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"""Implementation of :class:`GMPYIntegerRing` class. """
from sympy.polys.domains.groundtypes import (
GMPYInteger, SymPyInteger,
factorial as gmpy_factorial,
gmpy_gcdex, gmpy_gcd, gmpy_lcm, sqrt as gmpy_sqrt,
)
from sympy.core.numbers import int_valued
from sympy.polys.domains.integerring import IntegerRing
from sympy.polys.polyerrors import CoercionFailed
from sympy.utilities import public
@public
class GMPYIntegerRing(IntegerRing):
"""Integer ring based on GMPY's ``mpz`` type.
This will be the implementation of :ref:`ZZ` if ``gmpy`` or ``gmpy2`` is
installed. Elements will be of type ``gmpy.mpz``.
"""
dtype = GMPYInteger
zero = dtype(0)
one = dtype(1)
tp = type(one)
alias = 'ZZ_gmpy'
def __init__(self):
"""Allow instantiation of this domain. """
def to_sympy(self, a):
"""Convert ``a`` to a SymPy object. """
return SymPyInteger(int(a))
def from_sympy(self, a):
"""Convert SymPy's Integer to ``dtype``. """
if a.is_Integer:
return GMPYInteger(a.p)
elif int_valued(a):
return GMPYInteger(int(a))
else:
raise CoercionFailed("expected an integer, got %s" % a)
def from_FF_python(K1, a, K0):
"""Convert ``ModularInteger(int)`` to GMPY's ``mpz``. """
return K0.to_int(a)
def from_ZZ_python(K1, a, K0):
"""Convert Python's ``int`` to GMPY's ``mpz``. """
return GMPYInteger(a)
def from_QQ(K1, a, K0):
"""Convert Python's ``Fraction`` to GMPY's ``mpz``. """
if a.denominator == 1:
return GMPYInteger(a.numerator)
def from_QQ_python(K1, a, K0):
"""Convert Python's ``Fraction`` to GMPY's ``mpz``. """
if a.denominator == 1:
return GMPYInteger(a.numerator)
def from_FF_gmpy(K1, a, K0):
"""Convert ``ModularInteger(mpz)`` to GMPY's ``mpz``. """
return K0.to_int(a)
def from_ZZ_gmpy(K1, a, K0):
"""Convert GMPY's ``mpz`` to GMPY's ``mpz``. """
return a
def from_QQ_gmpy(K1, a, K0):
"""Convert GMPY ``mpq`` to GMPY's ``mpz``. """
if a.denominator == 1:
return a.numerator
def from_RealField(K1, a, K0):
"""Convert mpmath's ``mpf`` to GMPY's ``mpz``. """
p, q = K0.to_rational(a)
if q == 1:
return GMPYInteger(p)
def from_GaussianIntegerRing(K1, a, K0):
if a.y == 0:
return a.x
def gcdex(self, a, b):
"""Compute extended GCD of ``a`` and ``b``. """
h, s, t = gmpy_gcdex(a, b)
return s, t, h
def gcd(self, a, b):
"""Compute GCD of ``a`` and ``b``. """
return gmpy_gcd(a, b)
def lcm(self, a, b):
"""Compute LCM of ``a`` and ``b``. """
return gmpy_lcm(a, b)
def sqrt(self, a):
"""Compute square root of ``a``. """
return gmpy_sqrt(a)
def factorial(self, a):
"""Compute factorial of ``a``. """
return gmpy_factorial(a)
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