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arXiv · 1403.2283

About Gordan's algorithm for binary forms

Marc Olive
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Abstract

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 $\Sn{6}\oplus\Sn{4}$ and $\Sn{6}\oplus\Sn{4}\oplus \Sn{2}$.

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Marc Olive. 2014-03-04. About Gordan's algorithm for binary forms. https://arxiv.org/abs/1403.2283

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