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modernize Fraction and add doctests

This commit is contained in:
Lafrite 2014-12-27 16:04:30 +01:00
parent dfb056e1cf
commit 30f9554ff2
1 changed files with 107 additions and 23 deletions
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130
pymath/fraction.py
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@ -4,6 +4,9 @@
from .arithmetic import gcd from .arithmetic import gcd
from .generic import isNumber from .generic import isNumber
from .operator import op from .operator import op
from .expression import Expression
from .render import txt, tex
__all__ = ['Fraction'] __all__ = ['Fraction']
@ -26,6 +29,14 @@ class Fraction(object):
"""Simplify the fraction """Simplify the fraction
:returns: steps to simplify the fraction or the fraction if there is nothing to do :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 = [] steps = []
@ -47,29 +58,47 @@ class Fraction(object):
elif gcd_ != 1: elif gcd_ != 1:
n_frac = Fraction(n_frac._num // gcd_ , n_frac._denom // gcd_) n_frac = Fraction(n_frac._num // gcd_ , n_frac._denom // gcd_)
steps.append([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ]) steps.append(Expression([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ]))
steps.append(n_frac) steps.append(n_frac)
return steps return steps
def __str__(self): @property
def postfix(self):
"""Postfix form of the fraction
>>> f = Fraction(3, 5)
>>> f.postfix
[3, 5, '/']
"""
if self._denom == 1: if self._denom == 1:
return str(self._num) return [self._num]
else: else:
return str(self._num) + " / " + str(self._denom) return [self._num, self._denom, op.div]
def __str__(self):
return str(Expression(self.postfix))
def __repr__(self): def __repr__(self):
return "< Fraction " + self.__str__() + ">" return "< Fraction {num} / {denom}>".format(num=self._num, denom = self._denom)
def __txt__(self): def __txt__(self):
return str(self) old_render = Expression.get_render()
Expression.set_render(txt)
_txt = self.__str__()
Expression.set_render(old_render)
return _txt
def __tex__(self): def __tex__(self):
if self._denom == 1: old_render = Expression.get_render()
return str(self._num) Expression.set_render(tex)
else: _txt = self.__str__()
return "\\frac{{ {a} }}{{ {b} }}".format(a = self._num, b = self._denom) Expression.set_render(old_render)
return _txt
def __float__(self): def __float__(self):
return self._num / self._denom return self._num / self._denom
@ -85,6 +114,21 @@ class Fraction(object):
return number return number
def __add__(self, other): 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, 4, '+', 6, '/']>, < Fraction 7 / 6>]
>>> f + 2
[< Expression [1, 1, '*', 2, 1, '*', '/', 2, 2, '*', 1, 2, '*', '/', '+']>, < Expression [1, 4, '+', 2, '/']>, < Fraction 5 / 2>]
>>> f = Fraction(3, 4)
>>> g = Fraction(5, 4)
>>> f + g
[< Expression [3, 5, '+', 4, '/']>, < Fraction 8 / 4>, 2]
"""
if other == 0: if other == 0:
return [self] return [self]
@ -102,13 +146,13 @@ class Fraction(object):
coef1 = number._denom // gcd_denom coef1 = number._denom // gcd_denom
coef2 = self._denom // gcd_denom coef2 = self._denom // gcd_denom
steps.append([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]) steps.append(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]) )
com_denom = self._denom * coef1 com_denom = self._denom * coef1
num1 = self._num * coef1 num1 = self._num * coef1
num2 = number._num * coef2 num2 = number._num * coef2
steps.append([num1, num2, op.add, com_denom, op.div]) steps.append(Expression([num1, num2, op.add, com_denom, op.div]))
num = num1 + num2 num = num1 + num2
@ -127,6 +171,14 @@ class Fraction(object):
return number + self return number + self
def __sub__(self, other): 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, 4, '-', 6, '/']>, < Fraction -1 / 6>]
"""
if other == 0: if other == 0:
return [self] return [self]
@ -144,13 +196,13 @@ class Fraction(object):
coef1 = number._denom // gcd_denom coef1 = number._denom // gcd_denom
coef2 = self._denom // gcd_denom coef2 = self._denom // gcd_denom
steps.append([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]) steps.append(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]))
com_denom = self._denom * coef1 com_denom = self._denom * coef1
num1 = self._num * coef1 num1 = self._num * coef1
num2 = number._num * coef2 num2 = number._num * coef2
steps.append([num1, num2, op.sub, com_denom, op.div]) steps.append(Expression([num1, num2, op.sub, com_denom, op.div]))
num = num1 - num2 num = num1 - num2
@ -169,10 +221,36 @@ class Fraction(object):
return number - self return number - self
def __neg__(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) f = Fraction(-self._num, self._denom)
return [f] + f.simplify() return [f] + f.simplify()
def __mul__(self, other): def __mul__(self, other):
""" overload *
>>> f = Fraction(1, 2)
>>> g = Fraction(2, 3)
>>> f*g
[< Expression [1, 1, 2, '*', '*', 1, 2, '*', 3, '*', '/']>, < Fraction 1 / 3>]
>>> f * 0
[0]
>>> f*1
[< Fraction 1 / 2>]
>>> f*4
[< Expression [1, 2, '*', 2, '*', 1, 2, '*', '/']>, < Fraction 2 / 1>, 2]
"""
steps = [] steps = []
if other == 0: if other == 0:
@ -188,7 +266,7 @@ class Fraction(object):
else: else:
num = [self._num, other, op.mul] num = [self._num, other, op.mul]
denom = [self._denom] denom = [self._denom]
steps.append(num + denom + [op.div]) steps.append(Expression(num + denom + [op.div]))
num = int(self._num * other / gcd1) num = int(self._num * other / gcd1)
denom = int(self._denom / gcd1) denom = int(self._denom / gcd1)
@ -213,7 +291,7 @@ class Fraction(object):
denom1 = [self._denom] denom1 = [self._denom]
steps.append(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div]) steps.append(Expression(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div]))
num = int(self._num * number._num / (gcd1 * gcd2)) num = int(self._num * number._num / (gcd1 * gcd2))
denom = int(self._denom * number._denom / (gcd1 * gcd2)) denom = int(self._denom * number._denom / (gcd1 * gcd2))
@ -237,7 +315,7 @@ class Fraction(object):
steps = [] steps = []
number = Fraction(number._denom, number._num) number = Fraction(number._denom, number._num)
steps.append([self, number, op.mul]) steps.append(Expression([self, number, op.mul]))
steps += self * number steps += self * number
return steps return steps
@ -256,10 +334,10 @@ class Fraction(object):
>>> f**1 >>> f**1
[< Fraction 3 / 4>] [< Fraction 3 / 4>]
>>> f**3 >>> f**3
[[3, 3, '^', 4, 3, '^', '/'], < Fraction 27 / 64>] [< Expression [3, 3, '^', 4, 3, '^', '/']>, < Fraction 27 / 64>]
>>> f = Fraction(6, 4) >>> f = Fraction(6, 4)
>>> f**3 >>> f**3
[[6, 3, '^', 4, 3, '^', '/'], < Fraction 216 / 64>, [27, 8, '*', 8, 8, '*', '/'], < Fraction 27 / 8>] [< Expression [6, 3, '^', 4, 3, '^', '/']>, < Fraction 216 / 64>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>]
""" """
if not type(power) == int: if not type(power) == int:
@ -270,7 +348,7 @@ class Fraction(object):
elif power == 1: elif power == 1:
return [self] return [self]
else: else:
steps = [[self._num, power, op.pw, self._denom, power, op.pw, op.div]] steps = [Expression([self._num, power, op.pw, self._denom, power, op.pw, op.div])]
ans_frac = Fraction(self._num ** power, self._denom ** power) ans_frac = Fraction(self._num ** power, self._denom ** power)
steps.append(ans_frac) steps.append(ans_frac)
steps += ans_frac.simplify() steps += ans_frac.simplify()
@ -278,13 +356,19 @@ class Fraction(object):
def __xor__(self, power): def __xor__(self, power):
""" overload ^ """ overload ^
>>> f = Fraction(3, 4) >>> f = Fraction(3, 4)
>>> f^0
[1]
>>> f^1
[< Fraction 3 / 4>]
>>> f^3 >>> f^3
[[3, 3, '^', 4, 3, '^', '/'], < Fraction 27 / 64>] [< Expression [3, 3, '^', 4, 3, '^', '/']>, < Fraction 27 / 64>]
>>> f = Fraction(6, 4) >>> f = Fraction(6, 4)
>>> f^3 >>> f^3
[[6, 3, '^', 4, 3, '^', '/'], < Fraction 216 / 64>, [27, 8, '*', 8, 8, '*', '/'], < Fraction 27 / 8>] [< Expression [6, 3, '^', 4, 3, '^', '/']>, < Fraction 216 / 64>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>]
""" """
return self.__pow__(power) return self.__pow__(power)