CIRM - Videos & books LibraryDocuments

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research talks;Computer Science;Numerical Analysis and Scientific Computing

Classical invariant theory has essentially addressed the action of the general linear group on homogeneous polynomials. Yet the orthogonal group arises in applications as the relevant group of transformations, especially in 3 dimensional space. Having a complete set of invariants for its action on ternary quartics, i.e. degree 4 homogeneous polynomials in 3 variables, is, for instance, relevant in determining biomarkers for white matter from diffusion MRI.
We characterize a generating set of rational invariants of the orthogonal group acting on even degree forms by their restriction on a slice. These restrictions are invariant under the octahedral group and their explicit formulae are given compactly in terms of equivariant maps. The invariants of the orthogonal group can then be obtained in an explicit way, but their numerical evaluation can be achieved more robustly using their restrictions. The exhibited set of generators futhermore allows us to solve the inverse problem and the rewriting.
Central in obtaining the invariants for higher degree forms is the preliminary construction, with explicit formulae, for a basis of harmonic polynomials with octahedral symmetry, dif- ferent, though related, to cubic harmonics.
This is joint work with Paul Görlach (now at MPI Leipzig), in a joint project with Téo Papadopoulo (Inria Méditerranée). Classical invariant theory has essentially addressed the action of the general linear group on homogeneous polynomials. Yet the orthogonal group arises in applications as the relevant group of transformations, especially in 3 dimensional space. Having a complete set of invariants for its action on ternary quartics, i.e. degree 4 homogeneous polynomials in 3 variables, is, for instance, relevant in determining biomarkers for white matter from ...

Documents

Thesaurus

Revues

Documents 68W30 | enregistrements trouvés : 65

Invariants of ternary forms under the orthogonal group Hubert, Evelyne | CIRM H Nouveau

Symbolic computation and automated reasoning :the CALCULEMUS-2000 symposium#8th symposium on the integration of symbolic computation and mechanized reasoning, St. Andrews, Scotland, GB, August 6--7, 2000 Kerber, Manfred ; Kohlhase, Michael | A.K. Peters 2000 Nouveau

JNCF' 2003 :journées nationales de calcul formel#CIRM#Janv. 20-24 Boucher, Delphine ; Hanrot, Guillaume ; Rouillier, Fabrice ; Schost, Eric | CNRS;INRIA 2003 Nouveau

Orthogonal polynomials and special functions :lectures of the summer school took place at the Katholeike Universiteit Leuven#Aug. 12-16 Koelink, Erik ; Van Assche, Walter | Springer 2003 Nouveau

Algorithmic and quantitative real algebraic geometry :DIMACS workshop on ... in mathematics and computer science held at DIMACS Center#Rutgers University#March 12-16 Basu, Saugata ; Gonzalez-Vega, Laureano | American Mathematical Society 2003 Nouveau

Integer points in polyhedra-geometry, number theory, algebra, optimization :proceedings of an AMS-IMS-SIAM joint summer research conference on integer points in polyhedra#July 13-17 Barvinok, Alexander ; Beck, Matthias ; Haase, Christian ; Reznick, Bruce | American Mathematical Society 2005 Nouveau

Algebraic methods in cryptography :AMS/DMV joint international meeting#June 16-19international workshop on...#Nov. 17-18 Gerritzen, Lothar ; Goldfeld, Dorian ; Kreuzer, Martin ; Rosenberg, Gerhard | American Mathematical Society 2006 Nouveau

Symbolic-numeric computationjuly 19-21 Wang, Dongming ; Zhi, Lihong | Springer 2007 Nouveau

Principles and practice of constraint programming-CP'95:first international conference, CP'95#Sept.19-22 Montanari, Ugo ; Rossi, Francesca | Springer-Verlag 1995 Nouveau

Constraints in computational logics:first international conference, CCL'94#Sept.7-9 Jouannaud, Jean-Pierre | Springer-Verlag 1994 Nouveau

Software for algebraic geometry:papers of a workshopMinneapolis#october 23-27, 2006 Stillman, Michael E. ; Takayama, Nobuki ; Verschelde, Jan | Springer 2008 Nouveau

Algorithms in algebraic geometrybased on the workshopMinneapolis # september 18-22, 2006 Dickenstein, Alicia ; Schreyer, Frank-Olaf ; Sommese, Andrew J. | Springer 2008 Nouveau

Algorithmic number theory7th international symposium, ANTS-VIIBerlin # july 23-28, 2006proceedings Hess, Florian ; Pauli, Sebastian ; Pohst, Michael | Springer 2006 Nouveau

Nonlinear Computational GeometryMinneapolis # May 29-June 2, 2007 Emiris, Ioannis Z. ; Sottile, Frank ; Theobald, Thorsten | Springer 2010 Nouveau

Future directions for research in symbolic computation.Report of a workshop on symbolic and algebraic computationWashington # april 29-30, 1988 Boyle, Ann ; Caviness, B. F. | Society For Industrial And Applied Mathematics 1990 Nouveau

Operads 2009Marseille # april 20-25, 2009 Loday, Jean-Louis ; Vallette, Bruno | Société Mathématique de France 2013 Nouveau

SMT solving Monniaux, David | CIRM H Nouveau

Filtrer

Type

Domaine

Codes MSC

Documents

Références

Auteurs

Thesaurus

Symbolic computation and automated reasoning :
the CALCULEMUS-2000 symposium#8th symposium on the integration of symbolic computation and mechanized reasoning, St. Andrews, Scotland, GB, August 6--7, 2000 Kerber, Manfred ; Kohlhase, Michael | A.K. Peters 2000 Nouveau

JNCF' 2003 :
journées nationales de calcul formel#CIRM#Janv. 20-24 Boucher, Delphine ; Hanrot, Guillaume ; Rouillier, Fabrice ; Schost, Eric | CNRS;INRIA 2003 Nouveau

Orthogonal polynomials and special functions :
lectures of the summer school took place at the Katholeike Universiteit Leuven#Aug. 12-16 Koelink, Erik ; Van Assche, Walter | Springer 2003 Nouveau

Algorithmic and quantitative real algebraic geometry :
DIMACS workshop on ... in mathematics and computer science held at DIMACS Center#Rutgers University#March 12-16 Basu, Saugata ; Gonzalez-Vega, Laureano | American Mathematical Society 2003 Nouveau

Algebraic methods in cryptography :
AMS/DMV joint international meeting#June 16-19
international workshop on...#Nov. 17-18 Gerritzen, Lothar ; Goldfeld, Dorian ; Kreuzer, Martin ; Rosenberg, Gerhard | American Mathematical Society 2006 Nouveau

Symbolic-numeric computation
july 19-21 Wang, Dongming ; Zhi, Lihong | Springer 2007 Nouveau

Principles and practice of constraint programming-CP'95:
first international conference, CP'95#Sept.19-22 Montanari, Ugo ; Rossi, Francesca | Springer-Verlag 1995 Nouveau

Constraints in computational logics:
first international conference, CCL'94#Sept.7-9 Jouannaud, Jean-Pierre | Springer-Verlag 1994 Nouveau

Software for algebraic geometry:
papers of a workshop
Minneapolis#october 23-27, 2006 Stillman, Michael E. ; Takayama, Nobuki ; Verschelde, Jan | Springer 2008 Nouveau

Algorithms in algebraic geometry
based on the workshop
Minneapolis # september 18-22, 2006 Dickenstein, Alicia ; Schreyer, Frank-Olaf ; Sommese, Andrew J. | Springer 2008 Nouveau

Algorithmic number theory
7th international symposium, ANTS-VII
Berlin # july 23-28, 2006
proceedings Hess, Florian ; Pauli, Sebastian ; Pohst, Michael | Springer 2006 Nouveau

Nonlinear Computational Geometry
Minneapolis # May 29-June 2, 2007 Emiris, Ioannis Z. ; Sottile, Frank ; Theobald, Thorsten | Springer 2010 Nouveau

Future directions for research in symbolic computation.
Report of a workshop on symbolic and algebraic computation
Washington # april 29-30, 1988 Boyle, Ann ; Caviness, B. F. | Society For Industrial And Applied Mathematics 1990 Nouveau

Operads 2009
Marseille # april 20-25, 2009 Loday, Jean-Louis ; Vallette, Bruno | Société Mathématique de France 2013 Nouveau