A new method for solving algebraic systems of positive dimension
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
Solving parametric algebraic systems
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
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
Localization and primary decomposition of polynomial ideals
Journal of Symbolic Computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Factorization-free decomposition algorithms in differential algebra
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Lifting techniques for triangular decompositions
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Characteristic set method for differential-difference polynomial systems
Journal of Symbolic Computation
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computations modulo regular chains
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Comprehensive triangular decomposition
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Computing with semi-algebraic sets represented by triangular decomposition
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Inverting matrices modulo regular chains
ACM Communications in Computer Algebra
Algorithms for computing triangular decomposition of polynomial systems
Journal of Symbolic Computation
A new algorithmic scheme for computing characteristic sets
Journal of Symbolic Computation
Triangular decomposition of semi-algebraic systems
Journal of Symbolic Computation
On Fulton's algorithm for computing intersection multiplicities
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Computing with semi-algebraic sets: Relaxation techniques and effective boundaries
Journal of Symbolic Computation
Univariate real root isolation in multiple extension fields
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a weakened notion of a polynomial GCD modulo a regular chain, which permits to greatly simplify and optimize the sub-algorithms. Extracting common work from similar expensive computations is also a key feature of our algorithms. In our experimental results the implementation of our new algorithms, realized with the RegularChains library in MAPLE, outperforms solvers with similar specifications by several orders of magnitude on sufficiently difficult problems.