[FOM] When is it appropriate to treat isomorphism as identity?

[karim zahidi]

>
> Here is an example: a well educated computer scientist typically knows
> that a polynomial (with real coefficients) has finitely many roots. He
> therefore naturally expects that there is a thing called "the number of
> distinct roots of a polynomial". Surely, such a simple number can be
> computed, yes? No.
>

I'm a bit confused by this remark. Surely if the coefficients themselves
are rational numbers (or even computable real numbers) then this number is
computable. I guess it comes out of the elimination theory for the reals.

Karim