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