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modernize Fraction and add doctests

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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 .generic import isNumber
from .operator import op
from .expression import Expression
from .render import txt, tex
__all__ = ['Fraction']
@ -26,6 +29,14 @@ class Fraction(object):
"""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 = []
@ -47,29 +58,47 @@ class Fraction(object):
elif gcd_ != 1:
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)
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:
return str(self._num)
return [self._num]
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):
return "< Fraction " + self.__str__() + ">"
return "< Fraction {num} / {denom}>".format(num=self._num, denom = self._denom)
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):
if self._denom == 1:
return str(self._num)
else:
return "\\frac{{ {a} }}{{ {b} }}".format(a = self._num, b = self._denom)
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
@ -85,6 +114,21 @@ class Fraction(object):
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, 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:
return [self]
@ -102,13 +146,13 @@ class Fraction(object):
coef1 = number._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
num1 = self._num * coef1
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
@ -127,6 +171,14 @@ class Fraction(object):
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, 4, '-', 6, '/']>, < Fraction -1 / 6>]
"""
if other == 0:
return [self]
@ -144,13 +196,13 @@ class Fraction(object):
coef1 = number._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
num1 = self._num * coef1
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
@ -169,10 +221,36 @@ class Fraction(object):
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)
return [f] + f.simplify()
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 = []
if other == 0:
@ -188,7 +266,7 @@ class Fraction(object):
else:
num = [self._num, other, op.mul]
denom = [self._denom]
steps.append(num + denom + [op.div])
steps.append(Expression(num + denom + [op.div]))
num = int(self._num * other / gcd1)
denom = int(self._denom / gcd1)
@ -213,7 +291,7 @@ class Fraction(object):
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))
denom = int(self._denom * number._denom / (gcd1 * gcd2))
@ -237,7 +315,7 @@ class Fraction(object):
steps = []
number = Fraction(number._denom, number._num)
steps.append([self, number, op.mul])
steps.append(Expression([self, number, op.mul]))
steps += self * number
return steps
@ -256,10 +334,10 @@ class Fraction(object):
>>> f**1
[< Fraction 3 / 4>]
>>> f**3
[[3, 3, '^', 4, 3, '^', '/'], < Fraction 27 / 64>]
[< Expression [3, 3, '^', 4, 3, '^', '/']>, < Fraction 27 / 64>]
>>> f = Fraction(6, 4)
>>> 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:
@ -270,7 +348,7 @@ class Fraction(object):
elif power == 1:
return [self]
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)
steps.append(ans_frac)
steps += ans_frac.simplify()
@ -278,13 +356,19 @@ class Fraction(object):
def __xor__(self, power):
""" overload ^
>>> f = Fraction(3, 4)
>>> f^0
[1]
>>> f^1
[< Fraction 3 / 4>]
>>> f^3
[[3, 3, '^', 4, 3, '^', '/'], < Fraction 27 / 64>]
[< Expression [3, 3, '^', 4, 3, '^', '/']>, < Fraction 27 / 64>]
>>> f = Fraction(6, 4)
>>> 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)