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Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
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A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
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Journal of Symbolic Computation
Representation for the radical of a finitely generated differential ideal
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Journal of Symbolic Computation
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Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
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Journal of Symbolic Computation - Special issue on differential algebra and differential equations
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Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
Journal of Symbolic Computation
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Proceedings of the 2001 international symposium on Symbolic and algebraic computation
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Proceedings of the 2001 international symposium on Symbolic and algebraic computation
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Proceedings of the 2005 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
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Journal of Symbolic Computation
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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
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In this paper, we give three theoretical and practical contributions for solving polynomial ODE or PDE systems. The first one is practical: an algorithm which improves the purely algebraic part of Rosenfeld—Gröbner (the polynomial ODE or PDE systems simplifier which is the core of the Maple 5.5 diffalg package). It is a variant of lextriangular but does not need any Gröbner basis computation. The second one is theoretical: a characterization of the output of Rosenfeld—Gröbner and a clarification of the existing relationship between algebraic and differential characteristic sets. The third one is theoretical as well as practical: an algorithm to compute canonical representatives of differential polynomials modulo regular differential ideals without any use of Gröbner bases. This algorithm simplifies the theory (somehow a “pedagogic” contribution) but permits us also to perform easily linear algebra over the base field in the factor differential ring defined by a regular differential ideal.