2016
DOI: 10.1007/s10208-016-9324-x
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About Gordan’s Algorithm for Binary Forms

Abstract: In this paper, we present a modern version of Gordan's algorithm on binary forms. Symbolic method is reinterpreted in terms of SL(2, 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 basis of binary forms. To illustrate the power of this method, we obtain for the first time a minimal covariant bases for S6 ⊕ S4, S6 ⊕ S4 ⊕ S2 and a minimal invariant bases of S8 ⊕ S4 ⊕ S4.

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Cited by 32 publications
(53 citation statements)
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“…Both of them rely on the resolution of a Diophantine equation such as (6). It is the second version that has been used to produce the tables of section 7 and that we shortly outline next (a more detailed treatment of these algorithms is provided in [64]).…”
Section: 2mentioning
confidence: 99%
See 1 more Smart Citation
“…Both of them rely on the resolution of a Diophantine equation such as (6). It is the second version that has been used to produce the tables of section 7 and that we shortly outline next (a more detailed treatment of these algorithms is provided in [64]).…”
Section: 2mentioning
confidence: 99%
“…Indeed, a degree 11 joint invariant in Inv(S 8 ⊕ S 4 ) (which needs to be counted twice for our purpose) was superfluous. This mistake has been corrected in [64].…”
Section: Explicit Computationsmentioning
confidence: 99%
“…In continuous and discrete mathematics, group actions are widespread. They also arise in various fields of applied science, especially in classical mechanics [2,7,29]. Invariants may be used e.g.…”
Section: Introductionmentioning
confidence: 99%
“…In 2014, an integrity basis with thirteen isotropic invariants of a symmetric third order three-dimensional tensor was presented by Olive and Auffray [15]. It was noted that the Olive-Auffray integrity basis is actually a minimal integrity basis [14]. In 2017, Olive, Kolev and Auffray [16] gave a minimal integrity basis of the elasticity tensors, with 297 invariants.…”
Section: Introductionmentioning
confidence: 99%