loss of digits in multivariate polynomial ring quotients with base ring RR

[nbruin]

Steps To Reproduce

From https://groups.google.com/g/sage-support/c/gbBYEbxv8Ow:

there is a suspicious loss of digits with coercion into multivariate polynomial quotient rings over RR:

sage: R.<x,y>=RR[]
sage: I=R.ideal(x)
sage: Q=R.quotient(I)
sage: Q(1/3)
0.333300000000000
sage: Q(99998/99999)
1.00000000000000

there is no actual arithmetic happening and note that the rounding is happening at a very precise number of decimal digits, so it looks more like a very naive approximation of floats by small-denominator rational numbers.

Expected Behavior

I would expect an error because imprecise base rings aren't supported for multivariate quotient rings or an approximate answer that doesn't introduce such an egregious and unnecessary rounding error.

Actual Behavior

as above

Additional Information

No response

Environment

any recent sage

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

[nbruin]

A little digging seems to indicate this is how singular converts floats:

sage: RR[x,y](1/3)._singular_()
(3.333e-01)

so we should just not use singular here. Somewhere in the quotient ring code, apparently the use of singular is attempted. We should make sure that attempt explicitly fails with base ring RR etc.

Probably the code in question just does a "try/except" somewhere hoping that the absence of an error means a meaningful result. That hope is unjustified here, unfortunately.