bpo-22486 added math.gcd() and deprecated fractions.gcd() in Python 3.5: commit48e47aaa28d6dfdae128142ffcbc4b0642422e90.The function was deprecated during 4 cycles (3.5, 3.6, 3.7, 3.8): I propose attached PR to remove it.

New changeset4691a2f2a2b8174a6c958ce6976ed5f3354c9504 by Victor Stinner in branch 'master':bpo-39350: Remove deprecated fractions.gcd() (GH-18021)https://github.com/python/cpython/commit/4691a2f2a2b8174a6c958ce6976ed5f3354c9504

I believe there is a regression here.numpy fails to build with Python 3.9.0a3.________________________ TestMatmul.test_matmul_object _________________________self = <numpy.core.tests.test_multiarray.TestMatmul object at 0x7ff9bc008ca0>    def test_matmul_object(self):        import fractions            f = np.vectorize(fractions.Fraction)        def random_ints():            return np.random.randint(1, 1000, size=(10, 3, 3))>       M1 = f(random_ints(), random_ints())f          = <numpy.vectorize object at 0x7ff9bc6751f0>fractions  = <module 'fractions' from '/usr/lib64/python3.9/fractions.py'>random_ints = <function TestMatmul.test_matmul_object.<locals>.random_ints at 0x7ff9bcc2d700>self       = <numpy.core.tests.test_multiarray.TestMatmul object at 0x7ff9bc008ca0>numpy/core/tests/test_multiarray.py:6259: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ numpy/lib/function_base.py:2091: in __call__    return self._vectorize_call(func=func, args=vargs)numpy/lib/function_base.py:2161: in _vectorize_call    ufunc, otypes = self._get_ufunc_and_otypes(func=func, args=args)numpy/lib/function_base.py:2121: in _get_ufunc_and_otypes    outputs = func(*inputs)_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ cls = <class 'fractions.Fraction'>, numerator = 483, denominator = 809    def __new__(cls, numerator=0, denominator=None, *, _normalize=True):        """Constructs a Rational.            Takes a string like '3/2' or '1.5', another Rational instance, a        numerator/denominator pair, or a float.            Examples        --------            >>> Fraction(10, -8)        Fraction(-5, 4)        >>> Fraction(Fraction(1, 7), 5)        Fraction(1, 35)        >>> Fraction(Fraction(1, 7), Fraction(2, 3))        Fraction(3, 14)        >>> Fraction('314')        Fraction(314, 1)        >>> Fraction('-35/4')        Fraction(-35, 4)        >>> Fraction('3.1415') # conversion from numeric string        Fraction(6283, 2000)        >>> Fraction('-47e-2') # string may include a decimal exponent        Fraction(-47, 100)        >>> Fraction(1.47)  # direct construction from float (exact conversion)        Fraction(6620291452234629, 4503599627370496)        >>> Fraction(2.25)        Fraction(9, 4)        >>> Fraction(Decimal('1.47'))        Fraction(147, 100)            """        self = super(Fraction, cls).__new__(cls)            if denominator is None:            if type(numerator) is int:                self._numerator = numerator                self._denominator = 1                return self                elif isinstance(numerator, numbers.Rational):                self._numerator = numerator.numerator                self._denominator = numerator.denominator                return self                elif isinstance(numerator, (float, Decimal)):                # Exact conversion                self._numerator, self._denominator = numerator.as_integer_ratio()                return self                elif isinstance(numerator, str):                # Handle construction from strings.                m = _RATIONAL_FORMAT.match(numerator)                if m is None:                    raise ValueError('Invalid literal for Fraction: %r' %                                     numerator)                numerator = int(m.group('num') or '0')                denom = m.group('denom')                if denom:                    denominator = int(denom)                else:                    denominator = 1                    decimal = m.group('decimal')                    if decimal:                        scale = 10**len(decimal)                        numerator = numerator * scale + int(decimal)                        denominator *= scale                    exp = m.group('exp')                    if exp:                        exp = int(exp)                        if exp >= 0:                            numerator *= 10**exp                        else:                            denominator *= 10**-exp                if m.group('sign') == '-':                    numerator = -numerator                else:                raise TypeError("argument should be a string "                                "or a Rational instance")            elif type(numerator) is int is type(denominator):            pass # *very* normal case            elif (isinstance(numerator, numbers.Rational) and            isinstance(denominator, numbers.Rational)):            numerator, denominator = (                numerator.numerator * denominator.denominator,                denominator.numerator * numerator.denominator                )        else:            raise TypeError("both arguments should be "                            "Rational instances")            if denominator == 0:            raise ZeroDivisionError('Fraction(%s, 0)' % numerator)        if _normalize:            if type(numerator) is int is type(denominator):                # *very* normal case                g = math.gcd(numerator, denominator)                if denominator < 0:                    g = -g            else:>               g = _gcd(numerator, denominator)E               NameError: name '_gcd' is not defined__class__  = <class 'fractions.Fraction'>_normalize = Truecls        = <class 'fractions.Fraction'>denominator = 809numerator  = 483self       = <[AttributeError("_numerator") raised in repr()] Fraction object at 0x7ff9bc6753a0>/usr/lib64/python3.9/fractions.py:164: NameErrorThis removed _gcd, but it is still called in:https://github.com/python/cpython/blob/58a4054760bffbb20aff90290dd0f3554f7bea42/Lib/fractions.py#L164

Reproducer:class myint(int):    def __mul__(self, other):        return type(self)(int(self)*int(other))    @property    def numerator(self):        return type(self)(super().numerator)    @property    def denominator(self):        return type(self)(super().denominator)Before:>>> fractions.Fraction(myint(1), myint(2))Fraction(1, 2)After:>>> fractions.Fraction(myint(1), myint(2))Traceback (most recent call last):  File "<stdin>", line 1, in <module>  File "/usr/lib64/python3.9/fractions.py", line 164, in __new__    g = _gcd(numerator, denominator)NameError: name '_gcd' is not defined

The relevant piece of Python code from fractions.py looks like this:    if type(numerator) is int is type(denominator):        # *very* normal case        g = math.gcd(numerator, denominator)        if denominator < 0:            g = -g    else:        g = _gcd(numerator, denominator)I wonder whether we should simply drop the type check: math.gcd should accept anything that supports __index__ (and that includes NumPy integer types and anything that implements numbers.Integral).OTOH, math.gcd will return a plain int, and if we have some subclass myint of int, we might want all the arithmetic to stay in the domain of myints (though I'm not really sure _why_ we'd want that). In that case we'll need to restore the pure Python _gcd implementation.

Naively implementing this code, I'd use isinstance(numerator, int) over type(numerator) is int. Is that strict type check really needed?I could not find anywhere whether numerator and denominator of numbers.Rational need to be numbers.Integral. I would expect so, however this is not written in the documentation of numbers.Rational. If that's the case, I think checking it for being numbers.Integral and failing hard if not is a reasonable thing to do.

Apologies, I think I moved the discussion off-track. The first order of business should be to fix the regression. We can discuss behaviour changes after that.I've openedGH-18309 as a quick fix for the regression.

I tried but failed to write a test to mimick numpy.int64 type. I tried to build a type which implements numbers.Rational but don't inherit from int, but there are way too many methods that I have to implement :-(Morever, installing numpy on a Python 3.9 virtual environment is quite tricky. Lhe latest Cython release (0.29.14) isn't compatible with Python 3.9.Miro gave me a command to install Cython on Python 3.9:python -m pip installhttps://github.com/cython/cython/archive/master.tar.gz --install-option="--no-cython-compile"But then "pip install numpy" tries to reinstall Cython which fails :-/

I managed to test my PR with numpy:$ env/bin/python >>> import fractions>>> import numpy>>> f=fractions.Fraction(numpy.int64(1*3), numpy.int64(2*3))>>> fFraction(1, 2)>>> type(f.numerator)<class 'numpy.int64'>>>> type(f.denominator)<class 'numpy.int64'>So it works as expected: numerator and denominator have the expected type, and there is no exception ;-)I used the following commands to get numpy in a Python 3.9 virtual environment:./python -m venv envenv/bin/python -m pip installhttps://github.com/cython/cython/archive/master.tar.gz --install-option="--no-cython-compile"curl -Ohttps://files.pythonhosted.org/packages/40/de/0ea5092b8bfd2e3aa6fdbb2e499a9f9adf810992884d414defc1573dca3f/numpy-1.18.1.zipunzip -d . numpy-1.18.1.zipcd numpy-1.18.1/../env/bin/python setup.py install

FYI the full numpy test suite pass withPR 18375:(env)vstinner@apu$ python runtests.py  -v(...)======================= 9879 passed, 443 skipped, 180 deselected, 17 xfailed, 3 xpassed in 305.17s (0:05:05) =======================

New changesetdc7a50d73a3d16918529669ff7b8783c08cff090 by Victor Stinner in branch 'master':bpo-39350: Fix fractions for int subclasses (GH-18375)https://github.com/python/cpython/commit/dc7a50d73a3d16918529669ff7b8783c08cff090

Thanks Miro for the bug report and thanks Mark for the great review and discussion! It should now be fixed. I tested manually that my change fix numpy test suite.