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TitleÉlie Cartanís geometrical vision or how to avoid expression swell
Author(s) Raouf Dridi, Sylvain Neut, Michel Petitot
TypeArticle in Journal
AbstractThe aim of the paper is to demonstrate the superiority of Cartanís method over direct methods based on differential elimination for handling otherwise intractable equivalence problems. In this sense, using our implementation of Cartanís method, we establish two new equivalence results. We establish when a system of second order ODEs is equivalent to flat system (second derivations are zero), and when a system of holomorphic PDEs with two independent variables and one dependent variable is flat. We consider the problem of finding transformation that brings a given equation to the target one. We shall see that this problem becomes algebraic when the symmetry pseudogroup of the target equation is zerodimensional. We avoid the swelling of the expressions, by using non-commutative derivations adapted to the problem.
KeywordsCartanís equivalence method, Differential algebra
URL http://www.sciencedirect.com/science/article/pii/S0747717108001132
JournalJournal of Symbolic Computation
Pages261 - 270
NotePolynomial System Solving in honor of Daniel Lazard
Translation No
Refereed No