Mapytex/pymath/fraction.py

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#!/usr/bin/env python
# encoding: utf-8
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from .arithmetic import gcd
from .generic import isNumber
from .operator import op
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__all__ = ['Fraction']
class Fraction(object):
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"""Fractions!"""
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def __init__(self, num, denom = 1):
"""To initiate a fraction we need a numerator and a denominator
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:param num: the numerator
:param denom: the denominator
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"""
self._num = num
self._denom = denom
self.isNumber = 1
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def simplify(self):
"""Simplify the fraction
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:returns: steps to simplify the fraction or the fraction if there is nothing to do
"""
steps = []
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if self._num == 0:
steps.append(0)
return steps
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if self._denom < 0:
n_frac = Fraction(-self._num, -self._denom)
steps.append(n_frac)
else:
n_frac = self
gcd_ = gcd(abs(n_frac._num), abs(n_frac._denom))
if gcd_ == n_frac._denom:
n_frac = n_frac._num // gcd_
steps.append(n_frac)
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elif gcd_ != 1:
n_frac = Fraction(n_frac._num // gcd_ , n_frac._denom // gcd_)
steps.append([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ])
steps.append(n_frac)
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return steps
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def __str__(self):
if self._denom == 1:
return str(self._num)
else:
return str(self._num) + " / " + str(self._denom)
def __repr__(self):
return "< Fraction " + self.__str__() + ">"
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def __txt__(self):
return str(self)
def __tex__(self):
if self._denom == 1:
return str(self._num)
else:
return "\\frac{{ {a} }}{{ {b} }}".format(a = self._num, b = self._denom)
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def __float__(self):
return self._num / self._denom
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def convert2fraction(self, other):
""" Convert a other into a fraction """
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if type(other) == Fraction:
#cool
number = other
else:
number = Fraction(other)
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return number
def __add__(self, other):
if other == 0:
return [self]
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number = self.convert2fraction(other)
steps = []
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if self._denom == number._denom:
com_denom = self._denom
num1 = self._num
num2 = number._num
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else:
gcd_denom = gcd(self._denom, number._denom)
coef1 = number._denom // gcd_denom
coef2 = self._denom // gcd_denom
steps.append([self._num, coef1, op.mul, self._denom, coef1, op.mul, op.div, number._num, coef2, op.mul, number._denom, coef2, op.mul, op.div,op.add])
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com_denom = self._denom * coef1
num1 = self._num * coef1
num2 = number._num * coef2
steps.append([num1, num2, op.add, com_denom, op.div])
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num = num1 + num2
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ans_frac = Fraction(num, com_denom)
steps.append(ans_frac)
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steps += ans_frac.simplify()
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return steps
def __radd__(self, other):
if other == 0:
return [self]
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number = self.convert2fraction(other)
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return number + self
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def __sub__(self, other):
if other == 0:
return [self]
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number = self.convert2fraction(other)
steps = []
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if self._denom == number._denom:
com_denom = self._denom
num1 = self._num
num2 = number._num
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else:
gcd_denom = gcd(self._denom, number._denom)
coef1 = number._denom // gcd_denom
coef2 = self._denom // gcd_denom
steps.append([self._num, coef1, op.mul, self._denom, coef1, op.mul, op.div, number._num, coef2, op.mul, number._denom, coef2, op.mul, op.div,op.sub])
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com_denom = self._denom * coef1
num1 = self._num * coef1
num2 = number._num * coef2
steps.append([num1, num2, op.sub, com_denom, op.div])
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num = num1 - num2
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ans_frac = Fraction(num, com_denom)
steps.append(ans_frac)
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steps += ans_frac.simplify()
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return steps
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def __rsub__(self, other):
if other == 0:
return [self]
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number = self.convert2fraction(other)
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return number - self
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def __neg__(self):
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f = Fraction(-self._num, self._denom)
return [f] + f.simplify()
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def __mul__(self, other):
steps = []
if other == 0:
return [0]
elif other == 1:
return [self]
elif type(other) == int:
gcd1 = gcd(other, self._denom)
if gcd1 != 1:
num = [self._num, int(other/gcd1), op.mul, gcd1,op.mul]
denom = [int(self._denom/gcd1), gcd1, op.mul]
else:
num = [self._num, other, op.mul]
denom = [self._denom]
steps.append(num + denom + [op.div])
num = int(self._num * other / gcd1)
denom = int(self._denom / gcd1)
else:
number = self.convert2fraction(other)
gcd1 = gcd(self._num, number._denom)
if gcd1 != 1:
num1 = [int(self._num/ gcd1), gcd1, op.mul]
denom2 = [int(number._denom/ gcd1), gcd1, op.mul]
else:
num1 = [self._num]
denom2 = [number._denom]
gcd2 = gcd(self._denom, number._num)
if gcd2 != 1:
num2 = [int(number._num/ gcd2), gcd2, op.mul]
denom1 = [int(self._denom/ gcd2), gcd2, op.mul]
else:
num2 = [number._num]
denom1 = [self._denom]
steps.append(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div])
num = int(self._num * number._num / (gcd1 * gcd2))
denom = int(self._denom * number._denom / (gcd1 * gcd2))
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ans_frac = Fraction(num, denom)
steps.append(ans_frac)
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steps += ans_frac.simplify()
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return steps
def __rmul__(self, other):
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return self * other
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def __truediv__(self, other):
if other == 0:
raise ZeroDivisionError("division by zero")
elif other == 1:
return [self]
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number = self.convert2fraction(other)
steps = []
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number = Fraction(number._denom, number._num)
steps.append([self, number, op.mul])
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steps += self * number
return steps
def __rtruediv__(self, other):
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number = self.convert2fraction(other)
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return number / self
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def __pow__(self, power):
""" overload **
>>> f = Fraction(3, 4)
>>> f**0
[1]
>>> f**1
[< Fraction 3 / 4>]
>>> f**3
[[3, 3, '^', 4, 3, '^', '/'], < Fraction 27 / 64>]
>>> f = Fraction(6, 4)
>>> f**3
[[6, 3, '^', 4, 3, '^', '/'], < Fraction 216 / 64>, [27, 8, '*', 8, 8, '*', '/'], < Fraction 27 / 8>]
"""
if not type(power) == int:
raise ValueError("Can't raise fraction to power {}".format(str(power)))
if power == 0:
return [1]
elif power == 1:
return [self]
else:
steps = [[self._num, power, op.pw, self._denom, power, op.pw, op.div]]
ans_frac = Fraction(self._num ** power, self._denom ** power)
steps.append(ans_frac)
steps += ans_frac.simplify()
return steps
def __xor__(self, power):
""" overload ^
>>> f = Fraction(3, 4)
>>> f^3
[[3, 3, '^', 4, 3, '^', '/'], < Fraction 27 / 64>]
>>> f = Fraction(6, 4)
>>> f^3
[[6, 3, '^', 4, 3, '^', '/'], < Fraction 216 / 64>, [27, 8, '*', 8, 8, '*', '/'], < Fraction 27 / 8>]
"""
return self.__pow__(power)
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def __abs__(self):
return Fraction(abs(self._num), abs(self._denom))
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def __eq__(self, other):
""" == """
if isNumber(other):
number = self.convert2fraction(other)
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return self._num * number._denom == self._denom * number._num
else:
return 0
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def __lt__(self, other):
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""" < """
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return float(self) < float(other)
def __le__(self, other):
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""" <= """
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return float(self) <= float(other)
def __gt__(self, other):
""" > """
return float(self) > float(other)
def __ge__(self, other):
""" >= """
return float(self) >= float(other)
if __name__ == '__main__':
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#f = Fraction(1, 12)
#g = Fraction(1, 12)
#h = Fraction(1,-5)
#t = Fraction(10,3)
#print("---------")
#print("1 + ", str(h))
#for i in (1 + h):
# print(i)
#print("---------")
#print(str(f) , "+", str(t))
#for i in (f + t):
# print(i)
#print("---------")
#print(str(f) , "+", str(g))
#for i in (f + g):
# print(i)
#print("---------")
#print(str(f) , "-", str(g))
#for i in (f - g):
# print(i)
#print("---------")
#print(str(f) , "*", str(g))
#for i in (f * g):
# print(i)
#print("---------")
#print(str(h) , "+", str(t))
#for i in (h + t):
# print(i)
#print("---------")
#print(str(h) , "-", str(t))
#for i in (h - t):
# print(i)
#print("---------")
#print(str(h) , "*", str(t))
#for i in (h * t):
# print(i)
#print("---------")
#print("-", str(h) )
#for i in (-h):
# print(i)
#print("---------")
#print(str(h) , "/", str(t))
#for i in (h / t):
# print(i)
#print("---------")
#print(str(h) , "+", str(0))
#for i in (h + 0):
# print(i)
#print("---------")
#print(str(h) , "*", str(1))
#for i in (h * 1):
# print(i)
#print("---------")
#print(str(h) , "*", str(0))
#for i in (h * 0):
# print(i)
#print("---------")
#print(str(h) , "*", str(4))
#for i in (h * 4):
# print(i)
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#print(f.simplify())
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import doctest
doctest.testmod()
# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del