Re: ellsaturation command seems to stall

[American Citizen <website.reader3@gmail.com>]

Bill:

I see your 2024 paper on the "Flatter algorithm" 
https://megrez.math.u-bordeaux.fr/Events/PARI2024/talks/flatter.pdf#1#1

can this help out in finding a minimal height basis for an elliptic curve?

Randall

On 9/19/26 11:24 AM, Bill Allombert wrote:
> On Sat, Sep 19, 2026 at 11:01:01AM -0700, American Citizen wrote:
> > Bill:
> >
> > Are you recommending that I first do a
> >
> > newpts = ellsaturation(E, ellrank(E,,pts)[4],100);
> >
> > or do a check on the height matrix determinant?
> >
> > if (matdet(ellheightmatrix(E,pts))>0, newpts=ellsaturation(E,pts,100); )
> >
> > which will be faster? (we have to be careful of the compare > to 0, of
> > course for the second method)
> The second method is much faster. However the first one is garanteed to work
> and gives you a set of points which is proven to be independent, and does not
> depend on the accuracy.
>
> In your example one get with the default precision:
> ? matdet(ellheightmatrix(E,pts))
> %8 = 1.8701363718673120851E-25
> which is ambiguous.
> In particular:
> ? matdet(ellheightmatrix(E,pts))>0
> %17 = 1
> is a false positive.
>
> Cheers,
> Bill.