Help me calculate with maple the gcd of two polynomials

Question

I can't calculate the gcd of two polynomials $x^2 + (\beta^3 +1)x + \beta^4 + \beta^3 + \beta^2 + \beta$ and $(\beta^5 + \beta^3 + 1)x + \beta^5 + \beta^3 + \beta^2$ where beta is the root of $x^6 + x + 1$, beta belong Field[2],$F_{2}[x]$ , and all polynomials belong $F_{64}[x]$. Help me please. I am using maple 12, but I can't calculate it myself or by using maple.

Answer 1

I'm amazed that no one has yet answered this easy Question---easy if you know Maple, that is.

restart:
alias(beta = RootOf(y^6+y+1)):
Gcd(
     x^2+(beta^3+1)*x+beta^4+beta^3+beta^2+beta,
     (beta^5+beta^3+1)*x + beta^5+beta^3+beta^2
) mod 2;

Maple's response is 1, so the polynomials are relatively prime.