On Feb 10, 6:05 pm, David Harvey <[EMAIL PROTECTED]> wrote:
> On Feb 10, 2007, at 8:35 PM, Carl Witty wrote:
>
>
>
> > I have a design question about interval arithmetic comparisons.
>
> [...]
>
> I don't quite know the answer to these questions, but I reckon one
> thing: for consistency, you want interval comparison to match up with
> comparison of reals and comparison of p-adic integers. What I mean
> is: a real number (i.e. an IEEE double, or an MPFR real, or whatever)
> is only ever given up to some finite precision, and therefore really
> it's just an interval. Similarly, a p-adic integer is only given up
> to congruence mod some power of p, and so also corresponds to an
> "interval" (really a ball). But p-adics are easier, since two balls
> overlap if and only if one is contained in the other, which is not at
> all true for real intervals. In particular the "overlap test" for p-
> adic balls gives a transitive relation, which seems to be the main
> ingredient missing in the real interval case.
Some IEEE doubles are exact -- you can't tell just by looking at it
whether a value of 0.5 is intended to be exact or approximate.
> Do you have any other examples of undesirable behaviour apart from
> the business with the leading term of a polynomial? My feeling is
> that it's the code in the polynomials that needs to change, rather
> than anything else.
Just taking a quick look: the function element_is_zero() at the end of
matrix_window.pyx would break, and multivariate polynomials also break
in various ways. I would be surprised if there weren't more examples;
I didn't spend long looking.
Carl Witty
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