diff --git a/pymath/fraction.py b/pymath/fraction.py index 4b9ff3e..9cf4c91 100644 --- a/pymath/fraction.py +++ b/pymath/fraction.py @@ -4,13 +4,15 @@ from .arithmetic import gcd from .generic import isNumber from .operator import op -from .expression import Expression +from .expression import Expression, Renderable +from .explicable import Explicable from .render import txt, tex +from copy import copy __all__ = ['Fraction'] -class Fraction(object): +class Fraction(Explicable, Renderable): """Fractions!""" def __init__(self, num, denom = 1): @@ -20,6 +22,7 @@ class Fraction(object): :param denom: the denominator """ + super(Fraction, self).__init__() self._num = num self._denom = denom @@ -32,44 +35,57 @@ class Fraction(object): >>> f = Fraction(3, 6) >>> f.simplify() - [< Expression [1, 3, '*', 2, 3, '*', '/']>, < Fraction 1 / 2>] + < 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] + 0 """ - steps = [] + ini_step = [Expression(self.postfix_tokens)] if self._num == 0: - steps.append(0) + return Expression([0]) - return steps - - if self._denom < 0: + elif self._denom < 0: n_frac = Fraction(-self._num, -self._denom) - steps.append(n_frac) - else: - n_frac = self + ans = n_frac.simplify() + ans.steps = ini_step + ans.steps + return ans - 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) + 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(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 ])) + 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 ])] - steps.append(n_frac) + n_frac.steps = ini_step + n_frac.steps + return n_frac - return steps + else: + return self @property - def postfix(self): + def postfix_tokens(self): """Postfix form of the fraction >>> f = Fraction(3, 5) - >>> f.postfix + >>> f.postfix_tokens [3, 5, '/'] """ @@ -79,12 +95,13 @@ class Fraction(object): return [self._num, self._denom, op.div] def __str__(self): - return str(Expression(self.postfix)) + 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__() @@ -119,18 +136,28 @@ class Fraction(object): >>> 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>] + < Fraction 7 / 6> + >>> (f+g).steps + [< [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 - [< 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>] + < Fraction 5 / 2> + >>> (f+2).steps + [< [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 - [< Expression [3, 5, '+', 4, '/']>, < Expression [8, 4, '/']>, 2] + 2 + >>> (f+g).steps + [< [3, 4, '/', 5, 4, '/', '+'] >, [3, 5, '+', 4, '/'], [8, 4, '/']] + >>> f+0 + < Fraction 3 / 4> + >>> (f+0).steps + [] """ if other == 0: - return [self] + return copy(self) number = self.convert2fraction(other) @@ -148,14 +175,14 @@ class Fraction(object): 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 + 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 [self] + return Expression(self.postfix_tokens) number = self.convert2fraction(other) @@ -167,11 +194,17 @@ class Fraction(object): >>> 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>] + < Fraction -1 / 6> + >>> (f-g).steps + [< [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 [self] + return copy(self) number = self.convert2fraction(other) @@ -189,38 +222,40 @@ class Fraction(object): 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 + 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 [self] + return copy(self) number = self.convert2fraction(other) return number - self def __neg__(self): - """ overload - (as arity 1 operator + """ overload - (as arity 1 operator) >>> f = Fraction(1, 2) >>> -f - [< Fraction -1 / 2>] + < Fraction -1 / 2> + >>> (-f).steps + [] >>> f = Fraction(1, -2) >>> f < Fraction 1 / -2> >>> -f - [< Fraction -1 / -2>, < Fraction 1 / 2>] + < Fraction 1 / 2> + >>> (-f).steps + [< [-1, -2, '/'] >] """ f = Fraction(-self._num, self._denom) + ans = f.simplify() - with Expression.tmp_render(): - steps = [f] + f.simplify() - - return steps + return ans def __mul__(self, other): """ overload * @@ -228,21 +263,29 @@ class Fraction(object): >>> 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>] + < Fraction 1 / 3> + >>> (f*g).steps + [< [1, 2, '/', 2, 3, '/', '*'] >, [1, 1, 2, '*', '*', 1, 2, '*', 3, '*', '/'], [1, 2, '*', 2, 3, '*', '/'], [2, 6, '/'], < [2, 6, '/'] >, < [1, 2, '*', 3, 2, '*', '/'] >] >>> f * 0 - [0] + 0 + >>> (f*0).steps + [] >>> f*1 - [< Fraction 1 / 2>] + < Fraction 1 / 2> + >>> (f*1).steps + [] >>> f*4 - [< Expression [1, 2, '*', 2, '*', 1, 2, '*', '/']>, < Expression [2, 2, '*', 2, '/']>, < Expression [4, 2, '/']>, 2] + 2 + >>> (f*4).steps + [< [1, 2, '/', 4, '*'] >, [1, 2, '*', 2, '*', 1, 2, '*', '/'], [2, 2, '*', 2, '/'], [4, 2, '/']] """ steps = [] if other == 0: - return [0] + return Expression([0]) elif other == 1: - return [self] + return copy(self) # TODO: Changer dans le cas où il y a trop de 1 |dim. déc. 28 10:44:10 CET 2014 @@ -256,6 +299,7 @@ class Fraction(object): denom = [self._denom] exp = Expression(num + denom + [op.div]) + ini_step = Expression(self.postfix_tokens) * Expression([other]) else: number = self.convert2fraction(other) @@ -279,28 +323,45 @@ class Fraction(object): exp = Expression(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div]) - with Expression.tmp_render(): - steps = list(exp.simplify()) - - return steps + 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 [self] + return copy(self) number = self.convert2fraction(other) - steps = [] - number = Fraction(number._denom, number._num) - steps.append(Expression([self, number, op.mul])) - steps += self * number + ini_step = Expression(self.postfix_tokens) / Expression(number.postfix_tokens) - return steps + 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) @@ -312,44 +373,51 @@ class Fraction(object): >>> f = Fraction(3, 4) >>> f**0 - [1] + 1 + >>> (f**0).steps + [] >>> f**1 - [< Fraction 3 / 4>] + < Fraction 3 / 4> + >>> (f**1).steps + [] >>> f**3 - [< Expression [3, 3, '^', 4, 3, '^', '/']>, < Expression [27, 64, '/']>, < Fraction 27 / 64>] + < Fraction 27 / 64> + >>> (f**3).steps + [< [3, 4, '/', 3, '^'] >, [3, 3, '^', 4, 3, '^', '/'], [27, 64, '/'], [27, 64, '/']] >>> f = Fraction(6, 4) >>> f**3 - [< Expression [6, 3, '^', 4, 3, '^', '/']>, < Expression [216, 64, '/']>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>] + < Fraction 27 / 8> + >>> (f**3).steps + [< [6, 4, '/', 3, '^'] >, [6, 3, '^', 4, 3, '^', '/'], [216, 64, '/'], < [216, 64, '/'] >, < [27, 8, '*', 8, 8, '*', '/'] >] """ if not type(power) == int: raise ValueError("Can't raise fraction to power {}".format(str(power))) if power == 0: - return [1] + return Expression([1]) elif power == 1: - return [self] + 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]) - with Expression.tmp_render(): - steps = list(exp.simplify()) - return steps + + 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] + 1 >>> f^1 - [< Fraction 3 / 4>] + < 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>] - + < Fraction 27 / 64> """ return self.__pow__(power) @@ -382,17 +450,22 @@ class Fraction(object): """ >= """ 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(1, 12) - #h = Fraction(1,-5) - #t = Fraction(10,3) - #print("---------") - #print("1 + ", str(h)) - #for i in (1 + h): - # print(i) + 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):