .gf2 import GF2
from .gf2m import GF2mBase, GF2m_factory
from .gfp import GFpBase, GFp_factory
from .poly import Poly
# Create the default GF2 class and target the numba ufuncs for "cpu" (lowest overhead)
GF2.target("cpu")
GF2.alpha = GF2(1)
# Define the GF2 primitve polynomial here, not in gf2.py, to avoid a circular dependency.
# The primitive polynomial is p(x) = x - alpha, where alpha=1. Over GF2, this is equivalent
# to p(x) = x + 1
GF2.prim_poly = min_poly(GF2.alpha, GF2, 1)
[docs]def GF_factory(p, m, prim_poly=None, rebuild=False): # pylint: disable=redefined-outer-name
"""
Factory function to construct Galois field array classes of type GF(p^m).
If `p = 2` and `m = 1`, this function will return `galois.GF2`. If `p = 2` and `m > 1`, this function will
invoke `galois.GF2m_factory()`. If `p is prime` and `m = 1`, this function will invoke `galois.GFp_factory()`.
If `p is prime` and `m > 1`, this function will invoke `galois.GFpm_factory()`.
Parameters
----------
p : int
The prime characteristic of the field GF(p^m).
m : int
The degree of the prime characteristic of the field GF(p^m).
prim_poly : galois.Poly, optional
The primitive polynomial of the field. Default is `None` which will auto-determine the primitive polynomial.
rebuild : bool, optional
A flag to force a rebuild of the class and its lookup tables. Default is `False` which will return the cached,
previously-built class if it exists.
Returns
-------
galois.GF2Base or galois.GFpBase
A new Galois field class that is a sublcass of `galois.GFBase`.
"""
if not isinstance(p, int):
raise TypeError(f"Galois field prime characteristic `p` must be an integer, not {type(p)}")
if not isinstance(m, int):
raise TypeError(f"Galois field characteristic degree `m` must be an integer, not {type(m)}")
if not (prim_poly is None or isinstance(prim_poly, Poly)):
raise TypeError(f"Primitive polynomial `prim_poly` must be either None or galois.Poly, not {type(prim_poly)}")
if not isinstance(rebuild, bool):
raise TypeError(f"Rebuild Galois field class flag `rebuild` must be a bool, not {type(rebuild)}")
if not is_prime(p):
raise ValueError(f"Galois field prime characteristic `p` must be prime, not {p}")
if not m >= 1:
raise ValueError(f"Galois field characteristic degree `m` must be >= 1, not {m}")
if p == 2 and m == 1:
if not (prim_poly is None or prim_poly is GF2.prim_poly):
raise ValueError(f"In GF(2), the primitive polynomial `prim_poly` must be either None or {GF2.prim_poly}, not {prim_poly}")
cls = GF2
elif p == 2:
cls = GF2m_factory(m, rebuild=rebuild)
else:
cls = GFp_factory(p, rebuild=rebuild)
return cls