  Central issues of the Dirac constraint formalism are discussed in relation to
the algorithmic methods of commutative algebra based on the Groebner basis
techniques. For a wide class of finite dimensional polynomial degenerate
Lagrangian systems, we describe an algorithmic scheme of computation of the
complete set of constraints, their separation into subsets of first and second
class constraints as well as the construction of a generator of local symmetry
transformations. The proposed scheme is exemplified by considering the
so-called light-cone Yang-Mills mechanics with an SU(2) gauge structure group.
