William corrected my mistake.  The code was working correctly.  I
wanted the number of distinct prime divisors of each f.  That's
exactly what the code was giving me.

Thank you for replying!

NS



On Mar 9, 4:29 pm, Carl Witty <[email protected]> wrote:
> On Mon, Mar 9, 2009 at 1:21 PM, Noel <[email protected]> wrote:
>
> > Thank you all for your replies!  Now I have another problem:
>
> > sage: for f in list(GF(2)['x'].polynomials(of_degree=2)):
> > ....:     print len(prime_divisors(f)), f
> > ....:
> > 1 x^2
> > 1 x^2 + 1
> > 2 x^2 + x
> > 1 x^2 + x + 1
>
> > Only one of these polynomials should have a 1 in the first column (the
> > polynomial that's irreducible).  What am I doing wrong?
>
> prime_divisors() gives you the distinct prime divisors:
> sage: prime_divisors(8)
> [2]
>
> What do you really want?  If you want the factorization, you can use
> factor(f); if you want to know if f is irreducible, you can use
> f.is_irreducible().
>
> Carl
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