# Question:[Finite-field arithmetic] not working...

## Question:[Finite-field arithmetic] not working...

Maple

Ok I am still not further... Lets assume wie have F_q with q=3^2 and the irreducible polynomial T^2+2T+2...
Be tau the alsias(tau=RootOf(T^2+2T+2));
Then I get in Maple the wrong (??) calculation

(tau+1)(2tau+2)= tau+1 \neq 1, which is supposed to be the right answer: =2tau^2+4tau+2=2(tau^2+2tau+2)-2=0-2=1 because our prime number is 3... WHY does Maple not calculate that stuff correctly??

Another problem:
Be f:= x^2+tau*x;
When I enter Rem(x^q,f,x) mod 3 then Maple returns x, whereas I calculate (tau+1)x...
Where is the mistake?
I build my finite field either via firred := T^2+2*T+2; alias(tau = RootOf(firred))

or
G := GF(3, 2); a := G:-extension; aOut := G:-ConvertOut(a); alias(tau = RootOf(aOut))

But both times the calculations are not correct... I dont know why?