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

[Jay Sulzberger]

On Wed, 20 May 2009, Andrej Bauer <andrej.bauer at andrej.com> wrote:

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> Classical mathematics creates the wrong kind of mathematical
> intuition and expectations for a computer scientist to have. He
> is much better off knowing (also) constructive mathematics,
> because it fits more naturally with the nature of computation.
>
> 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.

Given a polynomial in one variable of degree 10 with rational
coefficients, which can be written out in the usual high school
notation with less than 1000 characters, can you compute the
"number of distinct roots"?  The polynomial is to be given as an
ascii string placed before you, so you can see it.

Free example:

x^10 + (7777777777777/666666666666666)x^5 + (-1111111111111)x^4 + (17)x^0

oo--JS.