Rewriting tables and memorized semirings

The following is intended to be a contribution in the area of what could be called efficient algebraic structures or efficient data structures. In fact, we define and construct a new data structure, the tables (abstract and reduced), which are at first special multisets of two-raws arrays. The first raw is filled with words (or more generally, elements taken in some semigroup) and the second with some coefficients taken in a semiring.