modernize Fraction and add doctests
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Lafrite
parent
dfb056e1cf
commit
30f9554ff2
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@ -4,6 +4,9 @@
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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 .render import txt, tex
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__all__ = ['Fraction']
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@ -26,6 +29,14 @@ class Fraction(object):
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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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[< Expression [1, 3, '*', 2, 3, '*', '/']>, < Fraction 1 / 2>]
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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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steps = []
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@ -47,29 +58,47 @@ class Fraction(object):
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elif gcd_ != 1:
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n_frac = Fraction(n_frac._num // gcd_ , n_frac._denom // gcd_)
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steps.append([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ])
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steps.append(Expression([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ]))
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steps.append(n_frac)
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return steps
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def __str__(self):
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@property
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def postfix(self):
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"""Postfix form of the fraction
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>>> f = Fraction(3, 5)
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>>> f.postfix
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[3, 5, '/']
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"""
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if self._denom == 1:
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return str(self._num)
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return [self._num]
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else:
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return str(self._num) + " / " + str(self._denom)
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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))
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def __repr__(self):
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return "< Fraction " + self.__str__() + ">"
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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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return str(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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if self._denom == 1:
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return str(self._num)
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else:
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return "\\frac{{ {a} }}{{ {b} }}".format(a = self._num, b = self._denom)
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old_render = Expression.get_render()
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Expression.set_render(tex)
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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 __float__(self):
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return self._num / self._denom
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@ -85,6 +114,21 @@ class Fraction(object):
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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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[< Expression [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '+']>, < Expression [3, 4, '+', 6, '/']>, < Fraction 7 / 6>]
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>>> f + 2
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[< Expression [1, 1, '*', 2, 1, '*', '/', 2, 2, '*', 1, 2, '*', '/', '+']>, < Expression [1, 4, '+', 2, '/']>, < Fraction 5 / 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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[< Expression [3, 5, '+', 4, '/']>, < Fraction 8 / 4>, 2]
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"""
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if other == 0:
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return [self]
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@ -102,13 +146,13 @@ class Fraction(object):
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coef1 = number._denom // gcd_denom
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coef2 = self._denom // gcd_denom
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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])
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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]) )
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com_denom = self._denom * coef1
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num1 = self._num * coef1
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num2 = number._num * coef2
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steps.append([num1, num2, op.add, com_denom, op.div])
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steps.append(Expression([num1, num2, op.add, com_denom, op.div]))
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num = num1 + num2
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@ -127,6 +171,14 @@ class Fraction(object):
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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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[< Expression [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '-']>, < Expression [3, 4, '-', 6, '/']>, < Fraction -1 / 6>]
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"""
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if other == 0:
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return [self]
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@ -144,13 +196,13 @@ class Fraction(object):
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coef1 = number._denom // gcd_denom
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coef2 = self._denom // gcd_denom
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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])
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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]))
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com_denom = self._denom * coef1
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num1 = self._num * coef1
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num2 = number._num * coef2
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steps.append([num1, num2, op.sub, com_denom, op.div])
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steps.append(Expression([num1, num2, op.sub, com_denom, op.div]))
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num = num1 - num2
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@ -169,10 +221,36 @@ class Fraction(object):
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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 = 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>, < Fraction 1 / 2>]
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"""
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f = Fraction(-self._num, self._denom)
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return [f] + f.simplify()
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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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[< Expression [1, 1, 2, '*', '*', 1, 2, '*', 3, '*', '/']>, < Fraction 1 / 3>]
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>>> f * 0
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[0]
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>>> f*1
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[< Fraction 1 / 2>]
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>>> f*4
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[< Expression [1, 2, '*', 2, '*', 1, 2, '*', '/']>, < Fraction 2 / 1>, 2]
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"""
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steps = []
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if other == 0:
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@ -188,7 +266,7 @@ class Fraction(object):
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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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steps.append(num + denom + [op.div])
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steps.append(Expression(num + denom + [op.div]))
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num = int(self._num * other / gcd1)
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denom = int(self._denom / gcd1)
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@ -213,7 +291,7 @@ class Fraction(object):
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denom1 = [self._denom]
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steps.append(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div])
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steps.append(Expression(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div]))
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num = int(self._num * number._num / (gcd1 * gcd2))
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denom = int(self._denom * number._denom / (gcd1 * gcd2))
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@ -237,7 +315,7 @@ class Fraction(object):
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steps = []
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number = Fraction(number._denom, number._num)
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steps.append([self, number, op.mul])
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steps.append(Expression([self, number, op.mul]))
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steps += self * number
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return steps
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@ -256,10 +334,10 @@ class Fraction(object):
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>>> f**1
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[< Fraction 3 / 4>]
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>>> f**3
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[[3, 3, '^', 4, 3, '^', '/'], < Fraction 27 / 64>]
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[< Expression [3, 3, '^', 4, 3, '^', '/']>, < Fraction 27 / 64>]
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>>> f = Fraction(6, 4)
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>>> f**3
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[[6, 3, '^', 4, 3, '^', '/'], < Fraction 216 / 64>, [27, 8, '*', 8, 8, '*', '/'], < Fraction 27 / 8>]
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[< Expression [6, 3, '^', 4, 3, '^', '/']>, < Fraction 216 / 64>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>]
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"""
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if not type(power) == int:
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@ -270,7 +348,7 @@ class Fraction(object):
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elif power == 1:
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return [self]
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else:
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steps = [[self._num, power, op.pw, self._denom, power, op.pw, op.div]]
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steps = [Expression([self._num, power, op.pw, self._denom, power, op.pw, op.div])]
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ans_frac = Fraction(self._num ** power, self._denom ** power)
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steps.append(ans_frac)
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steps += ans_frac.simplify()
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@ -278,13 +356,19 @@ class Fraction(object):
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def __xor__(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^1
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[< Fraction 3 / 4>]
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>>> f^3
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[[3, 3, '^', 4, 3, '^', '/'], < Fraction 27 / 64>]
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[< Expression [3, 3, '^', 4, 3, '^', '/']>, < Fraction 27 / 64>]
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>>> f = Fraction(6, 4)
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>>> f^3
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[[6, 3, '^', 4, 3, '^', '/'], < Fraction 216 / 64>, [27, 8, '*', 8, 8, '*', '/'], < Fraction 27 / 8>]
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[< Expression [6, 3, '^', 4, 3, '^', '/']>, < Fraction 216 / 64>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>]
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"""
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return self.__pow__(power)
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