Mechanical theorem proving of differential geometries and some of its applications in mechanics
Journal of Automated Reasoning - Special issue on new trends in automated reasoning
Differential-algebraic decision methods and some applications to system theory
Theoretical Computer Science - Selected papers of the 2nd workshop on algebraic and computer-theoretic aspects of formal power series
Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
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Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Rankings of partial derivatives
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Existence and uniqueness theorems for formal power series solutions of analytic differential systems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
The differential ideal [P]: M∞
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Essential components of an algebraic differential equation
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Factorization-free decomposition algorithms in differential algebra
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Computing canonical representatives of regular differential ideals
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
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Proceedings of the 2001 international symposium on Symbolic and algebraic computation
A probabilistic algorithm to test local algebraic observability in polynomial time
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Polynomial Gcd Computations over Towers of Algebraic Extensions
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Computing power series solutions of a nonlinear PDE system
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Characteristic sets for ordinary differential equations
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Solving second order linear differential equations with Klein's theorem
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Application of numerical algebraic geometry and numerical linear algebra to PDE
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On the complexity of the resolvent representation of some prime differential ideals
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Symbolic-numeric computation of implicit riquier bases for PDE
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Universal characteristic decomposition of radical differential ideals
Journal of Symbolic Computation
A bound for the Rosenfeld–Gröbner algorithm
Journal of Symbolic Computation
Algebraic transformation of differential characteristic decompositions from one ranking to another
Journal of Symbolic Computation
Differential invariants of a Lie group action: Syzygies on a generating set
Journal of Symbolic Computation
On the complexity of the resolvent representation of some prime differential ideals
Journal of Complexity
Thomas decomposition of algebraic and differential systems
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
A new definition for passivity and its relation to coherence
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
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
A new algorithmic scheme for computing characteristic sets
Journal of Symbolic Computation
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This is the second in a series of two tutorial articles devoted to triangulation-decomposition algorithms. The value of these notes resides in the uniform presentation of triangulation-decomposition of polynomial and differential radical ideals with detailed proofs of all the presented results. We emphasize the study of the mathematical objects manipulated by the algorithms and show their properties independently of those. We also detail a selection of algorithms, one for each task. The present article deals with differential systems. It uses results presented in the first article on polynomial systems but can be read independently.