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python_symb/fraction.py

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