Re: ellsaturation command seems to stall

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

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.