My Rational class code:
from __future__ import division
import math as _math
def _gcf(a, b):
# Returns the greatest common factor of a and b.
a = abs(a)
b = abs(b)
while b:
a, b = b, a % b
return a
class Rational(object):
def __init__(self, numerator=0, denominator=1):
# Contructs the Rational object for numerator/denominator.
if not isinstance(numerator, (int)):
raise TypeError("Numerator must have integer type.")
if not isinstance(denominator, (int)):
raise TypeError("Denominator must have integer type.")
if not denominator:
raise ZeroDivisionError('rational construction')
self._d = denominator
self._n = numerator
self.normalize_self()
# Cancel the fraction to reduced form
def normalize_self(self):
factor = _gcf(self._n, self._d)
self._n = self._n // factor
self._d = self._d // factor
if self._d < 0:
self._n = -self._n
self._d = -self._d
def numerator(self):
return self._n
def denominator(self):
return self._d
def __repr__(self):
if self._d == 1:
return "Rational(%d)" % self._n
else:
return "Rational(%d, %d)" % (self._n, self._d)
def __str__(self):
if self._d == 1:
return str(self._n)
else:
return "%d/%d" % (self._n, self._d)
def __lt__(self, other):
selfNum = self._n * other._d
otherNum = other._n * self._d
def __hash__(self):
try:
return hash(float(self))
except OverflowError:
return hash(self)
def __float__(self):
return self._n / self._d
def __int__(self):
if self._n < 0:
return -int(-self._n // self._d)
else:
return int(self._n // self._d)
def __long__(self):
return int(self)
def __nonzero__(self):
return bool(self._n)
def __pos__(self):
return self
def __neg__(self):
return Rational(-self._n, self._d)
def __abs__(self):
if self._n < 0:
return -self
else:
return self
def __add__(self, other):
if isinstance(other, Rational):
return Rational(self._n * other._d + self._d * other._n,
self._d * other._d)
elif isinstance(other, (int)):
return Rational(self._n + self._d * other, self._d)
elif isinstance(other, (float, complex)):
return float(self) + other
else:
return NotImplemented
__radd__ = __add__
def __sub__(self, other):
if isinstance(other, Rational):
return Rational(self._n * other._d - self._d * other._n,
self._d * other._d)
elif isinstance(other, (int)):
return Rational(self._n - self._d * other, self._d)
elif isinstance(other, (float, complex)):
return float(self) - other
else:
return NotImplemented
def __rsub__(self, other):
if isinstance(other, (int)):
return Rational(other * self._d - self._n, self._d)
elif isinstance(other, (float, complex)):
return other - float(self)
else:
return NotImplemented
def __mul__(self, other):
if isinstance(other, Rational):
return Rational(self._n * other._n, self._d * other._d)
elif isinstance(other, (int)):
return Rational(self._n * other, self._d)
elif isinstance(other, (float, complex)):
return float(self) * other
else:
return NotImplemented
__rmul__ = __mul__
def __truediv__(self, other):
if isinstance(other, Rational):
return Rational(self._n * other._d, self._d * other._n)
elif isinstance(other, (int)):
return Rational(self._n, self._d * other)
elif isinstance(other, (float, complex)):
return float(self) / other
else:
return NotImplemented
__div__ = __truediv__
def __rtruediv__(self, other):
if isinstance(other, (int)):
return Rational(other * self._d, self._n)
elif isinstance(other, (float, complex)):
return other / float(self)
else:
return NotImplemented
__rdiv__ = __rtruediv__
def __floordiv__(self, other):
truediv = self / other
if isinstance(truediv, Rational):
return truediv._n // truediv._d
else:
return truediv // 1
def __rfloordiv__(self, other):
return (other / self) // 1
def __mod__(self, other):
return self - self // other * other
def __rmod__(self, other):
return other - other // self * self
def __divmod__(self, other):
return self // other, self % other
def __cmp__(self, other):
if other == 0:
return cmp(self._n, 0)
else:
return cmp(self - other, 0)
def __pow__(self, other):
if isinstance(other, (int)):
if other < 0:
return Rational(self._d ** -other, self._n ** -other)
else:
return Rational(self._n ** other, self._d ** other)
else:
return float(self) ** other
def __rpow__(self, other):
return other ** float(self)
def round(self, denominator):
# Return self rounded to nearest multiple of 1/denominator.
int_part, frac_part = divmod(self * denominator, 1)
round_direction = cmp(frac_part * 2, 1)
if round_direction == 0:
numerator = int_part + (int_part & 1) # round to even
elif round_direction < 0:
numerator = int_part
else:
numerator = int_part + 1
return Rational(numerator, denominator)
def rational_from_exact_float(x):
# Returns the exact Rational equivalent of x.
mantissa, exponent = _math.frexp(x)
mantissa = int(mantissa * 2 ** 53)
exponent -= 53
if exponent < 0:
return Rational(mantissa, 2 ** (-exponent))
else:
return Rational(mantissa * 2 ** exponent)
def rational_approx_smallest_denominator(x, tolerance):
tolerance = abs(tolerance)
n = 1
while True:
m = int(round(x * n))
result = Rational(m, n)
if abs(result - x) < tolerance:
return result
n += 1
def rational_approx_smallest_error(x, maxDenominator):
result = None
minError = x
for n in xrange(1, maxDenominator + 1):
m = int(round(x * n))
r = Rational(m, n)
error = abs(r - x)
if error == 0:
return r
elif error < minError:
result = r
minError = error
return result
def divide(x, y):
# Same as x/y, but returns a Rational if both are ints.
if isinstance(x, (int)) and isinstance(y, (int)):
return Rational(x, y)
else:
return x / y
I have this:
third = Rational(25, 10)
print ("third: {0}/{1}".format(third.numerator, third.denominator))
and it returns as an error of a sort: third: <bound method Rational.numerator of Rational(5, 2)>/<bound method Rational.denominator of Rational(5, 2)>
Not sure why that is?
And also, if the Rational number ends up being a whole number, how do I still make it a fraction? (If it equals 4, how to get it to say 4/1)
