Result: Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries

Title:
Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries
Authors:
Sedoglavic, Alexandre
Contributors:
Algebra for Digital Identification and Estimation (ALIEN), Centre Inria de l'Université de Lille, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre Inria de Saclay, Institut National de Recherche en Informatique et en Automatique (Inria)-Centrale Lille-École polytechnique (X), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique Fondamentale de Lille (LIFL), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS), Calcul Formel (CALFOR), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS), H. Anai and K. Horimoto and T. Kutsia
Source:
Algebraic Biology 2007. :277-291
Publisher Information:
CCSD; Springer, 2007.
Publication Year:
2007
Collection:
collection:X
collection:UNIV-LILLE3
collection:CNRS
collection:INRIA
collection:INRIA-LILLE
collection:INRIA-SACLAY
collection:LIFL
collection:X-DEP
collection:LAGIS
collection:INRIA_TEST
collection:TESTALAIN1
collection:CRISTAL-CFHP
collection:INRIA2
Subject Terms:
Algebraic system simplification, Lie symmetries, ACM: G.: Mathematics of Computing, G.4: MATHEMATICAL SOFTWARE, G.4.0: Algorithm design and analysis, [INFO.INFO-BI]Computer Science [cs], Bioinformatics [q-bio.QM], [SDV.BIBS]Life Sciences [q-bio], Quantitative Methods [q-bio.QM], [INFO.INFO-SC]Computer Science [cs], Symbolic Computation [cs.SC]
Subject Geographic:
RISC, Castle of Hagenberg, Austria, Austria
Original Identifier:
ARXIV: cs.SC/0612094
HAL:
Document Type:
Conference conferenceObject<br />Conference papers
Language:
English
Relation:
info:eu-repo/semantics/altIdentifier/arxiv/cs.SC/0612094; info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-540-73433-8_20
DOI:
10.1007/978-3-540-73433-8_20
Access URL:
https://inria.hal.science/inria-00120991
https://inria.hal.science/inria-00120991v1/document
https://inria.hal.science/inria-00120991v1/file/Sedoglavic2006.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.inria.00120991v1
Database:
HAL

Further Information

Before analysing an algebraic system (differential or not), one can generally reduce the number of parameters defining the system behavior by studying the system's Lie symmetries. A pilot Maple implementation is available at the url http://www2.lifl.fr/~sedoglav/Software
Lie group theory states that knowledge of a~$m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by~$m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that induces \emph{expanded} Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we \emph{reduce} the number of involved parameters. We present an algorithm based on this standpoint whose arithmetic complexity is \emph{quasi-polynomial} in input's size.