About Gordan's algorithm for binary forms

Marc Olive (1)

1 I2M - Institut de Mathématiques de Marseille

In this paper, we present a modern version of Gordan's algorithm on binary forms. Symbolic method is reinterpreted in terms of $\mathsf{SL}_2(\mathbb{C})$--equivariant homomorphisms defined upon Cayley operator and polarization operator. A graphical approach is thus developed to obtain Gordan's ideal, a central key to get covariant bases of binary forms. To illustrate the power of the method, we compute a covariant basis of $\Sn{6}\oplus\Sn{2}$ and $\Sn{8}$.

Mots clés: Classical invariant theory; Covariants; Algorithm

Domaines: Mathématiques générales [math.GM]

Marc Olive. About Gordan's algorithm for binary forms. 2014. ⟨hal-00952988v2⟩