Mapytex/pymath/calculus/fraction.py

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#!/usr/bin/env python
# encoding: utf-8
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from .arithmetic import gcd
from .generic import isNumber, postfix_op
from .operator import op
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from .expression import Expression
from .explicable import Explicable
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from .render import txt, tex
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
:param denom: the denominator
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"""
super(Fraction, self).__init__()
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self._num = num
if denom == 0:
raise ZeroDivisionError("Can't create Fraction: division by zero")
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self._denom = denom
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)
>>> f.simplify()
< 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 }
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>>> f = Fraction(0,3)
>>> f.simplify()
0
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"""
ini_step = [Expression(self.postfix_tokens)]
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if self._num == 0:
return Expression([0]).simplify()
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elif isinstance(self._num, Fraction) or isinstance(self._denom, Fraction):
return self._num / self._denom
elif self._denom < 0:
n_frac = Fraction(-self._num, -self._denom)
ans = n_frac.simplify()
ans.steps = ini_step + ans.steps
return ans
gcd_ = gcd(abs(self._num), abs(self._denom))
if gcd_ == self._denom:
n_frac = self._num // gcd_
return Expression([n_frac]).simplify()
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elif gcd_ != 1:
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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])]
n_frac.steps = ini_step + n_frac.steps
return n_frac
else:
return copy(self)
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@property
def postfix_tokens(self):
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"""Postfix form of the fraction
>>> f = Fraction(3, 5)
>>> f.postfix_tokens
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[3, 5, '/']
"""
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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]
def __str__(self):
return str(Expression(self.postfix_tokens))
def __repr__(self):
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return "< Fraction {num} / {denom}>".format(
num=self._num, denom=self._denom)
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def __float__(self):
return self._num / self._denom
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def convert2fraction(self, other):
""" Convert a other into a fraction """
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if isinstance(other, Fraction):
# cool
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number = other
else:
number = Fraction(other)
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return number
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def __add__(self, other):
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""" overload +
>>> f = Fraction(1, 2)
>>> g = Fraction(2, 3)
>>> f + g
< Fraction 7 / 6>
>>> print("\\n".join([repr(i) for i in (f+g).steps]))
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< <class 'pymath.calculus.expression.Expression'> [1, 2, '/', 2, 3, '/', '+'] >
< <class 'pymath.calculus.expression.Expression'> [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '+'] >
< <class 'pymath.calculus.expression.Expression'> [3, 6, '/', 4, 6, '/', '+'] >
< <class 'pymath.calculus.expression.Expression'> [< Fraction 3 / 6>, < Fraction 4 / 6>, '+'] >
< <class 'pymath.calculus.expression.Expression'> [3, 6, '/', 4, 6, '/', '+'] >
< <class 'pymath.calculus.expression.Expression'> [3, 4, '+', 6, '/'] >
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>>> f + 2
< Fraction 5 / 2>
>>> print("\\n".join([repr(i) for i in (f+2).steps]))
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< <class 'pymath.calculus.expression.Expression'> [1, 2, '/', 2, '+'] >
< <class 'pymath.calculus.expression.Expression'> [1, 1, '*', 2, 1, '*', '/', 2, 2, '*', 1, 2, '*', '/', '+'] >
< <class 'pymath.calculus.expression.Expression'> [1, 2, '/', 4, 2, '/', '+'] >
< <class 'pymath.calculus.expression.Expression'> [< Fraction 1 / 2>, < Fraction 4 / 2>, '+'] >
< <class 'pymath.calculus.expression.Expression'> [1, 2, '/', 4, 2, '/', '+'] >
< <class 'pymath.calculus.expression.Expression'> [1, 4, '+', 2, '/'] >
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>>> f = Fraction(3, 4)
>>> g = Fraction(5, 4)
>>> f + g
2
>>> print("\\n".join([repr(i) for i in (f+g).steps]))
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< <class 'pymath.calculus.expression.Expression'> [3, 4, '/', 5, 4, '/', '+'] >
< <class 'pymath.calculus.expression.Expression'> [3, 5, '+', 4, '/'] >
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< <class 'pymath.calculus.expression.Expression'> [8, 4, '/'] >
>>> f+0
< Fraction 3 / 4>
>>> (f+0).steps
[]
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"""
if other == 0:
return copy(self)
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number = self.convert2fraction(other)
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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])
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else:
gcd_denom = gcd(self._denom, number._denom)
coef1 = number._denom // gcd_denom
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])
ans = exp.simplify()
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ini_step = Expression(self.postfix_tokens +
number.postfix_tokens + [op.add])
ans.steps = [ini_step] + ans.steps
return ans
def __radd__(self, other):
if other == 0:
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 -
>>> f = Fraction(1, 2)
>>> g = Fraction(2, 3)
>>> f - g
< Fraction -1 / 6>
>>> print("\\n".join([repr(i) for i in (f-g).steps]))
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< <class 'pymath.calculus.expression.Expression'> [1, 2, '/', 2, 3, '/', '-'] >
< <class 'pymath.calculus.expression.Expression'> [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '-'] >
< <class 'pymath.calculus.expression.Expression'> [3, 6, '/', 4, 6, '/', '-'] >
< <class 'pymath.calculus.expression.Expression'> [< Fraction 3 / 6>, < Fraction 4 / 6>, '-'] >
< <class 'pymath.calculus.expression.Expression'> [3, 6, '/', 4, 6, '/', '-'] >
< <class 'pymath.calculus.expression.Expression'> [3, 4, '-', 6, '/'] >
>>> f - 0
< Fraction 1 / 2>
>>> (f-0).steps
[]
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"""
if other == 0:
return copy(self)
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number = self.convert2fraction(other)
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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])
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else:
gcd_denom = gcd(self._denom, number._denom)
coef1 = number._denom // gcd_denom
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])
ini_step = Expression(self.postfix_tokens +
number.postfix_tokens + [op.sub])
ans = exp.simplify()
ans.steps = [ini_step] + ans.steps
return ans
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def __rsub__(self, other):
if other == 0:
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):
""" overload - (as arity 1 operator)
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>>> f = Fraction(1, 2)
>>> -f
< Fraction -1 / 2>
>>> (-f).steps
[]
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>>> f = Fraction(1, -2)
>>> f
< Fraction 1 / -2>
>>> -f
< Fraction 1 / 2>
>>> (-f).steps
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[< <class 'pymath.calculus.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()
return ans
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def __mul__(self, other):
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""" overload *
>>> f = Fraction(1, 2)
>>> g = Fraction(2, 3)
>>> f*g
< Fraction 1 / 3>
>>> print("\\n".join([repr(i) for i in (f*g).steps]))
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< <class 'pymath.calculus.expression.Expression'> [< Fraction 1 / 2>, < Fraction 2 / 3>, '*'] >
< <class 'pymath.calculus.expression.Expression'> [1, 2, '*', 2, 3, '*', '/'] >
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< <class 'pymath.calculus.expression.Expression'> [1, 3, '/'] >
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>>> f * 0
0
>>> (f*0).steps
[< <class 'pymath.calculus.expression.Expression'> [< Fraction 1 / 2>, 0, '*'] >]
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>>> f*1
< Fraction 1 / 2>
>>> (f*1).steps
[< <class 'pymath.calculus.expression.Expression'> [< Fraction 1 / 2>, 1, '*'] >]
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>>> f*4
2
>>> print("\\n".join([repr(i) for i in (f*4).steps]))
< <class 'pymath.calculus.expression.Expression'> [< Fraction 1 / 2>, 4, '*'] >
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< <class 'pymath.calculus.expression.Expression'> [1, 2, '*', 2, '*', 1, 2, '*', '/'] >
< <class 'pymath.calculus.expression.Expression'> [1, 2, '*', 1, '/'] >
< <class 'pymath.calculus.expression.Expression'> [2, 1, '/'] >
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"""
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steps = [Expression([self, other, op.mul])]
if other == 0:
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exp = Expression([0])
elif other == 1:
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exp = copy(self)
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elif isinstance(other, int):
gcd1 = gcd(other, self._denom)
if gcd1 != 1:
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num_s = [self._num] + \
[int(other / gcd1), op.mul] * (int(other / gcd1) != 1) + \
[gcd1, op.mul]
denom_s = [int(self._denom / gcd1), gcd1, op.mul]
steps.append(Expression(num_s + denom_s + [op.div]))
num = [self._num] + [int(other / gcd1), op.mul]* (int(other / gcd1) != 1)
denom = [int(self._denom / gcd1)]
else:
num = [self._num, other, op.mul]
denom = [self._denom]
exp = Expression(num + denom + [op.div])
else:
number = self.convert2fraction(other)
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gcd1 = gcd(self._num, number._denom)
if gcd1 != 1:
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num1_s = [gcd1] + [int(self._num / gcd1), op.mul] * (int(self._num / gcd1) != 1)
denom2_s = [gcd1] + [int(number._denom / gcd1), op.mul] * (int(number._denom / gcd1) != 1)
num1 = [int(self._num / gcd1)] * (int(self._num / gcd1) != 1)
denom2 = [int(number._denom / gcd1)] * (int(self._denom / gcd1) != 1)
else:
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num1_s = [self._num]
denom2_s = [number._denom]
num1 = [self._num]
denom2 = [number._denom]
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gcd2 = gcd(self._denom, number._num)
if gcd2 != 1:
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num2_s = [gcd2] + [int(number._num / gcd2), op.mul] * (int(number._num / gcd2) != 1)
denom1_s = [gcd2] + [int(self._denom / gcd2), op.mul] * (int(self._denom / gcd2) != 1)
num2 = [int(number._num / gcd2)] * (int(number._num / gcd2) != 1)
denom1 = [int(self._denom / gcd2)] * (int(number._denom / gcd2) != 1)
else:
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num2_s = [number._num]
denom1_s = [self._denom]
num2 = [number._num]
denom1 = [self._denom]
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steps.append(Expression(num1_s + num2_s + [op.mul] + \
denom1_s + denom2_s + [op.mul, op.div]))
exp = Expression(postfix_op(num1 + num2, op.mul, 1) +
postfix_op(denom1 + denom2, op.mul, 1) +
[op.div])
ans = exp.simplify()
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ans.steps = steps + ans.steps
return ans
def __rmul__(self, other):
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return self * other
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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 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)
ans = self * number
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ans.steps = [ini_step] + ans.steps
return ans
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):
""" overload **
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>>> f = Fraction(3, 4)
>>> f**0
1
>>> (f**0).steps
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[< <class 'pymath.calculus.expression.Expression'> [< Fraction 3 / 4>, 0, '^'] >]
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>>> f**1
< Fraction 3 / 4>
>>> (f**1).steps
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[< <class 'pymath.calculus.expression.Expression'> [< Fraction 3 / 4>, 1, '^'] >]
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>>> f**3
< Fraction 27 / 64>
>>> print("\\n".join([repr(i) for i in (f**3).steps]))
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< <class 'pymath.calculus.expression.Expression'> [< Fraction 3 / 4>, 3, '^'] >
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< <class 'pymath.calculus.expression.Expression'> [3, 3, '^', 4, 3, '^', '/'] >
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< <class 'pymath.calculus.expression.Expression'> [27, 64, '/'] >
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>>> f = Fraction(6, 4)
>>> f**3
< Fraction 27 / 8>
>>> print("\\n".join([repr(i) for i in (f**3).steps]))
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< <class 'pymath.calculus.expression.Expression'> [< Fraction 6 / 4>, 3, '^'] >
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< <class 'pymath.calculus.expression.Expression'> [6, 3, '^', 4, 3, '^', '/'] >
< <class 'pymath.calculus.expression.Expression'> [216, 64, '/'] >
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< <class 'pymath.calculus.expression.Expression'> [216, 64, '/'] >
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< <class 'pymath.calculus.expression.Expression'> [27, 8, '*', 8, 8, '*', '/'] >
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"""
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if not isinstance(power, int):
raise ValueError(
"Can't raise fraction to power {}".format(
str(power)))
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ini_step = Expression([self, power, op.pw])
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if power == 0:
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exp = Expression([1])
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elif power == 1:
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exp = copy(self)
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else:
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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()
ans.steps = [ini_step] + ans.steps
return ans
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def __xor__(self, power):
""" overload ^
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Work like **
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>>> f = Fraction(3, 4)
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>>> f^0
1
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>>> f^1
< Fraction 3 / 4>
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>>> f^3
< Fraction 27 / 64>
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"""
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return self.__pow__(power)
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def __abs__(self):
return Fraction(abs(self._num), abs(self._denom))
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def __eq__(self, other):
""" == """
if isNumber(other):
number = self.convert2fraction(other)
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return self._num * number._denom == self._denom * number._num
else:
return 0
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def __lt__(self, other):
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""" < """
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return float(self) < float(other)
def __le__(self, other):
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""" <= """
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return float(self) <= float(other)
def __gt__(self, other):
""" > """
return float(self) > float(other)
def __ge__(self, other):
""" >= """
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(6, 12)
for i in g.simplify().explain():
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print("g = ", i)
h = Fraction(1, -5)
t = Fraction(10, 3)
print("---------")
for i in (0 + h).explain():
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print('0 + h = ', i)
# 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
doctest.testmod()
# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del