Rational calc value error

[ChisenZhang]

python 3.11, sympy 1.11.1
when calc Rational('0.5', '100'), the value is 1/100100; but Rational(0.5, 100) the value is 1/200, this value is the true value, and the version of sympy 1.8 is normal

[oscarbenjamin]

This should probably raise an error. The expected way to do this is:

In [1]: Rational('0.5/100')
Out[1]: 1/200

In [2]: Rational('0.5') / Rational('100')
Out[2]: 1/200

[sylee957]

Actually, this should be a flaw in the logic because string is multiplied somewhere in

sympy/sympy/core/numbers.py

Lines 1628 to 1640 in 68803e5

	if not isinstance(p, SYMPY_INTS):
	p = Rational(p)
	q *= p.q
	p = p.p
	else:
	p = int(p)
	if not isinstance(q, SYMPY_INTS):
	q = Rational(q)
	p *= q.q
	q = q.p
	else:
	q = int(q)

[smichr]

The logic should like like this:

        Q = 1
        gcd = 1

        if not isinstance(p, SYMPY_INTS):
            p = Rational(p)
            Q *= p.q
            p = p.p
        else:
            p = int(p)

        if not isinstance(q, SYMPY_INTS):
            q = Rational(q)
            p *= q.q
            Q *= q.p
        else:
            Q *= int(q)
        q = Q

A test can be added:

for p in ('1.5', 1.5, 2):
    for q in ('1.5', 1.5, 2):
        assert Rational(p, q).as_numer_denom() == Rational('%s/%s'%(p,q)).as_numer_denom()