Mapytex/pymath/fraction.py

458 lines
12 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 .render import txt, tex
__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
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()
[< Expression [1, 3, '*', 2, 3, '*', '/']>, < Fraction 1 / 2>]
>>> f = Fraction(0,3)
>>> f.simplify()
[0]
"""
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 gcd_ == n_frac._denom:
n_frac = n_frac._num // gcd_
steps.append(n_frac)
elif gcd_ != 1:
n_frac = Fraction(n_frac._num // gcd_ , n_frac._denom // gcd_)
steps.append(Expression([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ]))
steps.append(n_frac)
return steps
@property
def postfix(self):
"""Postfix form of the fraction
>>> f = Fraction(3, 5)
>>> f.postfix
[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))
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)
_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
[< Expression [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '+']>, < Expression [3, 6, '/', 4, 6, '/', '+']>, < Expression [< Fraction 3 / 6>, < Fraction 4 / 6>, '+']>, < Expression [3, 4, '+', 6, '/']>, < Expression [7, 6, '/']>, < Fraction 7 / 6>]
>>> f + 2
[< Expression [1, 1, '*', 2, 1, '*', '/', 2, 2, '*', 1, 2, '*', '/', '+']>, < Expression [1, 2, '/', 4, 2, '/', '+']>, < Expression [< Fraction 1 / 2>, < Fraction 4 / 2>, '+']>, < Expression [1, 4, '+', 2, '/']>, < Expression [5, 2, '/']>, < Fraction 5 / 2>]
>>> f = Fraction(3, 4)
>>> g = Fraction(5, 4)
>>> f + g
[< Expression [3, 5, '+', 4, '/']>, < Expression [8, 4, '/']>, 2]
"""
if other == 0:
return [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])
with Expression.tmp_render():
steps = list(exp.simplify())
return steps
def __radd__(self, other):
if other == 0:
return [self]
number = self.convert2fraction(other)
return number + self
def __sub__(self, other):
""" overload -
>>> f = Fraction(1, 2)
>>> g = Fraction(2, 3)
>>> f - g
[< Expression [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '-']>, < Expression [3, 6, '/', 4, 6, '/', '-']>, < Expression [< Fraction 3 / 6>, < Fraction 4 / 6>, '-']>, < Expression [3, 4, '-', 6, '/']>, < Expression [-1, 6, '/']>, < Fraction -1 / 6>]
"""
if other == 0:
return [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])
with Expression.tmp_render():
steps = list(exp.simplify())
return steps
def __rsub__(self, other):
if other == 0:
return [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 = Fraction(1, -2)
>>> f
< Fraction 1 / -2>
>>> -f
[< Fraction -1 / -2>, < Fraction 1 / 2>]
"""
f = Fraction(-self._num, self._denom)
with Expression.tmp_render():
steps = [f] + f.simplify()
return steps
def __mul__(self, other):
""" overload *
>>> f = Fraction(1, 2)
>>> g = Fraction(2, 3)
>>> f*g
[< Expression [1, 1, 2, '*', '*', 1, 2, '*', 3, '*', '/']>, < Expression [1, 2, '*', 2, 3, '*', '/']>, < Expression [2, 6, '/']>, < Expression [1, 2, '*', 3, 2, '*', '/']>, < Fraction 1 / 3>]
>>> f * 0
[0]
>>> f*1
[< Fraction 1 / 2>]
>>> f*4
[< Expression [1, 2, '*', 2, '*', 1, 2, '*', '/']>, < Expression [2, 2, '*', 2, '/']>, < Expression [4, 2, '/']>, 2]
"""
steps = []
if other == 0:
return [0]
elif other == 1:
return [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])
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])
with Expression.tmp_render():
steps = list(exp.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(Expression([self, number, op.mul]))
steps += self * number
return steps
def __rtruediv__(self, other):
number = self.convert2fraction(other)
return number / self
def __pow__(self, power):
""" overload **
>>> f = Fraction(3, 4)
>>> f**0
[1]
>>> f**1
[< Fraction 3 / 4>]
>>> f**3
[< Expression [3, 3, '^', 4, 3, '^', '/']>, < Expression [27, 64, '/']>, < Fraction 27 / 64>]
>>> f = Fraction(6, 4)
>>> f**3
[< Expression [6, 3, '^', 4, 3, '^', '/']>, < Expression [216, 64, '/']>, < Expression [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:
exp = Expression([self._num, power, op.pw, self._denom, power, op.pw, op.div])
with Expression.tmp_render():
steps = list(exp.simplify())
return steps
def __xor__(self, power):
""" overload ^
>>> f = Fraction(3, 4)
>>> f^0
[1]
>>> f^1
[< Fraction 3 / 4>]
>>> f^3
[< Expression [3, 3, '^', 4, 3, '^', '/']>, < Expression [27, 64, '/']>, < Fraction 27 / 64>]
>>> f = Fraction(6, 4)
>>> f^3
[< Expression [6, 3, '^', 4, 3, '^', '/']>, < Expression [216, 64, '/']>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>]
"""
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)
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())
import doctest
doctest.testmod()
# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del