Computing an equidimensional decomposition of an algebraic variety by means of geometric resolutions

Authors:
Grégoire Lecerf
Affiliations:
UMS MEDICIS, Laboratoire GAGE, École polytechnique, F-91128 Palaiseau, France
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

Citing 13
Cited 6

On computing the determinant in small parallel time using a small number of processors

Information Processing Letters
Parallel arithmetic computations: a survey

Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
On the computational complexity of polynomials and bilinear mappings

Proceedings of the 5th international conference, AAECC-5 on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Polynomial-time computation of the dimension of algebraic varieties in zero-characteristic

Journal of Symbolic Computation
A new algorithm for the geometric decomposition of a variety

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Complexity of computing the local dimension of a semialgebraic set

Journal of Symbolic Computation
The projective noether maple package: computing the dimension of a projective variety

Journal of Symbolic Computation
A Gröbner free alternative for polynomial system solving

Journal of Complexity
Kronecker's and Newton's approaches to solving: a first comparison

Journal of Complexity
How Lower and Upper Complexity Bounds Meet in Elimination Theory

AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
When Polynomial Equation Systems Can Be "Solved" Fast?

AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Probabilistic algorithms for sparse polynomials

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Probabilistic algorithms for verification of polynomial identities (invited)

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation

Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers

Journal of Complexity
Regular Decompositions

Computer Mathematics
Evaluation techniques for zero-dimensional primary decomposition

Journal of Symbolic Computation
Generators of the ideal of an algebraic space curve

Journal of Symbolic Computation
On a generalization of Stickelberger's Theorem

Journal of Symbolic Computation
On computing absolutely irreducible components of algebraic varieties with parameters

Computing

Quantified Score

Hi-index	0.01

Visualization

Abstract

Let ƒ1, … , ƒs be polynomials in n variables over a field of characteristic zero and d be the maximum of their total degree. We propose a new probabilistic algorithm for computing a geometric resolution of each equidimensional part of the variety defined by the system ƒ1 = ··· = ƒs = 0. The returned resolutions are encoded by means of Straight-Line Programs and the complexity of the algorithm is polynomial in a geometric degree of the system. In the worst case this complexity is asymptotically polynomial in sdn.