Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Decomposing polynomial systems into simple systems
Journal of Symbolic Computation
Involutive bases of polynomial ideals
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
Journal of Symbolic Computation
Fast Search for the Janet Divisor
Programming and Computing Software
On an Algorithmic Optimization in Computation of Involutive Bases
Programming and Computing Software
The RegularChains library in MAPLE
ACM SIGSAM Bulletin
Effectiveness of involutive criteria in computation of polynomial Janet bases
Programming and Computing Software
Computing representations for radicals of finitely generated differential ideals
Applicable Algebra in Engineering, Communication and Computing - Special Issue: Jacobi's Legacy
Parallel sparse polynomial multiplication using heaps
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Detecting unnecessary reductions in an involutive basis computation
Journal of Symbolic Computation
Notes on triangular sets and triangulation-decomposition algorithms I: polynomial systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Notes on triangular sets and triangulation-decomposition algorithms II: differential systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Thomas decomposition of algebraic and differential systems
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Comprehensive triangular decomposition
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Decomposing polynomial sets into simple sets over finite fields: The positive-dimensional case
Theoretical Computer Science
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In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, square-freeness and non-vanishing initials. Differential simplicity extends algebraic simplicity with involutivity. We build upon the constructive ideas of J. M. Thomas and develop them into a new algorithm for disjoint decomposition. The present paper is a revised version of Bachler et al. (2010) and includes the proofs of correctness and termination of our decomposition algorithm. In addition, we illustrate the algorithm with further instructive examples and describe its Maple implementation together with an experimental comparison to some other triangular decomposition algorithms.