Explicitly setting `()` and `repeat=1` to `itertools.product()` doesn't return `()`

[hyperkai]

Bug report

Bug description:

The doc of itertools.product() say below so the default value of *iterables is () and the default value of repeat is 1:

itertools.product(*iterables, repeat=1)

Then, setting no arguments to itertools.product() returns () as shown below:

from itertools import product

v = product()

print(next(v)) # ()
print(next(v)) # StopIteration:

But explicitly setting () and repeat=1 to itertools.product() doesn't return () as shown below:

from itertools import product

v = product((), repeat=1)

print(next(v)) # StopIteration:

So, explicitly setting () and repeat=1 to itertools.product() should return ().

CPython versions tested on:

3.12

Operating systems tested on:

Windows

[skirpichev]

You are assuming equivalency of product((), repeat=1) and product(repeat=1), but it's not true:

>>> v = product(repeat=1)
>>> next(v)
()
>>> next(v)
Traceback (most recent call last):
  File "<python-input-14>", line 1, in <module>
    next(v)
    ~~~~^^^
StopIteration

Note that same happens for code snippet, provided in docs. I've added a debug print statement to show you the difference:

>>> def product(*iterables, repeat=1):
...     # product('ABCD', 'xy') → Ax Ay Bx By Cx Cy Dx Dy
...     # product(range(2), repeat=3) → 000 001 010 011 100 101 110 111
...     if repeat < 0:
...         raise ValueError('repeat argument cannot be negative')
...     print(iterables)
...     pools = [tuple(pool) for pool in iterables] * repeat
...     result = [[]]
...     for pool in pools:
...         result = [x+[y] for x in result for y in pool]
...     for prod in result:  
...         yield tuple(prod)
...         
>>> v = product(repeat=1)
>>> next(v)
()
()
>>> next(v)
Traceback (most recent call last):
  File "<python-input-24>", line 1, in <module>
    next(v)
    ~~~~^^^
StopIteration
>>> v = product((), repeat=1)
>>> next(v)
((),)
Traceback (most recent call last):
  File "<python-input-27>", line 1, in <module>
    next(v)
    ~~~~^^^
StopIteration