A heuristic algorithm for computing the Poincaré series of the invariants of binary forms

Abstract

We propose a heuristic algorithm for fast computation of the Poincaré series $P_n(t)$ of the invariants of binary forms of degree $n$, viewed as rational functions. The algorithm is based on certain polynomial identities which remain to be proved rigorously. By using it, we have computed the $P_n(t)$ for $n\le 30$.

11 pages, 1 table. To appear in Int. J. Contemp. Math. Sci. Vol. 1 (2006), 557-568