We establish an efficient compatibility criterion for a system of generalized
complete intersection type in terms of certain multi-brackets of differential
operators. These multi-brackets generalize the higher Jacobi-Mayer brackets,
important in the study of evolutionary equations and the integrability problem.
We also calculate Spencer delta-cohomology of generalized complete
intersections and evaluate the formal functional dimension of the solutions
space. The results are applied to establish new integration methods and solve
several differential-geometric problems.Comment: Some modifications in sections 6.1-2; new references're adde
