• Publications
  • Influence
Factorization-free Decomposition Algorithms in Differential Algebra
  • E. Hubert
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 April 2000
TLDR
We show that the structure of differential ideals defined by coherent autoreduced set allows one to uncouple the differential and algebraic computations in a decomposition algorithm. Expand
  • 141
  • 14
  • PDF
Notes on Triangular Sets and Triangulation-Decomposition Algorithms I: Polynomial Systems
  • E. Hubert
  • Mathematics, Computer Science
  • SNSC
  • 12 September 2001
TLDR
This is the first in a series of two tutorial articles devoted to triangulation-decomposition of polynomial and differential radical ideals. Expand
  • 103
  • 10
  • PDF
Notes on Triangular Sets and Triangulation-Decomposition Algorithms II: Differential Systems
  • E. Hubert
  • Mathematics, Computer Science
  • SNSC
  • 12 September 2001
TLDR
This is the second in a series of two tutorial articles devoted to triangulation-decomposition algorithms devoted to differential systems. Expand
  • 98
  • 7
  • PDF
Resolvent Representation for Regular Differential Ideals
  • T. Cluzeau, E. Hubert
  • Mathematics, Computer Science
  • Applicable Algebra in Engineering, Communication…
  • 1 February 2003
TLDR
We show that the generic zeros of a differential ideal [A]:H∞A defined by a differential chain A are birationally equivalent to the general zos of a single regular differential polynomial. Expand
  • 29
  • 6
  • PDF
Improvements to a triangulation-decomposition algorithm for ordinary differential systems in higher degree cases
  • E. Hubert
  • Mathematics, Computer Science
  • ISSAC '04
  • 4 July 2004
TLDR
We introduce new ideas to improve the efficiency and rationality of a triangulation decomposition algorithm. Expand
  • 9
  • 4
Smooth and Algebraic Invariants of a Group Action: Local and Global Constructions
TLDR
We provide an algebraic formulation of the moving frame method for constructing local smooth invariants on a manifold under an action of a Lie group and provide algorithms for constructing rational and replacement invariants. Expand
  • 58
  • 3
  • PDF
Differential Algebra for Derivations with Nontrivial Commutation Rules
Abstract The classical assumption of differential algebra, differential elimination theory and formal integrability theory is that the derivations do commute. This is the standard case arising fromExpand
  • 40
  • 3
  • PDF
Differential invariants of a Lie group action: Syzygies on a generating set
  • E. Hubert
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 23 October 2007
TLDR
Given a group action, known by its infinitesimal generators, we exhibit a complete set of syzygies on a generating set of differential invariants. Expand
  • 47
  • 3
  • PDF
Essential Components of an Algebraic Differential Equation
  • E. Hubert
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 October 1999
TLDR
We present an algorithm to determine the set of essential singular solutions of an algebraic differential equation. Expand
  • 30
  • 2
  • PDF
Convolution surfaces based on polygons for infinite and compact support kernels
  • E. Hubert
  • Mathematics, Computer Science
  • Graph. Model.
  • 2012
TLDR
We provide formulae to create 3D smooth shapes fleshing out a skeleton made of line segments and planar polygons. Expand
  • 19
  • 2
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