gosper_iterator of continued fractions is unstable

[mwageringel]

sage -t --long --random-seed=5058 src/sage/rings/continued_fraction_gosper.py
**********************************************************************
File "src/sage/rings/continued_fraction_gosper.py", line 63, in sage.rings.continued_fraction_gosper.gosper_iterator.__init__
Failed example:
    continued_fraction((preperiod, period), x.value()) == continued_fraction((a*x.value()+b)/(c*x.value()+d))
Exception raised:
    Traceback (most recent call last):
      File "/usr/lib/python3.9/site-packages/sage/doctest/forker.py", line 714, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/usr/lib/python3.9/site-packages/sage/doctest/forker.py", line 1133, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.rings.continued_fraction_gosper.gosper_iterator.__init__[8]>", line 1, in <module>
        continued_fraction((preperiod, period), x.value()) == continued_fraction((a*x.value()+b)/(c*x.value()+d))
      File "/usr/lib/python3.9/site-packages/sage/rings/continued_fraction.py", line 2618, in continued_fraction
        x1, x2 = check_and_reduce_pair(x1, x2)
      File "/usr/lib/python3.9/site-packages/sage/rings/continued_fraction.py", line 2257, in check_and_reduce_pair
        raise ValueError("the elements of the period cannot be negative")
    ValueError: the elements of the period cannot be negative

which comes from this example and apparently should not return negative values:

sage: a, b, c, d = 6, -9, -2, 3
sage: from sage.rings.continued_fraction_gosper import gosper_iterator
sage: x = continued_fraction(([1,2],[3,4])); i = iter(gosper_iterator(a,b,c,d,x))
sage: list(i)
[-3]

Note that (6,-9) == -3 * (-2,3).

In #29979, a doctest was marked not tested because of this.

CC: @kliem @videlec

Component: number theory

Issue created by migration from https://trac.sagemath.org/ticket/32127

[mwageringel]

comment:1

See also [#29979 comment:27].