331 lines
8.2 KiB
Python
331 lines
8.2 KiB
Python
#!/usr/bin/env python
|
|
# encoding: utf-8
|
|
|
|
from .arithmetic import gcd
|
|
|
|
__all__ = ['Fraction']
|
|
|
|
class Fraction(object):
|
|
"""Fractions!"""
|
|
|
|
def __init__(self, num, denom = 1):
|
|
"""To initiate a fraction we need a numerator and a denominator
|
|
|
|
:param num: the numerator
|
|
:param denom: the denominator
|
|
|
|
"""
|
|
self._num = num
|
|
self._denom = denom
|
|
|
|
def simplify(self):
|
|
"""Simplify the fraction
|
|
|
|
:returns: steps to simplify the fraction or the fraction if there is nothing to do
|
|
"""
|
|
steps = []
|
|
|
|
if self._num == 0:
|
|
steps.append(0)
|
|
|
|
return steps
|
|
|
|
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 n_frac._num == n_frac._denom:
|
|
n_frac = Fraction(1,1)
|
|
steps.append(n_frac)
|
|
|
|
elif gcd_ != 1:
|
|
n_frac = Fraction(n_frac._num // gcd_ , n_frac._denom // gcd_)
|
|
steps.append([n_frac._num, gcd_, '*', n_frac._denom, gcd_, '*', '/' ])
|
|
|
|
steps.append(n_frac)
|
|
|
|
return steps
|
|
|
|
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__() + ">"
|
|
|
|
def __float__(self):
|
|
return self._num / self._denom
|
|
|
|
def convert2fraction(self, other):
|
|
""" Convert a other into a fraction """
|
|
if type(other) == Fraction:
|
|
#cool
|
|
number = other
|
|
else:
|
|
number = Fraction(other)
|
|
|
|
return number
|
|
|
|
def __add__(self, other):
|
|
if other == 0:
|
|
return [self]
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
steps = []
|
|
|
|
if self._denom == number._denom:
|
|
com_denom = self._denom
|
|
num1 = self._num
|
|
num2 = number._num
|
|
|
|
else:
|
|
gcd_denom = gcd(self._denom, number._denom)
|
|
coef1 = number._denom // gcd_denom
|
|
coef2 = self._denom // gcd_denom
|
|
|
|
steps.append([self._num, coef1, "*", self._denom, coef1, "*", '/', number._num, coef2, "*", number._denom, coef2, "*", "/",'+'])
|
|
|
|
com_denom = self._denom * coef1
|
|
num1 = self._num * coef1
|
|
num2 = number._num * coef2
|
|
|
|
steps.append([num1, num2, '+', com_denom, '/'])
|
|
|
|
num = num1 + num2
|
|
|
|
ans_frac = Fraction(num, com_denom)
|
|
steps.append(ans_frac)
|
|
steps += ans_frac.simplify()
|
|
|
|
return steps
|
|
|
|
def __radd__(self, other):
|
|
if other == 0:
|
|
return [self]
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
return number + self
|
|
|
|
def __sub__(self, other):
|
|
if other == 0:
|
|
return [self]
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
steps = []
|
|
|
|
if self._denom == number._denom:
|
|
com_denom = self._denom
|
|
num1 = self._num
|
|
num2 = number._num
|
|
|
|
else:
|
|
gcd_denom = gcd(self._denom, number._denom)
|
|
coef1 = number._denom // gcd_denom
|
|
coef2 = self._denom // gcd_denom
|
|
|
|
steps.append([self._num, coef1, "*", self._denom, coef1, "*", '/', number._num, coef2, "*", number._denom, coef2, "*", "/",'-'])
|
|
|
|
com_denom = self._denom * coef1
|
|
num1 = self._num * coef1
|
|
num2 = number._num * coef2
|
|
|
|
steps.append([num1, num2, '-', com_denom, '/'])
|
|
|
|
num = num1 - num2
|
|
|
|
ans_frac = Fraction(num, com_denom)
|
|
steps.append(ans_frac)
|
|
steps += ans_frac.simplify()
|
|
|
|
return steps
|
|
|
|
def __rsub__(self, other):
|
|
if other == 0:
|
|
return [self]
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
return number - self
|
|
|
|
def __neg__(self):
|
|
return Fraction(-self._num,self._denom).simplify()
|
|
|
|
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), "*", gcd1,"*"]
|
|
denom = [int(self._denom/gcd1), gcd1, "*"]
|
|
else:
|
|
num = [self._num, other, "*"]
|
|
denom = [self._denom]
|
|
steps.append(num + denom + ["/"])
|
|
|
|
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, "*"]
|
|
denom2 = [int(number._denom/ gcd1), gcd1, "*"]
|
|
else:
|
|
num1 = [self._num]
|
|
denom2 = [number._denom]
|
|
|
|
gcd2 = gcd(self._denom, number._num)
|
|
if gcd2 != 1:
|
|
num2 = [int(number._num/ gcd2), gcd2, "*"]
|
|
denom1 = [int(self._denom/ gcd2), gcd2, "*"]
|
|
else:
|
|
num2 = [number._num]
|
|
denom1 = [self._denom]
|
|
|
|
|
|
steps.append(num1 + num2 + [ '*'] + denom1 + denom2 + ['*', '/'])
|
|
|
|
num = int(self._num * number._num / (gcd1 * gcd2))
|
|
denom = int(self._denom * number._denom / (gcd1 * gcd2))
|
|
|
|
ans_frac = Fraction(num, denom)
|
|
steps.append(ans_frac)
|
|
steps += ans_frac.simplify()
|
|
|
|
return steps
|
|
|
|
def __rmul__(self, other):
|
|
return self * other
|
|
|
|
def __truediv__(self, other):
|
|
if other == 0:
|
|
raise ZeroDivisionError("division by zero")
|
|
elif other == 1:
|
|
return [self]
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
steps = []
|
|
number = Fraction(number._denom, number._num)
|
|
steps.append([self, number, "*"])
|
|
steps += self * number
|
|
|
|
return steps
|
|
|
|
def __rtruediv__(self, other):
|
|
number = self.convert2fraction(other)
|
|
|
|
return number / self
|
|
|
|
def __abs__(self):
|
|
return Fraction(abs(self._num), abs(self._denom))
|
|
|
|
def __eq__(self, other):
|
|
""" == """
|
|
number = self.convert2fraction(other)
|
|
|
|
return self._num * number._denom == self._denom * number._num
|
|
|
|
def __lt__(self, other):
|
|
""" < """
|
|
return float(self) < float(other)
|
|
|
|
def __le__(self, other):
|
|
""" <= """
|
|
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__':
|
|
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)
|
|
|
|
#print(f.simplify())
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|