Bill Allombert on Tue, 03 Jun 2025 00:49:37 +0200


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Re: inconsistent results from hyperellratpoints 

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


Cheers,
Bill