In this article, we prove that Dirac brackets for Hamiltonian and
non-Hamiltonian constrained systems can be derived recursively. We then study
the applicability of that formulation in analysis of some interesting physical
models. Particular attention is paid to the feasibility of implementation code
for Dirac brackets in Computer Algebra System and analytical techniques for
inversion of triangular matrices.Comment: 29 pages, Latex. Extended version of the article in Physica