IsNormalExtension(L)
An algebraic extension field is called a normal extension, if it is a splitting field of the defining polynomial. The second version returns whether L is a normal extension of K. The first version returns whether L is a normal extension of its definition field.
gap> IsNormalExtension(e); true gap> p2:=x^4+x+1;; gap> e2:=AlgebraicExtension(p2); AlgebraicExtension(Rationals,x^4 + x + 1) gap> IsNormalExtension(e2); false
GAP 3.4.4