On 2/12/07, sen1 at math.msu.edu <sen1 at math.msu.edu> wrote:
>
> Note, in my last post, I did not check to see if -56 is really a root.
>
> In trying to check it, one gets real nonsense.
>
> (%i6) subst(x=-56, x^51+x^22+1);
> (%o6) -
> 1437438846217273045233591279433697587696887228686919480393652546754508\
> 87538187253915320319
That's because you weren't calculating with modulus 197 (which only happens
in the rat package).
modulus:197$
ratsubst(-56,x,x^51+x^22+1) => 36
On the other hand,
>
> (%i17) modulus: 127;
> (%o17) 127
> (%i18) polymod(x^51+x^22+1);
> 51 22
> (%o18) x + x + 1
> (%i19) factor(%)$
>
> (%i20) p(u):= subst(x=u,factor(%o18));
> (%o20) p(u) := subst(x = u, factor(%o18))
> (%i21) p(-56);
> (%o21) 0
> (%i22)
>
> So, it seemed to find the root symbolically.
>
Sorry, I don't understand the relevance of the mod 127 result for mod 197.
Is this a typo, or some deep mathematical connection that's eluding me?
-s