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Pré-Publication, Document De Travail Année : 2014

About Gordan's algorithm for binary forms

Marc Olive

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 $\mathrm{S}_{6}\oplus\mathrm{S}_{4}\oplus\mathrm{S}_{2}$.
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Dates et versions

hal-00952988 , version 1 (28-02-2014)
hal-00952988 , version 2 (10-03-2014)
hal-00952988 , version 3 (24-06-2014)
hal-00952988 , version 4 (19-06-2015)

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  • HAL Id : hal-00952988 , version 3

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Marc Olive. About Gordan's algorithm for binary forms. 2014. ⟨hal-00952988v3⟩
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