[GAP Forum] Curious behavior of IsAlgExtRep

[Ha T. Lam]

Dear GAP forum,

I encountered a curious behavior when I tried to use IsAlgExtRep:

x:=Indeterminate(GF(2), "x");
f:=x^5+x^3+Z(2)^0;
gf:=GF(2,f);
prim:=PrimitiveElement(gf);
IsAlgExtRep(prim);

In the above code, I expected IsAlgExtRep(prim) to return true, but it
tells me that it's false instead. If I change the polynomial to:
f:=x^17+x^13+x^11+x^10+x^9+x^7+x^6+x^5+x^4+x^2+Z(2)^0, it correctly tells
me that IsAlgExtRep(prim) is true. I've tried a few other irreducible
polynomial of degree smaller than 17 but they all returned false.

Can you explain what's going on for me?

Best regards,

Ha T. Lam