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

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

2009-04-21

arxiv.org/abs/0904.3344v1

Linear and Multilinear Algebra,Volume 58, Issue 6 September 2010 , pages 789 - 803

Mathematics

Algebraic Geometry

11 pages

Scientific paper

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 Poincar\'e series $\mathcal{PI}_{d_1,d_2}(z),$ $ \mathcal{PC}_{d_1,d_2}(z)$ of the algebras is found. By using these formulas, we have computed the series for $d_1,d_2 \leq 20.$

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