[3.13] gh-119189: Fix the power operator for Fraction (GH-119242) (GH-119836)

When using the ** operator or pow() with Fraction as the base
and an exponent that is not rational, a float, or a complex, the
fraction is no longer converted to a float.
(cherry picked from commit b9965ef)

Co-authored-by: Joshua Herman <30265+zitterbewegung@users.noreply.github.com>

Author: miss-islington

Lib/fractions.py

@@ -875,8 +875,10 @@ def __pow__(a, b):
                 # A fractional power will generally produce an
                 # irrational number.
                 return float(a) ** float(b)
-        else:
+        elif isinstance(b, (float, complex)):
             return float(a) ** b
+        else:
+            return NotImplemented
 
     def __rpow__(b, a):
         """a ** b"""

Lib/test/test_fractions.py

@@ -922,21 +922,21 @@ def testMixedPower(self):
         self.assertTypedEquals(Root(4) ** F(2, 1), Root(4, F(1)))
         self.assertTypedEquals(Root(4) ** F(-2, 1), Root(4, -F(1)))
         self.assertTypedEquals(Root(4) ** F(-2, 3), Root(4, -3.0))
-        self.assertEqual(F(3, 2) ** SymbolicReal('X'), SymbolicReal('1.5 ** X'))
+        self.assertEqual(F(3, 2) ** SymbolicReal('X'), SymbolicReal('3/2 ** X'))
         self.assertEqual(SymbolicReal('X') ** F(3, 2), SymbolicReal('X ** 1.5'))
 
-        self.assertTypedEquals(F(3, 2) ** Rect(2, 0), Polar(2.25, 0.0))
-        self.assertTypedEquals(F(1, 1) ** Rect(2, 3), Polar(1.0, 0.0))
+        self.assertTypedEquals(F(3, 2) ** Rect(2, 0), Polar(F(9,4), 0.0))
+        self.assertTypedEquals(F(1, 1) ** Rect(2, 3), Polar(F(1), 0.0))
         self.assertTypedEquals(F(3, 2) ** RectComplex(2, 0), Polar(2.25, 0.0))
         self.assertTypedEquals(F(1, 1) ** RectComplex(2, 3), Polar(1.0, 0.0))
         self.assertTypedEquals(Polar(4, 2) ** F(3, 2), Polar(8.0, 3.0))
         self.assertTypedEquals(Polar(4, 2) ** F(3, 1), Polar(64, 6))
         self.assertTypedEquals(Polar(4, 2) ** F(-3, 1), Polar(0.015625, -6))
         self.assertTypedEquals(Polar(4, 2) ** F(-3, 2), Polar(0.125, -3.0))
-        self.assertEqual(F(3, 2) ** SymbolicComplex('X'), SymbolicComplex('1.5 ** X'))
+        self.assertEqual(F(3, 2) ** SymbolicComplex('X'), SymbolicComplex('3/2 ** X'))
         self.assertEqual(SymbolicComplex('X') ** F(3, 2), SymbolicComplex('X ** 1.5'))
 
-        self.assertEqual(F(3, 2) ** Symbolic('X'), Symbolic('1.5 ** X'))
+        self.assertEqual(F(3, 2) ** Symbolic('X'), Symbolic('3/2 ** X'))
         self.assertEqual(Symbolic('X') ** F(3, 2), Symbolic('X ** 1.5'))
 
     def testMixingWithDecimal(self):

Misc/ACKS

@@ -751,6 +751,7 @@ Kasun Herath
 Chris Herborth
 Ivan Herman
 Jürgen Hermann
+Joshua Jay Herman
 Gary Herron
 Ernie Hershey
 Thomas Herve

Misc/NEWS.d/next/Library/2024-05-20-13-48-37.gh-issue-119189.dhJVs5.rst

@@ -0,0 +1,3 @@
+When using the ``**`` operator or :func:`pow` with :class:`~fractions.Fraction`
+as the base and an exponent that is not rational, a float, or a complex, the
+fraction is no longer converted to a float.