Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
Solving parametric algebraic systems
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Solving some overdetermined polynomial systems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
A new algorithm for the geometric decomposition of a variety
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Deformation techniques for efficient polynomial equation solving
Journal of Complexity
Bounds on numers of vectors of multiplicities for polynomials which are easy to compute
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Computing an equidimensional decomposition of an algebraic variety by means of geometric resolutions
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
A Gröbner free alternative for polynomial system solving
Journal of Complexity
A new algorithm for discussing Gröbner bases with parameters
Journal of Symbolic Computation
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
SIAM Journal on Numerical Analysis
Complexity of Quantifier Elimination in the Theory of Algebraically Closed Fields
Proceedings of the Mathematical Foundations of Computer Science 1984
Complexity of quantifier elimination in the theory of ordinary differential equations
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Complexity results for triangular sets
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Elimination Practice: Software Tools and Applications
Elimination Practice: Software Tools and Applications
Sharp estimates for triangular sets
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Complexity of the resolution of parametric systems of polynomial equations and inequations
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Solving parametric polynomial systems
Journal of Symbolic Computation
Minimal canonical comprehensive Gröbner systems
Journal of Symbolic Computation
Solving Polynomial Equations: Foundations, Algorithms, and Applications
Solving Polynomial Equations: Foundations, Algorithms, and Applications
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This paper presents a new algorithm for computing absolutely irreducible components of n-dimensional algebraic varieties defined implicitly by parametric homogeneous polynomial equations over Q, the field of rational numbers. The algorithm computes a finite partition of the parameters space into constructible sets such that the absolutely irreducible components are given uniformly in each constructible set. Each component will be represented by two items: first by a parametric representative system, i.e., the equations that define the component and second by a parametric effective generic point which gives a parametric rational univariate representation of the elements of the component. The number of absolutely irreducible components is constant in each constructible set. The complexity bound of this algorithm is δO(r4)dr4dO(n3), being double exponential in n, where d (resp. δ) is an upper bound on the degrees of the input parametric polynomials w.r.t. the main n variables (resp. w.r.t. r parameters).