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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

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