About Gordan's algorithm for binary forms
Résumé
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 this method, we obtain for the first time a minimal covariant basis for $\mathrm{S}_{6}\oplus\mathrm{S}_{4}$ and $\mathrm{S}_{6}\oplus\mathrm{S}_{4}\oplus\mathrm{S}_{2}$.
Domaines
Mathématiques générales [math.GM]
Origine : Fichiers produits par l'(les) auteur(s)