38.15 Operations for Algebras

A ^ n

The operator ^ evaluates to the n-fold direct product of A, viewed as a free A-module.

    gap> a:= FreeAlgebra( GF(2), 2 );
    UnitalAlgebra( GF(2), [ a.1, a.2 ] )
    gap> a^2;
    Module( UnitalAlgebra( GF(2), [ a.1, a.2 ] ), 
    [ [ a.one, a.zero ], [ a.zero, a.one ] ] ) 

a in A

The operator in evaluates to true if a is an element of A and false otherwise. a must be an element of the parent algebra of A.

    gap> a.1^3 + a.2 in a;
    true
    gap> 1 in a;
    false 

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