Re: bug in polredabs?

[Bill Allombert <allomber@math.u-bordeaux.fr>]

On Mon, Oct 14, 2002 at 10:32:25AM -0700, Carl R. Witty wrote:
> Version: Debian packages version 2.1.4-1 (x86 linux).
> 
> There is an example in the documentation for polcompositum that
> demonstrates taking the result of polcompositum and calling polredabs
> on it, and using subst on the result of that.  After the last line of
> the example, you can type "a^5 - 5" and get 0.
> 
> I'm trying to do exactly the same thing, except with different
> polynomials.  Here's my example:
> 
> ? z = polcompositum(x^2-3, 12*x^2-1, 1)[1];
> ? pol = z[1]
> %2 = 12*x^2 - 49
> ? a = z[2]; a^2-3
> %3 = 0
> ? z = polredabs(pol, 1);
> ? pol = z[1]
> %5 = x^2 - 3
> ? a = subst(a.pol, x, z[2])
> %6 = Mod(-6*x, x^2 - 3)
> ? a^2 - 3
> %7 = Mod(105, x^2 - 3)
> 
> I was hoping, based on the polcompositum example, that the last line
> would return 0; this would have worked if the second element returned
> by polredabs were 7/6*x instead of 7*x.
> 
> I don't know if this is a bug, because the polredabs documentation
> says the second element returned by polredabs(..., 1) is
> "an element expressed on a root of the polynomial $P$,
> whose minimal polynomial is equal to $x$", and I don't know what
> "minimal polynomial" means.

Karim have fixed this bug in the stable branch of the CVS,
so the fix will appear in GP 2.1.5.
Thanks for your report !

Cheers,
Bill.