530 lines
15 KiB
Python
530 lines
15 KiB
Python
#!/usr/bin/env python
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# encoding: utf-8
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from .arithmetic import gcd
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from .generic import isNumber
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from .operator import op
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from .expression import Expression
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from .explicable import Explicable
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from .render import txt, tex
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from copy import copy
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__all__ = ['Fraction']
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class Fraction(Explicable):
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"""Fractions!"""
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def __init__(self, num, denom = 1):
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"""To initiate a fraction we need a numerator and a denominator
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:param num: the numerator
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:param denom: the denominator
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"""
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super(Fraction, self).__init__()
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self._num = num
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self._denom = denom
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self.isNumber = 1
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def simplify(self):
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"""Simplify the fraction
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:returns: steps to simplify the fraction or the fraction if there is nothing to do
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>>> f = Fraction(3, 6)
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>>> f.simplify()
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< Fraction 1 / 2>
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>>> for i in f.simplify().explain():
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... print(i)
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\\frac{ 3 }{ 6 }
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\\frac{ 1 \\times 3 }{ 2 \\times 3 }
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\\frac{ 1 }{ 2 }
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>>> f = Fraction(6,9)
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>>> f.simplify()
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< Fraction 2 / 3>
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>>> for i in f.simplify().explain():
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... print(i)
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\\frac{ 6 }{ 9 }
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\\frac{ 2 \\times 3 }{ 3 \\times 3 }
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\\frac{ 2 }{ 3 }
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>>> f = Fraction(0,3)
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>>> f.simplify()
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0
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"""
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ini_step = [Expression(self.postfix_tokens)]
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if self._num == 0:
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return Expression([0])
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elif self._denom < 0:
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n_frac = Fraction(-self._num, -self._denom)
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ans = n_frac.simplify()
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ans.steps = ini_step + ans.steps
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return ans
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gcd_ = gcd(abs(self._num), abs(self._denom))
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if gcd_ == self._denom:
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n_frac = self._num // gcd_
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return Expression([n_frac])
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elif gcd_ != 1:
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n_frac = Fraction(self._num // gcd_ , self._denom // gcd_)
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ini_step += [Expression([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ])]
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n_frac.steps = ini_step + n_frac.steps
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return n_frac
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else:
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return self
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@property
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def postfix_tokens(self):
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"""Postfix form of the fraction
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>>> f = Fraction(3, 5)
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>>> f.postfix_tokens
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[3, 5, '/']
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"""
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if self._denom == 1:
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return [self._num]
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else:
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return [self._num, self._denom, op.div]
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def __str__(self):
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return str(Expression(self.postfix_tokens))
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def __repr__(self):
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return "< Fraction {num} / {denom}>".format(num=self._num, denom = self._denom)
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def __txt__(self):
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old_render = Expression.get_render()
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Expression.set_render(txt)
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_txt = self.__str__()
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Expression.set_render(old_render)
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return _txt
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def __tex__(self):
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old_render = Expression.get_render()
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Expression.set_render(tex)
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_tex = self.__str__()
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Expression.set_render(old_render)
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return _tex
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def __float__(self):
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return self._num / self._denom
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def convert2fraction(self, other):
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""" Convert a other into a fraction """
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if type(other) == Fraction:
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#cool
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number = other
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else:
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number = Fraction(other)
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return number
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def __add__(self, other):
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""" overload +
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>>> f = Fraction(1, 2)
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>>> g = Fraction(2, 3)
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>>> f + g
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< Fraction 7 / 6>
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>>> (f+g).steps
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[< <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>, '+']]
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>>> f + 2
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< Fraction 5 / 2>
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>>> (f+2).steps
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[< <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>, '+']]
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>>> f = Fraction(3, 4)
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>>> g = Fraction(5, 4)
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>>> f + g
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2
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>>> (f+g).steps
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[< <class 'pymath.expression.Expression'> [3, 4, '/', 5, 4, '/', '+'] >, [3, 5, '+', 4, '/'], [8, 4, '/']]
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>>> f+0
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< Fraction 3 / 4>
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>>> (f+0).steps
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[]
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"""
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if other == 0:
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return copy(self)
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number = self.convert2fraction(other)
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if self._denom == number._denom:
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com_denom = self._denom
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num1 = self._num
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num2 = number._num
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exp = Expression([num1, num2, op.add, com_denom, op.div])
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else:
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gcd_denom = gcd(self._denom, number._denom)
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coef1 = number._denom // gcd_denom
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coef2 = self._denom // gcd_denom
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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])
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ini_step = Expression(self.postfix_tokens + number.postfix_tokens + [op.add])
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ans = exp.simplify()
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ans.steps = [ini_step] + ans.steps
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return ans
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def __radd__(self, other):
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if other == 0:
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return Expression(self.postfix_tokens)
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number = self.convert2fraction(other)
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return number + self
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def __sub__(self, other):
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""" overload -
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>>> f = Fraction(1, 2)
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>>> g = Fraction(2, 3)
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>>> f - g
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< Fraction -1 / 6>
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>>> (f-g).steps
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[< <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>, '-']]
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>>> f - 0
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< Fraction 1 / 2>
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>>> (f-0).steps
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[]
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"""
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if other == 0:
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return copy(self)
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number = self.convert2fraction(other)
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if self._denom == number._denom:
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com_denom = self._denom
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num1 = self._num
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num2 = number._num
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exp = Expression([num1, num2, op.sub, com_denom, op.div])
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else:
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gcd_denom = gcd(self._denom, number._denom)
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coef1 = number._denom // gcd_denom
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coef2 = self._denom // gcd_denom
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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])
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ini_step = Expression(self.postfix_tokens + number.postfix_tokens + [op.sub])
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ans = exp.simplify()
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ans.steps = [ini_step] + ans.steps
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return ans
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def __rsub__(self, other):
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if other == 0:
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return copy(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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""" overload - (as arity 1 operator)
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>>> f = Fraction(1, 2)
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>>> -f
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< Fraction -1 / 2>
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>>> (-f).steps
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[]
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>>> f = Fraction(1, -2)
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>>> f
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< Fraction 1 / -2>
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>>> -f
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< Fraction 1 / 2>
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>>> (-f).steps
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[< <class 'pymath.expression.Expression'> [-1, -2, '/'] >]
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"""
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f = Fraction(-self._num, self._denom)
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ans = f.simplify()
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return ans
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def __mul__(self, other):
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""" overload *
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>>> f = Fraction(1, 2)
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>>> g = Fraction(2, 3)
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>>> f*g
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< Fraction 1 / 3>
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>>> (f*g).steps
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[< <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, '*', '/'] >]
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>>> f * 0
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0
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>>> (f*0).steps
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[]
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>>> f*1
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< Fraction 1 / 2>
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>>> (f*1).steps
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[]
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>>> f*4
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2
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>>> (f*4).steps
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[< <class 'pymath.expression.Expression'> [1, 2, '/', 4, '*'] >, [1, 2, '*', 2, '*', 1, 2, '*', '/'], [2, 2, '*', 2, '/'], [4, 2, '/']]
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"""
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steps = []
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if other == 0:
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return Expression([0])
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elif other == 1:
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return copy(self)
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# TODO: Changer dans le cas où il y a trop de 1 |dim. déc. 28 10:44:10 CET 2014
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elif type(other) == int:
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gcd1 = gcd(other, self._denom)
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if gcd1 != 1:
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num = [self._num, int(other/gcd1), op.mul, gcd1,op.mul]
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denom = [int(self._denom/gcd1), gcd1, op.mul]
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else:
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num = [self._num, other, op.mul]
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denom = [self._denom]
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exp = Expression(num + denom + [op.div])
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ini_step = Expression(self.postfix_tokens + [other, op.mul])
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else:
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number = self.convert2fraction(other)
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gcd1 = gcd(self._num, number._denom)
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if gcd1 != 1:
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num1 = [int(self._num/ gcd1), gcd1, op.mul]
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denom2 = [int(number._denom/ gcd1), gcd1, op.mul]
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else:
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num1 = [self._num]
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denom2 = [number._denom]
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gcd2 = gcd(self._denom, number._num)
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if gcd2 != 1:
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num2 = [int(number._num/ gcd2), gcd2, op.mul]
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denom1 = [int(self._denom/ gcd2), gcd2, op.mul]
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else:
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num2 = [number._num]
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denom1 = [self._denom]
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exp = Expression(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div])
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ini_step = Expression(self.postfix_tokens + number.postfix_tokens + [op.mul])
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ans = exp.simplify()
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ans.steps = [ini_step] + ans.steps
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return ans
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def __rmul__(self, other):
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return self * other
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def __truediv__(self, other):
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""" overload /
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>>> f = Fraction(1,2)
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>>> g = Fraction(3,4)
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>>> f / 0
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Traceback (most recent call last):
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...
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ZeroDivisionError: division by zero
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>>> f / 1
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< Fraction 1 / 2>
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>>> (f/1).steps
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[]
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>>> f / g
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< Fraction 2 / 3>
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"""
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if other == 0:
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raise ZeroDivisionError("division by zero")
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elif other == 1:
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return copy(self)
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number = self.convert2fraction(other)
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ini_step = Expression(self.postfix_tokens + number.postfix_tokens + [op.div])
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number = Fraction(number._denom, number._num)
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ans = self * number
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ans.steps = [ini_step] + ans.steps
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return ans
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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):
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""" overload **
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>>> f = Fraction(3, 4)
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>>> f**0
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1
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>>> (f**0).steps
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[]
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>>> f**1
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< Fraction 3 / 4>
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>>> (f**1).steps
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[]
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>>> f**3
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< Fraction 27 / 64>
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>>> (f**3).steps
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[< <class 'pymath.expression.Expression'> [3, 4, '/', 3, '^'] >, [3, 3, '^', 4, 3, '^', '/'], [27, 64, '/'], [27, 64, '/']]
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>>> f = Fraction(6, 4)
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>>> f**3
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< Fraction 27 / 8>
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>>> (f**3).steps
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[< <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, '*', '/'] >]
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"""
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if not type(power) == int:
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raise ValueError("Can't raise fraction to power {}".format(str(power)))
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if power == 0:
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return Expression([1])
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elif power == 1:
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return copy(self)
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else:
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ini_step = Expression(self.postfix_tokens + [power, op.pw])
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exp = Expression([self._num, power, op.pw, self._denom, power, op.pw, op.div])
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ans = exp.simplify()
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ans.steps = [ini_step] + ans.steps
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return ans
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def __xor__(self, power):
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""" overload ^
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Work like **
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>>> f = Fraction(3, 4)
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>>> f^0
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1
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>>> f^1
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< Fraction 3 / 4>
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>>> f^3
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< Fraction 27 / 64>
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"""
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return self.__pow__(power)
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def __abs__(self):
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return Fraction(abs(self._num), abs(self._denom))
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def __eq__(self, other):
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""" == """
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if isNumber(other):
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number = self.convert2fraction(other)
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return self._num * number._denom == self._denom * number._num
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else:
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return 0
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def __lt__(self, other):
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""" < """
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return float(self) < float(other)
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def __le__(self, other):
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""" <= """
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return float(self) <= float(other)
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def __gt__(self, other):
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""" > """
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return float(self) > float(other)
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def __ge__(self, other):
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""" >= """
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return float(self) >= float(other)
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def __copy__(self):
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""" Copying the fraction removing steps where it is from """
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return Fraction(self._num, self._denom)
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if __name__ == '__main__':
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f = Fraction(1, 12)
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g = Fraction(6, 12)
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for i in g.simplify().explain():
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print("g = ",i)
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h = Fraction(1,-5)
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t = Fraction(10,3)
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print("---------")
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for i in (0 + h).explain():
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print('0 + h = ',i)
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#print("---------")
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#print(str(f) , "+", str(t))
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#for i in (f + t):
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# print(i)
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#print("---------")
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#print(str(f) , "+", str(g))
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#for i in (f + g):
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# print(i)
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#print("---------")
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#print(str(f) , "-", str(g))
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#for i in (f - g):
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# print(i)
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#print("---------")
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#print(str(f) , "*", str(g))
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#for i in (f * g):
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# print(i)
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#print("---------")
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#print(str(h) , "+", str(t))
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#for i in (h + t):
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# print(i)
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#print("---------")
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#print(str(h) , "-", str(t))
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#for i in (h - t):
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# print(i)
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#print("---------")
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#print(str(h) , "*", str(t))
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#for i in (h * t):
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# print(i)
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#print("---------")
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#print("-", str(h) )
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#for i in (-h):
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# print(i)
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#print("---------")
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#print(str(h) , "/", str(t))
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#for i in (h / t):
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# print(i)
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#print("---------")
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#print(str(h) , "+", str(0))
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#for i in (h + 0):
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# print(i)
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#print("---------")
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#print(str(h) , "*", str(1))
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#for i in (h * 1):
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# print(i)
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#print("---------")
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#print(str(h) , "*", str(0))
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#for i in (h * 0):
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# print(i)
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#print("---------")
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#print(str(h) , "*", str(4))
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#for i in (h * 4):
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# print(i)
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#print(f.simplify())
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import doctest
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doctest.testmod()
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# -----------------------------
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# Reglages pour 'vim'
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# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del
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