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svn+ssh://pythondev@svn.python.org/python/trunk ........ r60364 | neal.norwitz | 2008-01-27 19:09:48 +0100 (Sun, 27 Jan 2008) | 4 lines Update the comment and remove the close. If we close we can't flush anymore. We might still need to close after the for loop if flushing 6! times still doesn't cause the signal/exception. ........ r60365 | georg.brandl | 2008-01-27 19:14:43 +0100 (Sun, 27 Jan 2008) | 2 lines Remove effectless expression statement. ........ r60367 | neal.norwitz | 2008-01-27 19:19:04 +0100 (Sun, 27 Jan 2008) | 1 line Try to handle socket.errors properly in is_unavailable ........ r60370 | christian.heimes | 2008-01-27 20:01:45 +0100 (Sun, 27 Jan 2008) | 1 line Change isbasestring function as discussed on the cvs list a while ago ........ r60372 | neal.norwitz | 2008-01-27 21:03:13 +0100 (Sun, 27 Jan 2008) | 3 lines socket.error doesn't have a headers attribute like ProtocolError. Handle that situation where we catch socket.errors. ........ r60375 | georg.brandl | 2008-01-27 21:25:12 +0100 (Sun, 27 Jan 2008) | 2 lines Add refcounting extension to build config. ........ r60377 | jeffrey.yasskin | 2008-01-28 00:08:46 +0100 (Mon, 28 Jan 2008) | 6 lines Moved Rational._binary_float_to_ratio() to float.as_integer_ratio() because it's useful outside of rational numbers. This is my first C code that had to do anything significant. Please be more careful when looking over it. ........ r60378 | christian.heimes | 2008-01-28 00:34:59 +0100 (Mon, 28 Jan 2008) | 1 line Added clear cache methods to clear the internal type lookup cache for ref leak test runs. ........
460 lines
15 KiB
Python
Executable file
460 lines
15 KiB
Python
Executable file
# Originally contributed by Sjoerd Mullender.
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# Significantly modified by Jeffrey Yasskin <jyasskin at gmail.com>.
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"""Rational, infinite-precision, real numbers."""
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import math
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import numbers
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import operator
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import re
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__all__ = ["Rational"]
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RationalAbc = numbers.Rational
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def gcd(a, b):
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"""Calculate the Greatest Common Divisor of a and b.
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Unless b==0, the result will have the same sign as b (so that when
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b is divided by it, the result comes out positive).
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"""
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while b:
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a, b = b, a%b
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return a
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_RATIONAL_FORMAT = re.compile(
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r'^\s*(?P<sign>[-+]?)(?P<num>\d+)'
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r'(?:/(?P<denom>\d+)|\.(?P<decimal>\d+))?\s*$')
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class Rational(RationalAbc):
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"""This class implements rational numbers.
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Rational(8, 6) will produce a rational number equivalent to
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4/3. Both arguments must be Integral. The numerator defaults to 0
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and the denominator defaults to 1 so that Rational(3) == 3 and
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Rational() == 0.
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Rationals can also be constructed from strings of the form
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'[-+]?[0-9]+((/|.)[0-9]+)?', optionally surrounded by spaces.
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"""
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__slots__ = ('numerator', 'denominator')
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# We're immutable, so use __new__ not __init__
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def __new__(cls, numerator=0, denominator=1):
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"""Constructs a Rational.
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Takes a string like '3/2' or '1.5', another Rational, or a
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numerator/denominator pair.
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"""
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self = super(Rational, cls).__new__(cls)
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if denominator == 1:
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if isinstance(numerator, str):
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# Handle construction from strings.
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input = numerator
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m = _RATIONAL_FORMAT.match(input)
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if m is None:
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raise ValueError('Invalid literal for Rational: ' + input)
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numerator = m.group('num')
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decimal = m.group('decimal')
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if decimal:
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# The literal is a decimal number.
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numerator = int(numerator + decimal)
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denominator = 10**len(decimal)
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else:
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# The literal is an integer or fraction.
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numerator = int(numerator)
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# Default denominator to 1.
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denominator = int(m.group('denom') or 1)
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if m.group('sign') == '-':
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numerator = -numerator
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elif (not isinstance(numerator, numbers.Integral) and
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isinstance(numerator, RationalAbc)):
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# Handle copies from other rationals.
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other_rational = numerator
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numerator = other_rational.numerator
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denominator = other_rational.denominator
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if (not isinstance(numerator, numbers.Integral) or
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not isinstance(denominator, numbers.Integral)):
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raise TypeError("Rational(%(numerator)s, %(denominator)s):"
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" Both arguments must be integral." % locals())
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if denominator == 0:
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raise ZeroDivisionError('Rational(%s, 0)' % numerator)
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g = gcd(numerator, denominator)
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self.numerator = int(numerator // g)
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self.denominator = int(denominator // g)
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return self
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@classmethod
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def from_float(cls, f):
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"""Converts a finite float to a rational number, exactly.
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Beware that Rational.from_float(0.3) != Rational(3, 10).
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"""
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if not isinstance(f, float):
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raise TypeError("%s.from_float() only takes floats, not %r (%s)" %
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(cls.__name__, f, type(f).__name__))
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if math.isnan(f) or math.isinf(f):
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raise TypeError("Cannot convert %r to %s." % (f, cls.__name__))
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return cls(*f.as_integer_ratio())
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@classmethod
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def from_decimal(cls, dec):
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"""Converts a finite Decimal instance to a rational number, exactly."""
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from decimal import Decimal
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if not isinstance(dec, Decimal):
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raise TypeError(
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"%s.from_decimal() only takes Decimals, not %r (%s)" %
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(cls.__name__, dec, type(dec).__name__))
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if not dec.is_finite():
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# Catches infinities and nans.
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raise TypeError("Cannot convert %s to %s." % (dec, cls.__name__))
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sign, digits, exp = dec.as_tuple()
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digits = int(''.join(map(str, digits)))
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if sign:
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digits = -digits
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if exp >= 0:
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return cls(digits * 10 ** exp)
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else:
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return cls(digits, 10 ** -exp)
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@classmethod
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def from_continued_fraction(cls, seq):
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'Build a Rational from a continued fraction expessed as a sequence'
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n, d = 1, 0
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for e in reversed(seq):
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n, d = d, n
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n += e * d
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return cls(n, d) if seq else cls(0)
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def as_continued_fraction(self):
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'Return continued fraction expressed as a list'
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n = self.numerator
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d = self.denominator
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cf = []
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while d:
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e = int(n // d)
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cf.append(e)
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n -= e * d
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n, d = d, n
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return cf
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def approximate(self, max_denominator):
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'Best rational approximation with a denominator <= max_denominator'
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# XXX First cut at algorithm
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# Still needs rounding rules as specified at
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# http://en.wikipedia.org/wiki/Continued_fraction
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if self.denominator <= max_denominator:
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return self
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cf = self.as_continued_fraction()
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result = Rational(0)
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for i in range(1, len(cf)):
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new = self.from_continued_fraction(cf[:i])
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if new.denominator > max_denominator:
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break
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result = new
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return result
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def __repr__(self):
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"""repr(self)"""
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return ('Rational(%r,%r)' % (self.numerator, self.denominator))
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def __str__(self):
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"""str(self)"""
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if self.denominator == 1:
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return str(self.numerator)
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else:
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return '%s/%s' % (self.numerator, self.denominator)
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""" XXX This section needs a lot more commentary
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* Explain the typical sequence of checks, calls, and fallbacks.
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* Explain the subtle reasons why this logic was needed.
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* It is not clear how common cases are handled (for example, how
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does the ratio of two huge integers get converted to a float
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without overflowing the long-->float conversion.
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"""
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def _operator_fallbacks(monomorphic_operator, fallback_operator):
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"""Generates forward and reverse operators given a purely-rational
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operator and a function from the operator module.
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Use this like:
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__op__, __rop__ = _operator_fallbacks(just_rational_op, operator.op)
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"""
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def forward(a, b):
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if isinstance(b, RationalAbc):
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# Includes ints.
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return monomorphic_operator(a, b)
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elif isinstance(b, float):
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return fallback_operator(float(a), b)
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elif isinstance(b, complex):
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return fallback_operator(complex(a), b)
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else:
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return NotImplemented
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forward.__name__ = '__' + fallback_operator.__name__ + '__'
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forward.__doc__ = monomorphic_operator.__doc__
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def reverse(b, a):
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if isinstance(a, RationalAbc):
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# Includes ints.
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return monomorphic_operator(a, b)
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elif isinstance(a, numbers.Real):
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return fallback_operator(float(a), float(b))
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elif isinstance(a, numbers.Complex):
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return fallback_operator(complex(a), complex(b))
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else:
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return NotImplemented
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reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
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reverse.__doc__ = monomorphic_operator.__doc__
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return forward, reverse
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def _add(a, b):
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"""a + b"""
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return Rational(a.numerator * b.denominator +
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b.numerator * a.denominator,
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a.denominator * b.denominator)
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__add__, __radd__ = _operator_fallbacks(_add, operator.add)
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def _sub(a, b):
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"""a - b"""
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return Rational(a.numerator * b.denominator -
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b.numerator * a.denominator,
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a.denominator * b.denominator)
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__sub__, __rsub__ = _operator_fallbacks(_sub, operator.sub)
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def _mul(a, b):
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"""a * b"""
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return Rational(a.numerator * b.numerator, a.denominator * b.denominator)
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__mul__, __rmul__ = _operator_fallbacks(_mul, operator.mul)
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def _div(a, b):
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"""a / b"""
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return Rational(a.numerator * b.denominator,
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a.denominator * b.numerator)
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__truediv__, __rtruediv__ = _operator_fallbacks(_div, operator.truediv)
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def __floordiv__(a, b):
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"""a // b"""
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return math.floor(a / b)
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def __rfloordiv__(b, a):
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"""a // b"""
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return math.floor(a / b)
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def __mod__(a, b):
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"""a % b"""
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div = a // b
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return a - b * div
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def __rmod__(b, a):
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"""a % b"""
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div = a // b
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return a - b * div
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def __pow__(a, b):
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"""a ** b
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If b is not an integer, the result will be a float or complex
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since roots are generally irrational. If b is an integer, the
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result will be rational.
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"""
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if isinstance(b, RationalAbc):
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if b.denominator == 1:
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power = b.numerator
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if power >= 0:
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return Rational(a.numerator ** power,
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a.denominator ** power)
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else:
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return Rational(a.denominator ** -power,
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a.numerator ** -power)
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else:
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# A fractional power will generally produce an
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# irrational number.
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return float(a) ** float(b)
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else:
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return float(a) ** b
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def __rpow__(b, a):
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"""a ** b"""
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if b.denominator == 1 and b.numerator >= 0:
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# If a is an int, keep it that way if possible.
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return a ** b.numerator
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if isinstance(a, RationalAbc):
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return Rational(a.numerator, a.denominator) ** b
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if b.denominator == 1:
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return a ** b.numerator
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return a ** float(b)
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def __pos__(a):
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"""+a: Coerces a subclass instance to Rational"""
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return Rational(a.numerator, a.denominator)
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def __neg__(a):
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"""-a"""
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return Rational(-a.numerator, a.denominator)
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def __abs__(a):
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"""abs(a)"""
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return Rational(abs(a.numerator), a.denominator)
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def __trunc__(a):
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"""trunc(a)"""
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if a.numerator < 0:
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return -(-a.numerator // a.denominator)
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else:
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return a.numerator // a.denominator
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__int__ = __trunc__
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def __floor__(a):
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"""Will be math.floor(a) in 3.0."""
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return a.numerator // a.denominator
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def __ceil__(a):
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"""Will be math.ceil(a) in 3.0."""
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# The negations cleverly convince floordiv to return the ceiling.
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return -(-a.numerator // a.denominator)
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def __round__(self, ndigits=None):
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"""Will be round(self, ndigits) in 3.0.
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Rounds half toward even.
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"""
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if ndigits is None:
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floor, remainder = divmod(self.numerator, self.denominator)
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if remainder * 2 < self.denominator:
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return floor
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elif remainder * 2 > self.denominator:
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return floor + 1
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# Deal with the half case:
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elif floor % 2 == 0:
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return floor
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else:
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return floor + 1
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shift = 10**abs(ndigits)
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# See _operator_fallbacks.forward to check that the results of
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# these operations will always be Rational and therefore have
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# round().
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if ndigits > 0:
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return Rational(round(self * shift), shift)
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else:
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return Rational(round(self / shift) * shift)
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def __hash__(self):
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"""hash(self)
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Tricky because values that are exactly representable as a
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float must have the same hash as that float.
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"""
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# XXX since this method is expensive, consider caching the result
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if self.denominator == 1:
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# Get integers right.
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return hash(self.numerator)
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# Expensive check, but definitely correct.
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if self == float(self):
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return hash(float(self))
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else:
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# Use tuple's hash to avoid a high collision rate on
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# simple fractions.
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return hash((self.numerator, self.denominator))
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def __eq__(a, b):
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"""a == b"""
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if isinstance(b, RationalAbc):
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return (a.numerator == b.numerator and
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a.denominator == b.denominator)
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if isinstance(b, numbers.Complex) and b.imag == 0:
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b = b.real
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if isinstance(b, float):
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return a == a.from_float(b)
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else:
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# XXX: If b.__eq__ is implemented like this method, it may
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# give the wrong answer after float(a) changes a's
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# value. Better ways of doing this are welcome.
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return float(a) == b
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def _subtractAndCompareToZero(a, b, op):
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"""Helper function for comparison operators.
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Subtracts b from a, exactly if possible, and compares the
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result with 0 using op, in such a way that the comparison
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won't recurse. If the difference raises a TypeError, returns
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NotImplemented instead.
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"""
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if isinstance(b, numbers.Complex) and b.imag == 0:
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b = b.real
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if isinstance(b, float):
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b = a.from_float(b)
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try:
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# XXX: If b <: Real but not <: RationalAbc, this is likely
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# to fall back to a float. If the actual values differ by
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# less than MIN_FLOAT, this could falsely call them equal,
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# which would make <= inconsistent with ==. Better ways of
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# doing this are welcome.
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diff = a - b
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except TypeError:
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return NotImplemented
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if isinstance(diff, RationalAbc):
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return op(diff.numerator, 0)
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return op(diff, 0)
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def __lt__(a, b):
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"""a < b"""
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return a._subtractAndCompareToZero(b, operator.lt)
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def __gt__(a, b):
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"""a > b"""
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return a._subtractAndCompareToZero(b, operator.gt)
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def __le__(a, b):
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"""a <= b"""
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return a._subtractAndCompareToZero(b, operator.le)
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def __ge__(a, b):
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"""a >= b"""
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return a._subtractAndCompareToZero(b, operator.ge)
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def __bool__(a):
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"""a != 0"""
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return a.numerator != 0
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# support for pickling, copy, and deepcopy
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def __reduce__(self):
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return (self.__class__, (str(self),))
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def __copy__(self):
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if type(self) == Rational:
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return self # I'm immutable; therefore I am my own clone
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return self.__class__(self.numerator, self.denominator)
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def __deepcopy__(self, memo):
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if type(self) == Rational:
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return self # My components are also immutable
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return self.__class__(self.numerator, self.denominator)
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