Source code for

"""Implementation of :class:`FiniteField` class. """

from __future__ import print_function, division

from import Field
from import SimpleDomain
from import SymPyInteger
from import ModularIntegerFactory

from sympy.polys.polyerrors import CoercionFailed
from sympy.utilities import public

[docs]class FiniteField(Field, SimpleDomain): """General class for finite fields. """ rep = 'FF' is_FiniteField = is_FF = True is_Numerical = True has_assoc_Ring = False has_assoc_Field = True dom = None mod = None def __init__(self, mod, dom=None, symmetric=True): if mod <= 0: raise ValueError('modulus must be a positive integer, got %s' % mod) if dom is None: from import ZZ dom = ZZ self.dtype = ModularIntegerFactory(mod, dom, symmetric, self) = self.dtype(0) = self.dtype(1) self.dom = dom self.mod = mod def __str__(self): return 'GF(%s)' % self.mod def __hash__(self): return hash((self.__class__.__name__, self.dtype, self.mod, self.dom)) def __eq__(self, other): """Returns ``True`` if two domains are equivalent. """ return isinstance(other, FiniteField) and \ self.mod == other.mod and self.dom == other.dom
[docs] def characteristic(self): """Return the characteristic of this domain. """ return self.mod
[docs] def get_field(self): """Returns a field associated with ``self``. """ return self
[docs] def to_sympy(self, a): """Convert ``a`` to a SymPy object. """ return SymPyInteger(int(a))
[docs] def from_sympy(self, a): """Convert SymPy's Integer to SymPy's ``Integer``. """ if a.is_Integer: return self.dtype(self.dom.dtype(int(a))) elif a.is_Float and int(a) == a: return self.dtype(self.dom.dtype(int(a))) else: raise CoercionFailed("expected an integer, got %s" % a)
[docs] def from_FF_python(K1, a, K0=None): """Convert ``ModularInteger(int)`` to ``dtype``. """ return K1.dtype(K1.dom.from_ZZ_python(a.val, K0.dom))
[docs] def from_ZZ_python(K1, a, K0=None): """Convert Python's ``int`` to ``dtype``. """ return K1.dtype(K1.dom.from_ZZ_python(a, K0))
[docs] def from_QQ_python(K1, a, K0=None): """Convert Python's ``Fraction`` to ``dtype``. """ if a.denominator == 1: return K1.from_ZZ_python(a.numerator)
[docs] def from_FF_gmpy(K1, a, K0=None): """Convert ``ModularInteger(mpz)`` to ``dtype``. """ return K1.dtype(K1.dom.from_ZZ_gmpy(a.val, K0.dom))
[docs] def from_ZZ_gmpy(K1, a, K0=None): """Convert GMPY's ``mpz`` to ``dtype``. """ return K1.dtype(K1.dom.from_ZZ_gmpy(a, K0))
[docs] def from_QQ_gmpy(K1, a, K0=None): """Convert GMPY's ``mpq`` to ``dtype``. """ if a.denominator == 1: return K1.from_ZZ_gmpy(a.numerator)
[docs] def from_RealField(K1, a, K0): """Convert mpmath's ``mpf`` to ``dtype``. """ p, q = K0.to_rational(a) if q == 1: return K1.dtype(self.dom.dtype(p))