Using ellgenerators function from pari

[Nikos Tzanakis]

Dear all,

I often use pari, and I have the following problem. Consider the following:

va=pari([1,-1,2,3,5])

e=va.ellinit()

In pari 2.5.0, one can use the function ellgenerators like so:

? ellgenerators(e)

Unfortunately, a function e.ellgenerators() is not available in Sage.

Is there a way to use ellgenerators in sage?

My sage version is 5.10.

Thank you in advance..

[John Cremona]

Dear Nikos!

On 4 January 2014 17:49, Nikos Tzanakis <ntza...@gmail.com> wrote:
> Dear all,
>
> I often use pari, and I have the following problem. Consider the following:
>
> va=pari([1,-1,2,3,5])
>
> e=va.ellinit()
>
> In pari 2.5.0, one can use the function ellgenerators like so:
>
> ? ellgenerators(e)
>
> Unfortunately, a function e.ellgenerators() is not available in Sage.
>
> Is there a way to use ellgenerators in sage?

There are two problems here. First, when new functions get added to
pari/gp they do not automatically get added to the Sage interface.
That is why e.<TAB> shows a lot of things you can do with e, but
e.generators() is not one of them.

That problem would be avoided by using

sage: pari('ellgenerators(ellinit([1,-1,2,3,5]))')

except that causes a run-time error, since the generators() function
only works in gp if the optional pari package with my elliptic curve
database has been installed. And Sage does not do that, since it has
its own version of my database.

The best solution, I think, is to use Sage directly. Assuming that
you have installed the optional spkg called database_cremona_ellcurve
this works:

sage: E = EllipticCurve([1,-1,2,3,5])
sage: E
Elliptic Curve defined by y^2 + x*y + 2*y = x^3 - x^2 + 3*x + 5 over
Rational Field
sage: E.label()
'24526a1'
sage: E.gens()
[(-1 : 0 : 1), (3/4 : 13/8 : 1)]

Alternatively, it should be possible to install the pari ellcurves
package into the right place in your Sage installation. I would need
to experiment to see how to do that.

>
> My sage version is 5.10.

I recommend upgrading to 6.0.

By the way, the elliptic curve database has been extended to 320000 as
of 1 January.

John Cremona

>
> Thank you in advance..
>
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[Jeroen Demeyer]

On 2014-01-04 19:08, John Cremona wrote:
> Alternatively, it should be possible to install the pari ellcurves
> package into the right place in your Sage installation.

That can be done with

sage -i database_pari