michel petitot - Academia.edu (original) (raw)

Papers by michel petitot

The goal of the present paper is to propose an enhanced ordinary differential equations solver by... more The goal of the present paper is to propose an enhanced ordinary differential equations solver by exploitation of the powerful equivalence method of Élie Cartan. This solver returns a target equation equivalent to the equation to be solved and the transformation realizing the equivalence. The target ODE is a member of a dictionary of ODE, that are regarded as well-known, or at least well-studied. The dictionary considered in this article are ODE in a book of Kamke. The major advantage of our solver is that the equivalence transformation is obtained without integrating differential equations. We provide also a theoretical contribution revealing the relationship between the change of coordinates that maps two differential equations and their symmetry pseudo-groups.

Abstract. This paper presents a symbolic algorithm for computing the ODE systems which describe t... more Abstract. This paper presents a symbolic algorithm for computing the ODE systems which describe the evolution of the moments associated to a chemical reaction system, considered from a stochastic point of view. The algorithm, which is formulated in the Weyl algebra, seems more efficient than the corresponding method, based on partial derivatives. In particular, an efficient method for handling conservation laws is presented. The output of the algorithm can be used for a further investigation of the system behaviour, by numerical methods. Relevant examples are carried out.

International audienceNo abstrac

Le formalisme des systemes de reactions chimiques (de maniere equivalente des reseaux de Petri st... more Le formalisme des systemes de reactions chimiques (de maniere equivalente des reseaux de Petri stochastiques) est tres souvent utilise en bilogie, en surete de fonctionnement etc. La serie generatrice associee a la master-equation est solution d'une equation d'evolution du type equation de Schrodinger. On adopte ici l'approche classique par le calcul des fonctions propres en se concentrant, dans cette premiere partie, sur le calcul de la distribution stationnaire pour un systeme comportant une seule espece chimique. On montre que, generiquement, la serie generatrice stationnaire est une fonction holomorphe dans tout le plan complexe. Des exemples de calcul (symbolique-numerique) sur ordinateur sont developpes.

This paper presents a symbolic algorithm for computing the ODE systems which describe the evoluti... more This paper presents a symbolic algorithm for computing the ODE systems which describe the evolution of the moments associated to a chemical reaction system, considered from a stochastic point of view. The algorithm, which is formulated in the Weyl algebra, seems more ecient than the corresponding method, based on partial derivatives. In particular, an ecient method for handling conservation laws is pre- sented. The output of the algorithm can be used for a further investiga- tion of the system behaviour, by numerical methods. Relevant examples are carried out.

IFAC Proceedings Volumes, 2001

Data Revues 1631073x 03350006 02025074, May 4, 2008

Proceedings of 1995 34th IEEE Conference on Decision and Control, 1995

ABSTRACT We introduce a new class of nonlinear systems called “finitely discretizable”. For a fin... more ABSTRACT We introduce a new class of nonlinear systems called “finitely discretizable”. For a finitely discretizable nonlinear system, any trajectory is completely determined by a finite number of the state derivatives. In the polynomial case, using the notion of dilations, we give sufficient conditions for a nonlinear system to be finitely discretizable and we relate this result to nilpotent Lie algebra of vector fields. We show that multirate sampling techniques can be an efficient tool to deal with the control problem of finitely discretizable systems. We conclude by some examples illustrating the relevance of finitely discretizable systems within the framework of control theory

Lecture Notes in Control and Information Sciences

ABSTRACT In this paper we give, an algorithm that computes the local minimal analytical realizati... more ABSTRACT In this paper we give, an algorithm that computes the local minimal analytical realization of finite generating power series. In the same time, this algorithm proves that any finite generating series has a polynomial realization: observation and vector fields components are commutative polynomials. That algorithm is implemented in the computer algebra system Scratchpad.

Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95, 1995

Lecture Notes in Computer Science, 2011

In this paper, we describe a new way to count isomor-phism classes of rooted triangular maps and ... more In this paper, we describe a new way to count isomor-phism classes of rooted triangular maps and unrooted triangular maps. We point out an explicit connection with the asymptotic expansion of the Airy function. The analysis presented here is used in a recent paper "Vidal (2007)" to present an algorithm that gen-erates in optimal amortized time an exhaustive list of triangular maps of a given size.

The goal of the present paper is to propose an enhanced ordinary differential equations solver by... more The goal of the present paper is to propose an enhanced ordinary differential equations solver by exploitation of the powerful equivalence method of Élie Cartan. This solver returns a target equation equivalent to the equation to be solved and the transformation realizing the equivalence. The target ODE is a member of a dictionary of ODE, that are regarded as well-known, or at least well-studied. The dictionary considered in this article are ODE in a book of Kamke. The major advantage of our solver is that the equivalence transformation is obtained without integrating differential equations. We provide also a theoretical contribution revealing the relationship between the change of coordinates that maps two differential equations and their symmetry pseudo-groups.

Abstract. This paper presents a symbolic algorithm for computing the ODE systems which describe t... more Abstract. This paper presents a symbolic algorithm for computing the ODE systems which describe the evolution of the moments associated to a chemical reaction system, considered from a stochastic point of view. The algorithm, which is formulated in the Weyl algebra, seems more efficient than the corresponding method, based on partial derivatives. In particular, an efficient method for handling conservation laws is presented. The output of the algorithm can be used for a further investigation of the system behaviour, by numerical methods. Relevant examples are carried out.

International audienceNo abstrac

Le formalisme des systemes de reactions chimiques (de maniere equivalente des reseaux de Petri st... more Le formalisme des systemes de reactions chimiques (de maniere equivalente des reseaux de Petri stochastiques) est tres souvent utilise en bilogie, en surete de fonctionnement etc. La serie generatrice associee a la master-equation est solution d'une equation d'evolution du type equation de Schrodinger. On adopte ici l'approche classique par le calcul des fonctions propres en se concentrant, dans cette premiere partie, sur le calcul de la distribution stationnaire pour un systeme comportant une seule espece chimique. On montre que, generiquement, la serie generatrice stationnaire est une fonction holomorphe dans tout le plan complexe. Des exemples de calcul (symbolique-numerique) sur ordinateur sont developpes.

This paper presents a symbolic algorithm for computing the ODE systems which describe the evoluti... more This paper presents a symbolic algorithm for computing the ODE systems which describe the evolution of the moments associated to a chemical reaction system, considered from a stochastic point of view. The algorithm, which is formulated in the Weyl algebra, seems more ecient than the corresponding method, based on partial derivatives. In particular, an ecient method for handling conservation laws is pre- sented. The output of the algorithm can be used for a further investiga- tion of the system behaviour, by numerical methods. Relevant examples are carried out.

IFAC Proceedings Volumes, 2001

Data Revues 1631073x 03350006 02025074, May 4, 2008

Proceedings of 1995 34th IEEE Conference on Decision and Control, 1995

ABSTRACT We introduce a new class of nonlinear systems called “finitely discretizable”. For a fin... more ABSTRACT We introduce a new class of nonlinear systems called “finitely discretizable”. For a finitely discretizable nonlinear system, any trajectory is completely determined by a finite number of the state derivatives. In the polynomial case, using the notion of dilations, we give sufficient conditions for a nonlinear system to be finitely discretizable and we relate this result to nilpotent Lie algebra of vector fields. We show that multirate sampling techniques can be an efficient tool to deal with the control problem of finitely discretizable systems. We conclude by some examples illustrating the relevance of finitely discretizable systems within the framework of control theory

Lecture Notes in Control and Information Sciences

ABSTRACT In this paper we give, an algorithm that computes the local minimal analytical realizati... more ABSTRACT In this paper we give, an algorithm that computes the local minimal analytical realization of finite generating power series. In the same time, this algorithm proves that any finite generating series has a polynomial realization: observation and vector fields components are commutative polynomials. That algorithm is implemented in the computer algebra system Scratchpad.

Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95, 1995

Lecture Notes in Computer Science, 2011

In this paper, we describe a new way to count isomor-phism classes of rooted triangular maps and ... more In this paper, we describe a new way to count isomor-phism classes of rooted triangular maps and unrooted triangular maps. We point out an explicit connection with the asymptotic expansion of the Airy function. The analysis presented here is used in a recent paper "Vidal (2007)" to present an algorithm that gen-erates in optimal amortized time an exhaustive list of triangular maps of a given size.