On the problem of algebraic completeness for the invariants of the Riemann Tensor: I

We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space-times into two distinct, invariantly characterized, classes: a general class M_G+, and a special, singular class M_S For each class, we provide an independent set of invariants (I_G+) ⊂ CZ and I_S ⊂ CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete.