Pedro Fortuny Ayuso on Thu, 02 Mar 2017 10:01:02 +0100

 Re: Mathematica "Reduce" function

• To: <pari-users@pari.math.u-bordeaux.fr>
• Subject: Re: Mathematica "Reduce" function
• From: Pedro Fortuny Ayuso <fortunypedro@uniovi.es>
• Date: Thu, 2 Mar 2017 10:00:48 +0100
• Delivery-date: Thu, 02 Mar 2017 10:01:02 +0100
• References: <20170301164507.GK1825@MBP-pfortuny.local> <20170301170514.GA23217@yellowpig> <20170301180155.GE23217@yellowpig>
• Spamdiagnosticoutput: 1:99
• User-agent: Mutt/1.5.20 (2009-06-14)

```Thanks to all.

My specific problem is trying to solve equations like

6x^2 + 12y^2 +20z^2 = 0

over Z/(2^k)Z. That is, finding the points of that surface
over that ring.

length([[x,y,z]|x<-[0..2^k-1];y<-[0..2^k-1];z<-[0..2^k-1],6*x^2+12*y^2+20*z^2==0])

is the fastest but it ***looks like*** a lot slower than
Mathematica (but please notice I am working on a system
with pari/gp and my colleague on a different one with Mathematica,
so that it may have nothing to do with pari/Mathematica).

I know nothing about number theory, I just can guess what
'solving on the p-adics and then lifting' might mean but
am not quite ready to implement it.

Thanks again,

Pedro.

--
Pedro Fortuny Ayuso
http://pfortuny.net

EPIG, Campus de Viesques, Gijon
Dpto. de Matematicas