531 lines
15 KiB
Python
531 lines
15 KiB
Python
#!/usr/bin/env python
|
|
# encoding: utf-8
|
|
|
|
from .arithmetic import gcd
|
|
from .generic import isNumber
|
|
from .operator import op
|
|
from .expression import Expression
|
|
from .explicable import Explicable
|
|
from .render import txt, tex
|
|
from copy import copy
|
|
|
|
|
|
__all__ = ['Fraction']
|
|
|
|
class Fraction(Explicable):
|
|
"""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
|
|
|
|
"""
|
|
super(Fraction, self).__init__()
|
|
self._num = num
|
|
self._denom = denom
|
|
|
|
self.isNumber = 1
|
|
|
|
def simplify(self):
|
|
"""Simplify the fraction
|
|
|
|
:returns: steps to simplify the fraction or the fraction if there is nothing to do
|
|
|
|
>>> f = Fraction(3, 6)
|
|
>>> f.simplify()
|
|
< Fraction 1 / 2>
|
|
>>> for i in f.simplify().explain():
|
|
... print(i)
|
|
\\frac{ 3 }{ 6 }
|
|
\\frac{ 1 \\times 3 }{ 2 \\times 3 }
|
|
\\frac{ 1 }{ 2 }
|
|
>>> f = Fraction(6,9)
|
|
>>> f.simplify()
|
|
< Fraction 2 / 3>
|
|
>>> for i in f.simplify().explain():
|
|
... print(i)
|
|
\\frac{ 6 }{ 9 }
|
|
\\frac{ 2 \\times 3 }{ 3 \\times 3 }
|
|
\\frac{ 2 }{ 3 }
|
|
>>> f = Fraction(0,3)
|
|
>>> f.simplify()
|
|
0
|
|
|
|
"""
|
|
ini_step = [Expression(self.postfix_tokens)]
|
|
|
|
if self._num == 0:
|
|
return Expression([0])
|
|
|
|
elif self._denom < 0:
|
|
n_frac = Fraction(-self._num, -self._denom)
|
|
ans = n_frac.simplify()
|
|
ans.steps = ini_step + ans.steps
|
|
return ans
|
|
|
|
gcd_ = gcd(abs(self._num), abs(self._denom))
|
|
if gcd_ == self._denom:
|
|
n_frac = self._num // gcd_
|
|
return Expression([n_frac])
|
|
|
|
elif gcd_ != 1:
|
|
n_frac = Fraction(self._num // gcd_ , self._denom // gcd_)
|
|
ini_step += [Expression([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ])]
|
|
|
|
n_frac.steps = ini_step + n_frac.steps
|
|
return n_frac
|
|
|
|
else:
|
|
return self
|
|
|
|
@property
|
|
def postfix_tokens(self):
|
|
"""Postfix form of the fraction
|
|
|
|
>>> f = Fraction(3, 5)
|
|
>>> f.postfix_tokens
|
|
[3, 5, '/']
|
|
|
|
"""
|
|
if self._denom == 1:
|
|
return [self._num]
|
|
else:
|
|
return [self._num, self._denom, op.div]
|
|
|
|
def __str__(self):
|
|
return str(Expression(self.postfix_tokens))
|
|
|
|
def __repr__(self):
|
|
return "< Fraction {num} / {denom}>".format(num=self._num, denom = self._denom)
|
|
|
|
def __txt__(self):
|
|
# TODO: À simplifier je ne comprends plus le pourquoi du comment de cette méthode. |ven. févr. 27 09:21:49 CET 2015
|
|
old_render = Expression.get_render()
|
|
Expression.set_render(txt)
|
|
_txt = self.__str__()
|
|
Expression.set_render(old_render)
|
|
|
|
return _txt
|
|
|
|
def __tex__(self):
|
|
old_render = Expression.get_render()
|
|
Expression.set_render(tex)
|
|
_txt = self.__str__()
|
|
Expression.set_render(old_render)
|
|
|
|
return _txt
|
|
|
|
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):
|
|
""" overload +
|
|
|
|
>>> f = Fraction(1, 2)
|
|
>>> g = Fraction(2, 3)
|
|
>>> f + g
|
|
< Fraction 7 / 6>
|
|
>>> (f+g).steps
|
|
[< <class 'pymath.expression.Expression'> [1, 2, '/', 2, 3, '/', '+'] >, [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '+'], [3, 6, '/', 4, 6, '/', '+'], [< Fraction 3 / 6>, < Fraction 4 / 6>, '+'], [< Fraction 3 / 6>, < Fraction 4 / 6>, '+']]
|
|
>>> f + 2
|
|
< Fraction 5 / 2>
|
|
>>> (f+2).steps
|
|
[< <class 'pymath.expression.Expression'> [1, 2, '/', 2, '+'] >, [1, 1, '*', 2, 1, '*', '/', 2, 2, '*', 1, 2, '*', '/', '+'], [1, 2, '/', 4, 2, '/', '+'], [< Fraction 1 / 2>, < Fraction 4 / 2>, '+'], [< Fraction 1 / 2>, < Fraction 4 / 2>, '+']]
|
|
>>> f = Fraction(3, 4)
|
|
>>> g = Fraction(5, 4)
|
|
>>> f + g
|
|
2
|
|
>>> (f+g).steps
|
|
[< <class 'pymath.expression.Expression'> [3, 4, '/', 5, 4, '/', '+'] >, [3, 5, '+', 4, '/'], [8, 4, '/']]
|
|
>>> f+0
|
|
< Fraction 3 / 4>
|
|
>>> (f+0).steps
|
|
[]
|
|
|
|
"""
|
|
|
|
if other == 0:
|
|
return copy(self)
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
if self._denom == number._denom:
|
|
com_denom = self._denom
|
|
num1 = self._num
|
|
num2 = number._num
|
|
|
|
exp = Expression([num1, num2, op.add, com_denom, op.div])
|
|
|
|
else:
|
|
gcd_denom = gcd(self._denom, number._denom)
|
|
coef1 = number._denom // gcd_denom
|
|
coef2 = self._denom // gcd_denom
|
|
|
|
exp = Expression([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])
|
|
|
|
ini_step = Expression(self.postfix_tokens) + Expression(number.postfix_tokens)
|
|
ans = exp.simplify()
|
|
ans.steps = [ini_step] + ans.steps
|
|
return ans
|
|
|
|
def __radd__(self, other):
|
|
if other == 0:
|
|
return Expression(self.postfix_tokens)
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
return number + self
|
|
|
|
def __sub__(self, other):
|
|
""" overload -
|
|
|
|
>>> f = Fraction(1, 2)
|
|
>>> g = Fraction(2, 3)
|
|
>>> f - g
|
|
< Fraction -1 / 6>
|
|
>>> (f-g).steps
|
|
[< <class 'pymath.expression.Expression'> [1, 2, '/', 2, 3, '/', '-'] >, [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '-'], [3, 6, '/', 4, 6, '/', '-'], [< Fraction 3 / 6>, < Fraction 4 / 6>, '-'], [< Fraction 3 / 6>, < Fraction 4 / 6>, '-']]
|
|
>>> f - 0
|
|
< Fraction 1 / 2>
|
|
>>> (f-0).steps
|
|
[]
|
|
|
|
"""
|
|
if other == 0:
|
|
return copy(self)
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
if self._denom == number._denom:
|
|
com_denom = self._denom
|
|
num1 = self._num
|
|
num2 = number._num
|
|
|
|
exp = Expression([num1, num2, op.sub, com_denom, op.div])
|
|
|
|
else:
|
|
gcd_denom = gcd(self._denom, number._denom)
|
|
coef1 = number._denom // gcd_denom
|
|
coef2 = self._denom // gcd_denom
|
|
|
|
exp = Expression([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])
|
|
|
|
ini_step = Expression(self.postfix_tokens) - Expression(number.postfix_tokens)
|
|
ans = exp.simplify()
|
|
ans.steps = [ini_step] + ans.steps
|
|
return ans
|
|
|
|
def __rsub__(self, other):
|
|
if other == 0:
|
|
return copy(self)
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
return number - self
|
|
|
|
def __neg__(self):
|
|
""" overload - (as arity 1 operator)
|
|
|
|
>>> f = Fraction(1, 2)
|
|
>>> -f
|
|
< Fraction -1 / 2>
|
|
>>> (-f).steps
|
|
[]
|
|
>>> f = Fraction(1, -2)
|
|
>>> f
|
|
< Fraction 1 / -2>
|
|
>>> -f
|
|
< Fraction 1 / 2>
|
|
>>> (-f).steps
|
|
[< <class 'pymath.expression.Expression'> [-1, -2, '/'] >]
|
|
|
|
"""
|
|
f = Fraction(-self._num, self._denom)
|
|
ans = f.simplify()
|
|
|
|
return ans
|
|
|
|
def __mul__(self, other):
|
|
""" overload *
|
|
|
|
>>> f = Fraction(1, 2)
|
|
>>> g = Fraction(2, 3)
|
|
>>> f*g
|
|
< Fraction 1 / 3>
|
|
>>> (f*g).steps
|
|
[< <class 'pymath.expression.Expression'> [1, 2, '/', 2, 3, '/', '*'] >, [1, 1, 2, '*', '*', 1, 2, '*', 3, '*', '/'], [1, 2, '*', 2, 3, '*', '/'], [2, 6, '/'], < <class 'pymath.expression.Expression'> [2, 6, '/'] >, < <class 'pymath.expression.Expression'> [1, 2, '*', 3, 2, '*', '/'] >]
|
|
>>> f * 0
|
|
0
|
|
>>> (f*0).steps
|
|
[]
|
|
>>> f*1
|
|
< Fraction 1 / 2>
|
|
>>> (f*1).steps
|
|
[]
|
|
>>> f*4
|
|
2
|
|
>>> (f*4).steps
|
|
[< <class 'pymath.expression.Expression'> [1, 2, '/', 4, '*'] >, [1, 2, '*', 2, '*', 1, 2, '*', '/'], [2, 2, '*', 2, '/'], [4, 2, '/']]
|
|
|
|
"""
|
|
steps = []
|
|
|
|
if other == 0:
|
|
return Expression([0])
|
|
elif other == 1:
|
|
return copy(self)
|
|
|
|
# TODO: Changer dans le cas où il y a trop de 1 |dim. déc. 28 10:44:10 CET 2014
|
|
|
|
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]
|
|
|
|
exp = Expression(num + denom + [op.div])
|
|
ini_step = Expression(self.postfix_tokens) * Expression([other])
|
|
|
|
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]
|
|
|
|
|
|
exp = Expression(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div])
|
|
|
|
ini_step = Expression(self.postfix_tokens) * Expression(number.postfix_tokens)
|
|
ans = exp.simplify()
|
|
ans.steps = [ini_step] + ans.steps
|
|
return ans
|
|
|
|
def __rmul__(self, other):
|
|
return self * other
|
|
|
|
def __truediv__(self, other):
|
|
""" overload /
|
|
|
|
>>> f = Fraction(1,2)
|
|
>>> g = Fraction(3,4)
|
|
>>> f / 0
|
|
Traceback (most recent call last):
|
|
...
|
|
ZeroDivisionError: division by zero
|
|
>>> f / 1
|
|
< Fraction 1 / 2>
|
|
>>> (f/1).steps
|
|
[]
|
|
>>> f / g
|
|
< Fraction 2 / 3>
|
|
|
|
"""
|
|
if other == 0:
|
|
raise ZeroDivisionError("division by zero")
|
|
elif other == 1:
|
|
return copy(self)
|
|
|
|
number = self.convert2fraction(other)
|
|
|
|
ini_step = Expression(self.postfix_tokens) / Expression(number.postfix_tokens)
|
|
|
|
number = Fraction(number._denom, number._num)
|
|
ans = self * number
|
|
|
|
ans.steps = [ini_step] + ans.steps
|
|
return ans
|
|
|
|
def __rtruediv__(self, other):
|
|
number = self.convert2fraction(other)
|
|
|
|
return number / self
|
|
|
|
def __pow__(self, power):
|
|
""" overload **
|
|
|
|
>>> f = Fraction(3, 4)
|
|
>>> f**0
|
|
1
|
|
>>> (f**0).steps
|
|
[]
|
|
>>> f**1
|
|
< Fraction 3 / 4>
|
|
>>> (f**1).steps
|
|
[]
|
|
>>> f**3
|
|
< Fraction 27 / 64>
|
|
>>> (f**3).steps
|
|
[< <class 'pymath.expression.Expression'> [3, 4, '/', 3, '^'] >, [3, 3, '^', 4, 3, '^', '/'], [27, 64, '/'], [27, 64, '/']]
|
|
>>> f = Fraction(6, 4)
|
|
>>> f**3
|
|
< Fraction 27 / 8>
|
|
>>> (f**3).steps
|
|
[< <class 'pymath.expression.Expression'> [6, 4, '/', 3, '^'] >, [6, 3, '^', 4, 3, '^', '/'], [216, 64, '/'], < <class 'pymath.expression.Expression'> [216, 64, '/'] >, < <class 'pymath.expression.Expression'> [27, 8, '*', 8, 8, '*', '/'] >]
|
|
|
|
"""
|
|
if not type(power) == int:
|
|
raise ValueError("Can't raise fraction to power {}".format(str(power)))
|
|
|
|
if power == 0:
|
|
return Expression([1])
|
|
elif power == 1:
|
|
return copy(self)
|
|
else:
|
|
ini_step = Expression(self.postfix_tokens) ** power
|
|
exp = Expression([self._num, power, op.pw, self._denom, power, op.pw, op.div])
|
|
|
|
ans = exp.simplify()
|
|
ans.steps = [ini_step] + ans.steps
|
|
return ans
|
|
|
|
def __xor__(self, power):
|
|
""" overload ^
|
|
|
|
Work like **
|
|
|
|
>>> f = Fraction(3, 4)
|
|
>>> f^0
|
|
1
|
|
>>> f^1
|
|
< Fraction 3 / 4>
|
|
>>> f^3
|
|
< Fraction 27 / 64>
|
|
"""
|
|
|
|
return self.__pow__(power)
|
|
|
|
def __abs__(self):
|
|
return Fraction(abs(self._num), abs(self._denom))
|
|
|
|
def __eq__(self, other):
|
|
""" == """
|
|
if isNumber(other):
|
|
number = self.convert2fraction(other)
|
|
|
|
return self._num * number._denom == self._denom * number._num
|
|
else:
|
|
return 0
|
|
|
|
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)
|
|
|
|
def __copy__(self):
|
|
""" Copying the fraction removing steps where it is from """
|
|
return Fraction(self._num, self._denom)
|
|
|
|
|
|
|
|
if __name__ == '__main__':
|
|
f = Fraction(1, 12)
|
|
g = Fraction(6, 12)
|
|
for i in g.simplify().explain():
|
|
print("g = ",i)
|
|
h = Fraction(1,-5)
|
|
t = Fraction(10,3)
|
|
print("---------")
|
|
for i in (0 + h).explain():
|
|
print('0 + h = ',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())
|
|
|
|
import doctest
|
|
doctest.testmod()
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|