A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
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
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
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
Factorization-free decomposition algorithms in differential algebra
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
New structure theorem for subresultants
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Computing canonical representatives of regular differential ideals
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Computing triangular systems and regular systems
Journal of Symbolic Computation
Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
Journal of Symbolic Computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Standard Bases of Differential Ideals
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Computing power series solutions of a nonlinear PDE system
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Rankings of derivatives for elimination algorithms and formal solvability of analytic partial differential equations
Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
A bound for the Rosenfeld–Gröbner algorithm
Journal of Symbolic Computation
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We introduce new ideas to improve the efficiency and rationality of a triangulation decomposition algorithm. On the one hand we identify and isolate the polynomial remainder sequences in the triangulation-decomposition algorithm. Subresultant polynomial remainder sequences are then used to compute them and their specialization properties are applied for the splittings. The gain is two fold: control of expression swell and reduction of the number of splittings. On the other hand, we remove the role that initials had in previous triangulation-decomposition algorithms. They are not needed in theoretical results and it was expected that they need not appear in the input and output of the algorithms. This is the case of the algorithm presented. New algorithms are presented to compute a subsequent characteristic decomposition from the output of the triangulation decomposition algorithm where the initials need not appear.