Steps To Reproduce

Check this out:

sage: is_square(Mod(2, 101010))
False
sage: sqrt(Mod(2, 101010))
sqrt2
sage: _.parent()
Univariate Quotient Polynomial Ring in sqrt2 over Ring of integers modulo 101010 with modulus x^2 + 101008

Expected Behavior

As is_square() tells us, Mod(2, 101010) is not a square and thus computing sqrt(Mod(2, 101010)) should raise a ValueError.

Actual Behavior

Instead, it produces a result from some extension ring. Sage should not do so, unless it is explicitly asked to look for a root in a wider ring.

Additional Information

See #38802 for a related issue with parameter all=True.

Environment

• OS: Ubuntu 24.04.1 LTS
• Sage Version: 10.5.beta6

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide