John Cremona on Sat, 05 Jul 2008 15:08:53 +0200

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Re: Derivation in finite fields

My reply to Benedikt went only to him and not to the list, so I am
sending it again:

I wrote a gp script to do exactly the same thing a few years ago.  You
can get it from here:

This does not answer your derivations question;  but I never needed to
do that in my script!

John Cremona

2008/7/5 Benedikt Berghammer <>:
> Hi all,
> I'm new in working with PARI and have the following problem. I'm working on
> a script for computing the Weil-Pairing over finite fields after Miller's
> algorithm.
> In one step I need to get the line tangent to an Elliptic Curve E at a point
> P. For computing the gradient of this tangent I need to compute the
> derivation of the square root.
> For example I have the Elliptic Curve E=x^3-48*x+1 in the field p=1009.
> When trying
> Mod(deriv(sqrt(x^3-48*x+1)),1009) I get the following error in PARI: Mod:
> incorrect type in Rg_to_Fl.
> Is there any possibility to compute such derivations in PARI or has PARI
> maybe functions for computing such a tangent line?
> Thanks
> Benedikt