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"""Rational number type based on Python integers. """
import operator
from sympy.core.numbers import Rational, Integer
from sympy.core.sympify import converter
from sympy.polys.polyutils import PicklableWithSlots
from sympy.polys.domains.domainelement import DomainElement
from sympy.printing.defaults import DefaultPrinting
from sympy.utilities import public
@public
class PythonRational(DefaultPrinting, PicklableWithSlots, DomainElement):
"""
Rational number type based on Python integers.
This was supposed to be needed for compatibility with older Python
versions which don't support Fraction. However, Fraction is very
slow so we don't use it anyway.
Examples
========
>>> from sympy.polys.domains import PythonRational
>>> PythonRational(1)
1
>>> PythonRational(2, 3)
2/3
>>> PythonRational(14, 10)
7/5
"""
__slots__ = ('p', 'q')
def parent(self):
from sympy.polys.domains import PythonRationalField
return PythonRationalField()
def __init__(self, p, q=1, _gcd=True):
from sympy.polys.domains.groundtypes import python_gcd as gcd
if isinstance(p, Integer):
p = p.p
elif isinstance(p, Rational):
p, q = p.p, p.q
if not q:
raise ZeroDivisionError('rational number')
elif q < 0:
p, q = -p, -q
if not p:
self.p = 0
self.q = 1
elif p == 1 or q == 1:
self.p = p
self.q = q
else:
if _gcd:
x = gcd(p, q)
if x != 1:
p //= x
q //= x
self.p = p
self.q = q
@classmethod
def new(cls, p, q):
obj = object.__new__(cls)
obj.p = p
obj.q = q
return obj
def __hash__(self):
if self.q == 1:
return hash(self.p)
else:
return hash((self.p, self.q))
def __int__(self):
p, q = self.p, self.q
if p < 0:
return -(-p//q)
return p//q
def __float__(self):
return float(self.p)/self.q
def __abs__(self):
return self.new(abs(self.p), self.q)
def __pos__(self):
return self.new(+self.p, self.q)
def __neg__(self):
return self.new(-self.p, self.q)
def __add__(self, other):
from sympy.polys.domains.groundtypes import python_gcd as gcd
if isinstance(other, PythonRational):
ap, aq, bp, bq = self.p, self.q, other.p, other.q
g = gcd(aq, bq)
if g == 1:
p = ap*bq + aq*bp
q = bq*aq
else:
q1, q2 = aq//g, bq//g
p, q = ap*q2 + bp*q1, q1*q2
g2 = gcd(p, g)
p, q = (p // g2), q * (g // g2)
elif isinstance(other, int):
p = self.p + self.q*other
q = self.q
else:
return NotImplemented
return self.__class__(p, q, _gcd=False)
def __radd__(self, other):
if not isinstance(other, int):
return NotImplemented
p = self.p + self.q*other
q = self.q
return self.__class__(p, q, _gcd=False)
def __sub__(self, other):
from sympy.polys.domains.groundtypes import python_gcd as gcd
if isinstance(other, PythonRational):
ap, aq, bp, bq = self.p, self.q, other.p, other.q
g = gcd(aq, bq)
if g == 1:
p = ap*bq - aq*bp
q = bq*aq
else:
q1, q2 = aq//g, bq//g
p, q = ap*q2 - bp*q1, q1*q2
g2 = gcd(p, g)
p, q = (p // g2), q * (g // g2)
elif isinstance(other, int):
p = self.p - self.q*other
q = self.q
else:
return NotImplemented
return self.__class__(p, q, _gcd=False)
def __rsub__(self, other):
if not isinstance(other, int):
return NotImplemented
p = self.q*other - self.p
q = self.q
return self.__class__(p, q, _gcd=False)
def __mul__(self, other):
from sympy.polys.domains.groundtypes import python_gcd as gcd
if isinstance(other, PythonRational):
ap, aq, bp, bq = self.p, self.q, other.p, other.q
x1 = gcd(ap, bq)
x2 = gcd(bp, aq)
p, q = ((ap//x1)*(bp//x2), (aq//x2)*(bq//x1))
elif isinstance(other, int):
x = gcd(other, self.q)
p = self.p*(other//x)
q = self.q//x
else:
return NotImplemented
return self.__class__(p, q, _gcd=False)
def __rmul__(self, other):
from sympy.polys.domains.groundtypes import python_gcd as gcd
if not isinstance(other, int):
return NotImplemented
x = gcd(self.q, other)
p = self.p*(other//x)
q = self.q//x
return self.__class__(p, q, _gcd=False)
def __truediv__(self, other):
from sympy.polys.domains.groundtypes import python_gcd as gcd
if isinstance(other, PythonRational):
ap, aq, bp, bq = self.p, self.q, other.p, other.q
x1 = gcd(ap, bp)
x2 = gcd(bq, aq)
p, q = ((ap//x1)*(bq//x2), (aq//x2)*(bp//x1))
elif isinstance(other, int):
x = gcd(other, self.p)
p = self.p//x
q = self.q*(other//x)
else:
return NotImplemented
return self.__class__(p, q, _gcd=False)
def __rtruediv__(self, other):
from sympy.polys.domains.groundtypes import python_gcd as gcd
if not isinstance(other, int):
return NotImplemented
x = gcd(self.p, other)
p = self.q*(other//x)
q = self.p//x
return self.__class__(p, q)
def __mod__(self, other):
return self.__class__(0)
def __divmod__(self, other):
return (self//other, self % other)
def __pow__(self, exp):
p, q = self.p, self.q
if exp < 0:
p, q, exp = q, p, -exp
return self.__class__(p**exp, q**exp, _gcd=False)
def __bool__(self):
return self.p != 0
def __eq__(self, other):
if isinstance(other, PythonRational):
return self.q == other.q and self.p == other.p
elif isinstance(other, int):
return self.q == 1 and self.p == other
else:
return NotImplemented
def __ne__(self, other):
return not self == other
def _cmp(self, other, op):
try:
diff = self - other
except TypeError:
return NotImplemented
else:
return op(diff.p, 0)
def __lt__(self, other):
return self._cmp(other, operator.lt)
def __le__(self, other):
return self._cmp(other, operator.le)
def __gt__(self, other):
return self._cmp(other, operator.gt)
def __ge__(self, other):
return self._cmp(other, operator.ge)
@property
def numer(self):
return self.p
@property
def denom(self):
return self.q
numerator = numer
denominator = denom
def sympify_pythonrational(arg):
return Rational(arg.p, arg.q)
converter[PythonRational] = sympify_pythonrational
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