Mapytex/pymath/fraction.py

530 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):
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)
_tex = self.__str__()
Expression.set_render(old_render)
return _tex
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 + number.postfix_tokens + [op.add])
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 + number.postfix_tokens + [op.sub])
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 + [other, op.mul])
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 + number.postfix_tokens + [op.mul])
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 + number.postfix_tokens + [op.div])
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, op.pw])
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()
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