>> sage: R.<x> = PolynomialRing(QQ)
>> sage: (x + 1/x).parent()
>> Fraction Field of Univariate Polynomial Ring in x over Rational Field
>
> Is it really expected by all users (I see a sum,
> not a fraction)? I thought algebraists don't touch
> symbolics with a long stick...

I would certainly yes! If f is in k[x] then I expect Sage to
accept 1/f as the respective element in k(x). It would be annoying to
have to convert explicitly (though, admittedly, the magic coercion
sometimes causes computation being done in k(x) by mistake).

And of course, adding an element in k(x) with one from k[x] gives
something in k(x) without warning.

Best,
Johan

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