[tombouctou]

For a rational number with a repeating expansion RealDigits

• returned the repeating digits as strings: RealDigits[1/7] was
  {{{"1", "4", "2", "8", "5", "7"}}, 0} (the output form hides the
  quotes, so the doctests and unit tests did not notice);
• took everything after the decimal point as the period:
  RealDigits[1/6] gave {{{1, 6}}, 0} (0.161616...) instead of
  {{1, {6}}, 0}, RealDigits[1/14] gave {{{7, 1, 4, 2, 8, 5, 0}}, -1};
• dropped the zeros of the integer part: RealDigits[703/7] (100.428...)
  gave {{1, {4, 2, 8, 5, 7, 1}}, 3};
• raised ZeroDivisionError or TypeError for a base 1 or -2.

The digits now come from a long division that records where the
remainders start to repeat, with leading zeros moved into the exponent and
the shortest pre-period, as before (RealDigits[20/3] is {{{6}}, 1}). A
base below 2 gets RealDigits::rbase.

To reproduce on master:

RealDigits[1/7] // InputForm   (* {{{"1", "4", "2", "8", "5", "7"}}, 0} *)
RealDigits[1/6]                (* {{{1, 6}}, 0} *)
RealDigits[703/7]              (* {{1, {4, 2, 8, 5, 7, 1}}, 3} *)

Tests: new cases in test/builtin/atomic/test_numbers.py (test_realdigits_rational). They fail on current master and pass with this change.

The full pytest suite and the doctests pass with this change (run together with the other fixes from the same audit; the only pytest failures, in test_main.py and test_returncode.py, are the same as on master and come from the mathics script not being on PATH in our environment).

Found in a correctness audit of Mathics3 (differential checks against SymPy/mpmath/exact computation, and calls of every builtin with edge-case arguments).

🤖 Generated with Claude Code

[rocky]

It would be nice to add a return signature here, e.g., tuple[int, int, int] or whatever.

(I have a hard time checking the exact type right now due to a local problem on my computer and the fact that this is not a branch in the repository.)

[rocky]

When making changes to the class, you'd do me a favor and look for missing argument checking. Here we are missing expected_args = 1 as a class variable.

[rocky]

LGTM