Dear GAP Forum,

Nicola Sottocornola wrote

let Q be the following quaternions field

Indeterminate(Rationals,"x");;
p:=UnivariatePolynomial(Rationals,[3/4,0,-1],1);;
e:=FieldExtension(Rationals,p);;
Q:=QuaternionAlgebra(e);
b:=BasisVectors(Basis(Q));

Is there a function f computing the norm of a quaternion?

I mean f( a b[1] + b b[2] + c b[3] + d b[4] ) = a^2 +b^2 +c^2 + d^2.

There is no GAP library function for that.
However, the following function will do the job.

NormQuat := function( quat )
    if not IsQuaternion( quat ) then
      Error( "<quat> must be a quaternion" );
    fi;
    return Sum( List( ExtRepOfObj( quat ), c -> c^2 ) );
end;

I hope this helps,
Thomas