Denote by (Xmi,Ymi) the non-constant parts of the generators of Tr(A,A'). To eliminate them we had to compute their syzygies with the generators (Xi,Yi). That means, if M=<(Xmi,Ymi)>+Tr(A,A') then V=<M,M> Syz(M) is just the vector space of constant transformations. The algorithm of the local case completes the computation.