Computations with parametric equations
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
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
An elimination method for polynomial systems
Journal of Symbolic Computation
A zero structure theorem for differential parametric systems
Journal of Symbolic Computation
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
Decomposing polynomial systems into simple systems
Journal of Symbolic Computation
Algorithmic properties of polynomial rings
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
Polynomial Gcd Computations over Towers of Algebraic Extensions
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Automated Geometric Reasoning: Dixon Resultants, Gröbner Bases, and Characteristic Sets
Selected Papers from the International Workshop on Automated Deduction in Geometry
Lifting techniques for triangular decompositions
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Fast arithmetic for triangular sets: from theory to practice
Proceedings of the 2007 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
Triangular decomposition of semi-algebraic systems
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Algorithms for computing triangular decompositions of polynomial systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Bit-size estimates for triangular sets in positive dimension
Journal of Complexity
Comprehensive triangular decomposition
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Univariate real root isolation in multiple extension fields
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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We discuss algorithmic advances which have extended the pioneer work of Wu on triangular decompositions. We start with an overview of the key ideas which have led to either better implementation techniques or a better understanding of the underlying theory. We then present new techniques that we regard as essential to the recent success and for future research directions in the development of triangular decomposition methods.