Algorithmic algebra
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
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
Journal of Symbolic Computation
Mathematics Mechanization: Mechanical Geometry Theorem-Proving, Mechanical Geometry Problem-Solving, and Polynomial Equations-Solving
Fast Search for the Janet Divisor
Programming and Computing Software
Elimination Practice: Software Tools and Applications
Elimination Practice: Software Tools and Applications
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
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
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Comprehensive triangular decomposition
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Chemical reaction systems, computer algebra and systems biology
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Involutive division generated by an antigraded monomial ordering
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Consistency analysis of finite difference approximations to PDE systems
MMCP'11 Proceedings of the 2011 international conference on Mathematical Modeling and Computational Science
Algorithmic Thomas decomposition of algebraic and differential systems
Journal of Symbolic Computation
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In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit THOMAS decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not only algebraic simplicity but also involutivity. The algorithm has been implemented in MAPLE.