Marc Olive
Université Paris-Saclay
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Publication
Featured researches published by Marc Olive.
Archive for Rational Mechanics and Analysis | 2017
Marc Olive; Boris Kolev; Nicolas Auffray
We definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth-order elasticity tensor C. Decomposing C into its SO(3)-irreducible components we reduce this problem to finding joint invariants of a triplet (a, b, D), where a and b are second-order harmonic tensors, and D is a fourth-order harmonic tensor. Combining theorems of classical invariant theory and formal computations, a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time.
Foundations of Computational Mathematics | 2017
Marc Olive
In this article, we present a modern viewpoint on the Gordan algorithm for binary forms. The symbolic method is recast in terms of
Mathematics and Mechanics of Solids | 2017
Nicolas Auffray; Boris Kolev; Marc Olive
Journal of Elasticity | 2018
Marc Olive; Boris Kolev; Boris Desmorat; Rodrigue Desmorat
\mathrm {SL}(2,{\mathbb {C}})
European Journal of Mechanics A-solids | 2018
Rodrigue Desmorat; Boris Desmorat; Marc Olive; Boris Kolev
arXiv: Mathematical Physics | 2013
Marc Olive; Nicolas Auffray
SL(2,C) equivariant homomorphisms. A graphical approach is used to define Gordan’s ideal, a central tool used to obtain an integrity basis for the covariant algebra of a binary form. To illustrate the power of this method, we compute for the first time a minimal integrity basis for the covariant algebra of
arXiv: Representation Theory | 2018
Boris Kolev; Marc Olive; Rodrigue Desmorat; Boris Desmorat
Symmetry and Computation | 2018
Boris Kolev; Nicolas Auffray; Boris Desmorat; Rodrigue Desmorat; Marc Olive; Michel Petitot
\mathrm {S}_{6}\oplus \mathrm {S}_{4}
arXiv: Representation Theory | 2017
Marc Olive
Effective moduli spaces and applications to cryptography | 2014
Boris Kolev; Marc Olive
S6⊕S4,
