Re: Mathematica "Reduce" function

[Rafael Guglielmetti <rafael.guglielmetti@unifr.ch>]

Dear all,
I step (maybe too late) in the discussion with a small question: If k is 
big, would it be interesting to parallelize the first (i.e. external) loop?

Best,

Rafael

On 03/02/2017 10:00 AM, Pedro Fortuny Ayuso wrote:
> 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.
>
> Bill's reply of counting
>
> 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.