The Poincaré series of the joint invariants and covariants of the two binary forms

Abstract

Let ${\mathcal{I}}_{d_1,d_2}$ and ${\mathcal{C}}_{d_1,d_2}$ be the algebras of joint invariants and joint covariants of the two binary forms of degrees $d_1$ and $d_2.$ Formulas for computation of the Poincaré series ${\mathcal{P}\mathcal{I}}_{d_1,d_2}(z),$ ${\mathcal{P}\mathcal{C}}_{d_1,d_2}(z)$ of the algebras is found. By using these formulas, we have computed the series for $d_1,d_2\le 20.$

arXiv comment11 pages