polmod ^ 0 loses base field modulo?

[Carlo Wood <carlo@alinoe.com>]

Hi all!

I'm very new to PARI/gp (since yesterday), so probably (hopefully)
I'm doing something wrong.  Nevertheless, I really don't understand
what that would be.

Here is what I did:

? T12 = Mod(1,2)*t^12 + Mod(1,2)*t^3 + Mod(1,2);
? g12 = Mod( Mod(1,2)*t^9 + Mod(1,2)*t^8 + Mod(1,2)*t^7 + Mod(1,2)*t^4 + Mod(1,2)*t^2 + Mod(1,2)*t, T12 );

Now g12 is a generator of the field F_2[t]/<t^12+t^3+1>.

Then I did:

? g = g12^0
%10 = Mod(1, Mod(1, 2)*t^12 + Mod(1, 2)*t^3 + Mod(1, 2))

This SHOULD be the unity of said field, however:

? a = (g + 1/g)
%12 = Mod(2, Mod(1, 2)*t^12 + Mod(1, 2)*t^3 + Mod(1, 2))

What is that 2 doing there?

? a == 0
%13 = 0

Can someone tell me what I'm doing wrong please?

-- 
Carlo Wood <carlo@alinoe.com>