Re: Using libpari

[Mike Rosing <eresrch@eskimo.com>]

Thanks Karim!

Since I had something working by hand, I tried it with gp2c.  I ended up 
with this:

while(a6coef < 0x3ffff)
  {
    mask = 1;
    a2 = gen_0;
    a6 = gen_0;
    for(i=0; i<64; i++)
    {
      if(mask & a2coef)
	a2 = gadd(gpowgs(y,i), a2);
      if(mask & a6coef)
	a6 = gadd(gpowgs(y,i), a6);
      mask <<= 1;
    }

I then alternate incrementing a2coef and a6coef.
This is very similar to your concat suggestion (and probably not as 
efficient).

I really appreciate your answer - I have a lot of functions to look at!
Mike

On Tue, 24 Feb 2015, Karim Belabas wrote:

> * Mike Rosing [2015-02-23 19:39]:
> > Hello,
> >
> > I am trying to use libpari as a stand alone C program rather than creating
> > useful functions for gp.  I can do things easily with gp (well, not so easy
> > the first time!) but when I try to do similar things in C I get a lot of
> > errors.
> >
> > What I would like to do is create GF(2^n) elements in "increasing" order:
> > 1
> > t
> > t + 1 t^2
> > t^2 + 1
> > t^2 + t
> > t^2 + t + 1
> > etc..
>
> This is not easy ! The "simple" way is to call ffgen + FF_primroot then
> compute its powers via 2^n-2 multiplications.
>
> > I start my program, and things are fine:
> >
> > #include <pari/pari.h>
> >
> > int main()
> > {
> >   GEN y, E, f, z, a1, a2;
> >
> >   pari_init(2*1024*1024, 5*1024*512);
> >   z = ffinit(gen_2, 10, -1);
> >   y = ffgen(z, -1);
>
> This creates a polynomial z in F_2[x], and create y as (x mod z(x))
>
> >   pari_printf("%Ps %ld\n", type0(y), lg(y));
> >
> > ----------------------
> >
> > I can give a2 a constant value like gen_1, but I have no idea how to give it
> > a value of y, let alone different t_FFELT values.
>
> For specific values:
>
> a2 = y;  // x mod z
> a2 = gadd(y, gen_1); // x+1
>
> More complicated:
>
> A = mkpoln(5, gen_1,gen_0,gen_1,gen_0,gen_0); // x^2+x^4
> a2 = gsubst(A, gvar(A), y);  // A(x), assuming A is a t_POL with coefs in Z, say
>
> To go through all finite fields elements in the order you requested, you
> need some backtracking algorithm emulating forvec(). It's a nice
> exercise, but I'd advise against it if you're beginning with libpari :-)
>
> Another (not too wasteful) posibility is to use something like
>
>  // assume 2^n is representable as an ulong
>  ulong i, N = upowuu(2,n);
>  GEN vy = concat( gpow(y,gen_0), vecpow(y,n-1) ); // vy[i] = y^(i-1)
>  for(i=0; i < N; i++)
>  {
>    GEN h = RgV_sum( shallowextract(vy, utoi(i)) );
>    ...
>  }
>
> (Easier in characteristic 2, but digits() allows to generalize ...)
>
> Cheers,
>
>    K.B.
> --
> Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
> Universite de Bordeaux         Fax: (+33) (0)5 40 00 69 50
> 351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
> F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
> `