On Thu, May 07, 2026 at 05:26:02PM +0800, Qian Yun wrote:
> (1) -> x := interval(-2.0,-1.0)$Interval Float
>
> (1) [- 2.0, - 1.0]
> Type: Interval(Float)
> (2) -> x^(2/1)
>
> (2) [0.0, 4.0000000000_000000001]
> Type: Interval(Float)
> (3) -> x^2
>
> (3) [0.9999999999_9999999999, 4.0000000000_000000001]
> Type: Interval(Float)
>
>
> Notice that for the fractional power (2/1), the answer is wrong.
As Ralf noted the anwer is not strictly speaking wrong, just
suboptimal. AFAICS one could get better intervals in other
case, by adding something like:
0 < lo => interval(lo^n, hi^n)
0 is only needed for case when lo <= 0 <= hi
> - Qian
>
> diff --git a/src/algebra/interval.spad b/src/algebra/interval.spad
> index 180b1c7b..8bd84ec1 100644
> --- a/src/algebra/interval.spad
> +++ b/src/algebra/interval.spad
> @@ -429,7 +429,7 @@
> error "fractional power only defined for x > 0"
> even?(numer(n)) =>
> hi < 0 =>
> - interval(0, lo^n)
> + interval(hi^n, lo^n)
> interval(0, max(lo^n, hi^n))
> interval(lo^n, hi^n)
> interval(lo^n, hi^n)
--
Waldek Hebisch
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