Multivariate Poincaré series for algebras of \( SL_2 \)-invariants (Q2844658)

Let \(d=(d_1,\ldots,d_n)\) be an \(n\)-tuple of integers and denote by \({\mathcal C}_d\) and \({\mathcal I}_d\) te algebras of joint covariants and joint invariants of \(n\) binary forms of degrees \(d_1,\ldots,d_n\). In this paper, the authors derive formulas for computation of the multivariate Poincaré series \({\mathcal P}({\mathcal C}_d,z_1,\ldots,z_n,t)\) and \({\mathcal P}({\mathcal I}_d,z_1,\ldots,z_n)\).