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"""Implementation of :class:`PythonIntegerRing` class. """
from sympy.core.numbers import int_valued
from sympy.polys.domains.groundtypes import (
PythonInteger, SymPyInteger, sqrt as python_sqrt,
factorial as python_factorial, python_gcdex, python_gcd, python_lcm,
)
from sympy.polys.domains.integerring import IntegerRing
from sympy.polys.polyerrors import CoercionFailed
from sympy.utilities import public
@public
class PythonIntegerRing(IntegerRing):
"""Integer ring based on Python's ``int`` type.
This will be used as :ref:`ZZ` if ``gmpy`` and ``gmpy2`` are not
installed. Elements are instances of the standard Python ``int`` type.
"""
dtype = PythonInteger
zero = dtype(0)
one = dtype(1)
alias = 'ZZ_python'
def __init__(self):
"""Allow instantiation of this domain. """
def to_sympy(self, a):
"""Convert ``a`` to a SymPy object. """
return SymPyInteger(a)
def from_sympy(self, a):
"""Convert SymPy's Integer to ``dtype``. """
if a.is_Integer:
return PythonInteger(a.p)
elif int_valued(a):
return PythonInteger(int(a))
else:
raise CoercionFailed("expected an integer, got %s" % a)
def from_FF_python(K1, a, K0):
"""Convert ``ModularInteger(int)`` to Python's ``int``. """
return K0.to_int(a)
def from_ZZ_python(K1, a, K0):
"""Convert Python's ``int`` to Python's ``int``. """
return a
def from_QQ(K1, a, K0):
"""Convert Python's ``Fraction`` to Python's ``int``. """
if a.denominator == 1:
return a.numerator
def from_QQ_python(K1, a, K0):
"""Convert Python's ``Fraction`` to Python's ``int``. """
if a.denominator == 1:
return a.numerator
def from_FF_gmpy(K1, a, K0):
"""Convert ``ModularInteger(mpz)`` to Python's ``int``. """
return PythonInteger(K0.to_int(a))
def from_ZZ_gmpy(K1, a, K0):
"""Convert GMPY's ``mpz`` to Python's ``int``. """
return PythonInteger(a)
def from_QQ_gmpy(K1, a, K0):
"""Convert GMPY's ``mpq`` to Python's ``int``. """
if a.denom() == 1:
return PythonInteger(a.numer())
def from_RealField(K1, a, K0):
"""Convert mpmath's ``mpf`` to Python's ``int``. """
p, q = K0.to_rational(a)
if q == 1:
return PythonInteger(p)
def gcdex(self, a, b):
"""Compute extended GCD of ``a`` and ``b``. """
return python_gcdex(a, b)
def gcd(self, a, b):
"""Compute GCD of ``a`` and ``b``. """
return python_gcd(a, b)
def lcm(self, a, b):
"""Compute LCM of ``a`` and ``b``. """
return python_lcm(a, b)
def sqrt(self, a):
"""Compute square root of ``a``. """
return python_sqrt(a)
def factorial(self, a):
"""Compute factorial of ``a``. """
return python_factorial(a)
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