Re: inconsistent results from hyperellratpoints

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Tue, Jun 03, 2025 at 12:49:32AM +0200, Bill Allombert wrote:
> On Mon, Jun 02, 2025 at 02:59:29PM -0700, American Citizen wrote:
> > Can anyone explain this one?
> > 
> > > ? P= -x^4 + 1396354*x^2 - 282104388225
> > > ? hyperellratpoints(P,975)
> > > %19 = [[-975, 376320], [-975, -376320], [-495, 0], [495, 0], [975,
> > > 376320], [975, -376320]]
> > > ? hyperellratpoints(P,1073)
> > > %20 = [[-1073, 0], [-495, 0], [495, 0], [1073, 0]]
> > > ? hyperellratpoints(P,1074)
> > > %21 = [[-1073, 0], [-975, 376320], [-975, -376320], [-495, 0], [495, 0],
> > > [975, 376320], [975, -376320], [1073, 0]]
> > what happened at x=1073? where did the rational pts at x= -975 and +975 go
> > to?
> 
> This seems like a bug.
> 
> The first "bad" commit is
> 
> commit ac281cdddcf2dfbf530d180ce0b3c816715aa9e6
> Author: Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>
> Date:   Wed Oct 16 19:55:04 2019 +0200
> 
>     change ZX_Uspensky so that it finds all rational roots first
> 
>     - negligible cost
>     - this is a often a big speed improvement
>     - guarantees that all rational roots are found

So the difference is that 
install(ZX_Uspensky,GGLb)
ZX_Uspensky(-x^4+1396354*x^2-282104388225,[-1073,1073],1)

now return
[-1073.0000000000000000000000000000000000,-495.00000000000000000000000000000000000,495.00000000000000000000000000000000000,1073.0000000000000000000000000000000000]~

instead of
[-1073, -495.00000000000000000000000000000000000, 495.00000000000000000000000000000000000, 1073]~

Cheers,
Bill.