For a set S of cyclotomic integers,
DefaultRing( S ) is the ring of integers in CF( S )
(see DefaultRing),
Ring( S ) is the ring of integers in NF( S ) (see Ring).
    gap> Ring( [ E(5) ] );
    Ring( E(5) )
    gap> Ring( [ EB(7) ] );
    Ring( E(7)+E(7)^2+E(7)^4 )
    gap> DefaultRing( [ EB(7) ] );
    Ring( E(7) ) 
GAP 3.4.4