lo <= 0 =>
even?(denom(n)) =>
error "fractional power only defined for x > 0"
even?(numer(n)) =>
hi < 0 =>
interval(hi^n, lo^n) -- lo < hi <=0
interval(0, max(lo^n, hi^n)) -- lo <=0 < hi
interval(lo^n, hi^n) -- lo <=0, odd power
interval(lo^n, hi^n) -- lo > 0
I think there is no problem in other branch?
Also, I just found out that Interval supports negative fractional
power, but not negative integer power.
AIntervalCategory does not support both.
I guess that Interval did not want to deal with inverse of
[a,b] where a<0<b?
- Qian
On 5/11/26 8:20 AM, Waldek Hebisch wrote:
> 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)
>
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