Computing a nonnegative matrix factorization? provably, Proceedings of the 44th symposium on Theory of Computing, pp.145-162, 2012. ,
Introduction to commutative algebra, 1969. ,
Polar Varieties, Real Equation Solving, and Data Structures: The Hypersurface Case, Journal of Complexity, vol.13, issue.1, pp.5-27, 1997. ,
DOI : 10.1006/jcom.1997.0432
Generalized polar varieties: geometry and algorithms, Journal of Complexity, vol.21, issue.4, pp.377-412, 2005. ,
DOI : 10.1016/j.jco.2004.10.001
URL : http://doi.org/10.1016/j.jco.2004.10.001
On the geometry of polar varieties, Applicable Algebra in Engineering, Communication and Computing, vol.43, issue.2, 2010. ,
DOI : 10.1007/s00200-009-0117-1
URL : https://hal.archives-ouvertes.fr/hal-01148162
Refined Bounds on the Number of Connected Components of Sign Conditions on a Variety, Discrete & Computational Geometry, vol.133, issue.2, pp.577-597, 2012. ,
DOI : 10.1007/s00454-011-9391-3
Refined bounds on the number of connected components of sign conditions II. arXiv preprint, 2013. ,
On bounding the Betti numbers and computing the Euler characteristic of semialgebraic sets, Proc. 28-th annual ACM Symposium on Theory of Computing, pp.408-417, 1996. ,
Computing the first few Betti numbers of semi-algebraic sets in single exponential time, Journal of Symbolic Computation, vol.41, issue.10, pp.1125-1154, 2006. ,
DOI : 10.1016/j.jsc.2006.07.001
Computing roadmaps of semi-algebraic sets (extended abstract), Proceedings of the twenty-eighth annual ACM symposium on Theory of computing , STOC '96, pp.168-173, 1996. ,
DOI : 10.1145/237814.237857
On the combinatorial and algebraic complexity of quantifier elimination, Journal of the ACM, vol.43, issue.6, pp.1002-1045, 1996. ,
DOI : 10.1145/235809.235813
Computing the first Betti number and the connected components of semi-algebraic sets, Proceedings of the thirty-seventh annual ACM symposium on Theory of computing , STOC '05, pp.304-312, 2005. ,
DOI : 10.1145/1060590.1060636
Algorithms in real algebraic geometry, Algorithms and Computation in Mathematics, vol.10, 2006. ,
DOI : 10.1007/978-3-662-05355-3
URL : https://hal.archives-ouvertes.fr/hal-01083587
Computing the dimension of a semi-algebraic set, Journal of Mathematical Sciences, vol.134, issue.5, pp.2346-2353, 2006. ,
DOI : 10.1007/s10958-006-0111-0
Bounding the radii of balls meeting every connected component of semi-algebraic sets, Journal of Symbolic Computation, vol.45, issue.12, pp.1270-1279, 2010. ,
DOI : 10.1016/j.jsc.2010.06.009
URL : https://hal.archives-ouvertes.fr/hal-00459481
On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, pp.387-397, 1988. ,
DOI : 10.1109/SFCS.1988.21955
The Algebraic Geometry of Perfect and Sequential Equilibrium, Econometrica, vol.62, issue.4, pp.783-794, 1994. ,
DOI : 10.2307/2951732
Géométrie algébrique réelle, 1987. ,
Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, 1998. ,
DOI : 10.1007/978-3-662-03718-8
The complexity of robot motion planning, 1987. ,
Stochastic limit-average games are in EXPTIME, International Journal of Game Theory, vol.158, issue.2, pp.219-234, 2008. ,
DOI : 10.1007/s00182-007-0110-5
Vandermonde Matrices, NP-Completeness, and Transversal Subspaces, Foundations of Computational Mathematics, vol.3, issue.4, pp.421-427, 2003. ,
DOI : 10.1007/s10208-002-0076-4
Polynomial-Time Computation of the Dimension of Algebraic Varieties in Zero-Characteristic, Journal of Symbolic Computation, vol.22, issue.1, pp.1-25, 1996. ,
DOI : 10.1006/jsco.1996.0039
Quantifier elimination for real closed fields by cylindrical algebraic decompostion, Automata Theory and Formal Languages, pp.134-183, 1975. ,
DOI : 10.1007/3-540-07407-4_17
Commutative algebra with a view toward algebraic geometry, Graduate Texts in Mathematics, vol.150, 1995. ,
La détermination de la dimension et des points isolées dune variété algébrique peuvent s effectuer en temps polynomial, Computational Algebraic Geometry and Commutative Algebra, pp.216-256, 1991. ,
Stable mappings and their singularities, 1973. ,
DOI : 10.1007/978-1-4615-7904-5
Complexity of deciding Tarski algebra, Journal of Symbolic Computation, vol.5, issue.1-2, pp.65-108, 1988. ,
DOI : 10.1016/S0747-7171(88)80006-3
Solving systems of polynomial inequalities in subexponential time, Journal of Symbolic Computation, vol.5, issue.1-2, pp.37-64, 1988. ,
DOI : 10.1016/S0747-7171(88)80005-1
Algebraic methods in discrete analogs of the Kakeya problem, Advances in Mathematics, vol.225, issue.5, pp.2828-2839, 2010. ,
DOI : 10.1016/j.aim.2010.05.015
Exact algorithms for solving stochastic games, Proceedings of the 43rd annual ACM symposium on Theory of computing, STOC '11, pp.205-214, 2011. ,
DOI : 10.1145/1993636.1993665
Single exponential path finding in semi-algebraic sets II: The general case. In Algebraic geometry and its applications, collections of papers from Abhyankar's 60-th birthday conference, 1994. ,
Overconstraint analysis on spatial 6-link loops. Mechanism and machine theory, pp.267-278, 2002. ,
Simple Proofs of Classical Theorems in Discrete Geometry via the Guth???Katz Polynomial Partitioning Technique, Discrete & Computational Geometry, vol.133, issue.70, pp.1-19, 2011. ,
DOI : 10.1007/s00454-012-9443-3
Randomized and deterministic algorithms for the dimension of algebraic varieties, Proceedings 38th Annual Symposium on Foundations of Computer Science, pp.36-45, 1997. ,
DOI : 10.1109/SFCS.1997.646091
The Real Dimension Problem Is NPR-Complete, Journal of Complexity, vol.15, issue.2, pp.227-238, 1999. ,
DOI : 10.1006/jcom.1999.0502
A computational proof of the Noether normalization lemma Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, pp.259-273, 1989. ,
An almost optimal algorithm for computing nonnegative rank, SIAM Symposium on Discrete Algorithms, pp.1454-1464, 2012. ,
Real Algebraic Tools in Stochastic Games, Stochastic Games and Applications, pp.57-75, 2003. ,
DOI : 10.1007/978-94-010-0189-2_6
Inverse Kinematics of the General 6R Manipulator and Related Linkages, Journal of Mechanical Design, vol.115, issue.3, p.502, 1993. ,
DOI : 10.1115/1.2919218
On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals, Journal of Symbolic Computation, vol.13, issue.3, pp.255-299, 1992. ,
DOI : 10.1016/S0747-7171(10)80003-3
Finding at Least One Point in Each Connected Component of a Real Algebraic Set Defined by a Single Equation, Journal of Complexity, vol.16, issue.4, pp.716-750, 2000. ,
DOI : 10.1006/jcom.2000.0563
URL : https://hal.archives-ouvertes.fr/inria-00107845
A Baby Steps/Giant Steps Probabilistic Algorithm for??Computing Roadmaps in Smooth Bounded Real Hypersurface, Discrete & Computational Geometry, vol.43, issue.3, pp.181-220, 2011. ,
DOI : 10.1007/s00454-009-9239-2
On the ???piano movers'??? problem I. The case of a two-dimensional rigid polygonal body moving amidst polygonal barriers, Communications on Pure and Applied Mathematics, vol.22, issue.3, pp.345-398, 1983. ,
DOI : 10.1002/cpa.3160360305
On the ???piano movers??? problem. II. General techniques for computing topological properties of real algebraic manifolds, Advances in Applied Mathematics, vol.4, issue.3, pp.298-351, 1983. ,
DOI : 10.1016/0196-8858(83)90014-3
Basic Algebraic Geometry 1, 1977. ,
DOI : 10.1007/978-3-642-57908-0
An Incidence Theorem in Higher Dimensions, Discrete & Computational Geometry, vol.4, issue.2, pp.1-26, 2012. ,
DOI : 10.1007/s00454-012-9420-x
On the Puiseux Series Expansion of the Limit Discount Equation of Stochastic Games, SIAM Journal on Control and Optimization, vol.35, issue.3, pp.860-875, 1997. ,
DOI : 10.1137/S0363012995284138
A Decision Method for Elementary Algebra and Geometry, 1951. ,
DOI : 10.1007/978-3-7091-9459-1_3
Complexity of Computing the Local Dimension of a Semialgebraic Set, Journal of Symbolic Computation, vol.27, issue.6, pp.565-579, 1999. ,
DOI : 10.1006/jsco.1999.0282