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: http://www.warwick.ac.uk/~masgaj/ftp/progs/pari/index.html This does not answer your derivations question; but I never needed to do that in my script! John Cremona 2008/7/5 Benedikt Berghammer <benedikt.berghammer@unibw.de>: > 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 >