• Publications
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About a New Method for Computing in Algebraic Number Fields
TLDR
• The other method cons is t s in fac tor iz ing PI(X) in ~[X] , then P2(X] in ~(C~l)[X] where ~( Ctl) = ~[ X] / I I I (X) , for each i r reducible factor II 1 of P1 ' and so on. Expand
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An Algorithm to Obtain Formal Solutions of a Linear Homogeneous Differential Equation at an Irregular Singular Point
TLDR
The algorithm DELIRE (Linear Differential Equation Irregular and REgular singularities) presented in this paper gives the formal solutions (normal and sub-normal) at an irregular singular point of a linear homogeneous differential operator, whose coefficients are formal Puiseux series. Expand
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  • 3
Computer Algebra and Parallelism
  • J. Dora, J. Fitch
  • Computer Science
  • Lecture Notes in Computer Science
  • 1 September 1989
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Formal solutions of differential equations in the neighborhood of singular points (Regular and Irregular)
TLDR
This paper presents an algorithm for building a fundamental system of formal solutions in the neighbourhood of every singularity of a linear homogenous differential operator. Expand
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  • 1
Numerical methods in the study of critical phenomena : proceedings of a colloquium, Carry-le-Rouet, France, June 2-4, 1980
1. Mathematical Methods.- 1.1 Study of Singularities.- Pade-Hermite Approximants.- Somme Comments About the Numerical Utilization of Factorial Series.- to Real Quasianalytic Classes and ContinuationExpand
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Further Reductions of Normal Forms for Dynamical Systems
Abstract We propose in this paper a method for obtaining a significant refinement of normal forms for dynamical systems or vector fields, with concrete and interesting applications. We use lowerExpand
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  • PDF
Rational normal form for dynamical systems by Carleman linearization
TLDR
We propose in t.his paper a rat,ional Itor~ml form for dynaniical systems or vector fidds that is a refinement of the classical normal forms. Expand
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  • 1
Normal forms for differentiable maps near a fixed point
  • G. Chen, J. Dora
  • Mathematics, Computer Science
  • Numerical Algorithms
  • 1 December 1999
TLDR
We propose in this paper a significant refinement of normal forms for differentiable maps near a fixed point. Expand
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  • 1
Hybrid computation
TLDR
The goal of this paper is twofold: first a rapid introduction to the concept of hybrid system and second the presentation of a new direction in computer algebra that we have called hybrid computation. Expand
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An Algorithm for Computing a New Normal Form for Dynamical Systems
  • G. Chen, J. Dora
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 March 2000
TLDR
We propose in this paper a new normal form for dynamical systems or vector fields which improves the classical normal forms in the sense that it is a further reduction of the classicalnormal forms. Expand
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