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
GAP 3.4.4