## Named-import Sage can fail on rational strings and mixed division

What happened: with `import numberdb.sage as numberdb` followed by the
named `QQ` import, `QQ('1/2')` raised `AttributeError: module 'sage.rings'
has no attribute 'real_mpfr'` in Sage 10.9. A separate check also hit the
same missing module when dividing `QQ(1)` by the Python integer `4`.
No wrong value was submitted; both failures occurred while the draft was empty.

What the skill says now: named imports may leave machinery uninitialized;
it specifically mentions decimal strings and says to divide Sage rationals.

What it should say: the string conversion failure can include ordinary
fraction strings as well as decimals. Parse a stored fraction into integer
numerator and denominator and use `QQ(int(p))/QQ(int(q))`. Keep both sides
of exact division in the explicitly initialized rational ring. This avoids
an accidental dependency on the real-field coercion path.

Evidence: the dry run for T533 initially stopped at `QQ(params['nu'])`.
`checks-failure-rational-coercion.log` retains the mixed-division traceback.
After explicit parsing and rational divisors, the dry run computed all 96
values and the independent exact checks passed. Environment: Sage 10.9,
Python 3.12.3, numberdb 0.1.10. The generator remains free of `sage.all`.