On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
Complexity of Bezout's theorem IV: probability of success; extensions
SIAM Journal on Numerical Analysis
A computational method for diophantine approximation
Algorithms in algebraic geometry and applications
Complexity and real computation
Complexity and real computation
Polar varieties, real equation solving, and data structures: the hypersurface case
Journal of Complexity
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
The Subresultant PRS Algorithm
ACM Transactions on Mathematical Software (TOMS)
Sylvester—Habicht sequences and fast Cauchy index computation
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
Approximating the volume of definable sets
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Testing polynomials which are easy to compute (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
On the probability distribution of singular varieties of given corank
Journal of Symbolic Computation
On the number of random digits required in montecarlo integration of definable functions
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Hi-index | 0.00 |
A new technique for the geometry of numbers is exhibited. This technique provides sharp estimates on the number of bounded height rational points in subsets of projective space whose "projective cone" is semi-algebraic. This technique improves existing techniques as the one introduced by Davenport in (J. London Math. Soc. 26 (1951) 179). As main outcome, we conclude that systems of rational polynomial equations of bounded bit length have polynomial size approximate zeros on the average. We also conclude that the average number of projective real solutions of systems of rational polynomial equations of bounded bit length equals the square root of the Bézout number of the given system.