131 lines
3.4 KiB
Python
131 lines
3.4 KiB
Python
from __future__ import annotations
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from typing import Iterable, Generator
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from tools import gcd
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class Fraction:
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"""
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Should represent a fraction not a division
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"""
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__slots__ = ['num', 'den']
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__match_args__ = ("num", "den")
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#todo check if num and den are part of a domain, so a/b as a meaning a gcd work well
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#todo implement __iadd__ etc... if performance needed
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def __init__(self, *args):
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match args:
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case num, den:
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self.num = num
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self.den = den
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case x, :
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self.num = x
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self.den = 1
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def __repr__(self):
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return f'Fractions({self.num}, {self.den})'
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def simplify_gcd(self):
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"""Simplify fraction by diving num and den by their gcd
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return None"""
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match self.num, self.den:
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case int(num), int(den):
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gcd_ = gcd(num, den)
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self.num //= gcd_
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self.den //= gcd_
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# can be completed with others objects that support gcd like polynomials etc...
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def simplify_to_num(self):
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"""from frac(a, 1) return a."""
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if self.den == 1:
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return self.num
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def simplify_nested(self, rec=True):
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"""simplify nested fractions.
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Fractions(1, Fractions(1, Fractions(1, Fractions(1, 2)))) -> Fractions(2, 1)
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For one simplification step put rec=False
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return None"""
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def aux(fract):
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match fract:
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case Fraction(Fraction(a, b), Fraction(c, d)):
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fract.num = a * d
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fract.den = b * c
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case Fraction(num, Fraction(a, b)):
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fract.num = num * b
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fract.den = a
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case Fraction(Fraction(a, b), den):
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fract.num = a
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fract.den = b * den
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if rec:
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num, den = self.num, self.den
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if isinstance(num, Fraction) or isinstance(den, Fraction):
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aux(fract)
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aux(self)
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def simplify_all_(self):
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self.simplify_gcd()
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self.simplify_nested()
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res = self.simplify_to_num()
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if res:
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return res
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return self
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def __add__(self, other):
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match other:
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case int(x):
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return Fraction(self.num + self.den * x, self.den)
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case Fraction(num, den):
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result = Fraction(self.num * den + num * self.den, self.den * den)
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return result
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return ValueError
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def __radd__(self, other):
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return other + self
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def __neg__(self):
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return Fraction(-self.num, self.den)
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def __mul__(self, other):
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match other:
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case int(x):
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return Fraction(self.num * x, self.den)
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case Fraction(num, den):
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result = Fraction(self.num * num, self.den * den)
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return result
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return ValueError
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def __rmul__(self, other):
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return self*other
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def __truediv__(self, other):
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match other:
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case int(x):
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return Fraction(self.num, self.den * x)
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case Fraction(num, den):
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return Fraction(self.num * den, self.den * num)
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def __rtruediv__(self, other):
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res = self/other
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return Fraction(res.den, res.num)
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if __name__ == "__main__":
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a = Fraction(1, 2)
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a += 1
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print(a)
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