On Wed, May 13, 2026 at 06:11:50AM +0800, Qian Yun wrote:
> On 5/13/26 12:44 AM, Waldek Hebisch wrote:
> > On Mon, May 11, 2026 at 11:52:08AM +0800, Qian Yun wrote:
> >> On 5/11/26 11:49 AM, Waldek Hebisch wrote:
> >>>>
> >>>> I guess that Interval did not want to deal with inverse of
> >>>> [a,b] where a<0<b?
> >>>
> >>> Yes, we do not want this: this is moral equivalent of division
> >>> by 0.
> >>>
> >>
> >> So for the "^" with negative Fraction Integer argument,
> >> shall we give an error for all intervals, or just for
> >> intervals that contains 0?
> >
> > Negative fractional power should be mostly eqivalent to computing
> > inverse and then positive power, but should avoid double
> > rounding impled by composition of operations. Negative
> > interval can not be raised to power 1/2, and it makes
> > sense to completely forbid raising negative numbers to
> > fractional powers (but current version allows this). But
> > if both lower bound and upper bound are positive, then negative
> > fractional power is well defined.
> >
>
> The implementation can be done as such.
>
> About Exports: "^ : (%, Integer) -> %" is naturally expressed in
> DivisionRing. I think it's ok for Interval to have this category.
> The original authors intention is to stop at Field?
Note that Interval requires FloatingPointSystem, that is Field.
And that was clearly the intent. Also, sound use of Interval
requires directed rounding. If you want more general domains,
then you get different thing, like AInterval.
--
Waldek Hebisch
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