Polar varieties and efficient real elimination, Mathematische Zeitschrift, vol.238, issue.1, pp.115-144, 2001. ,
DOI : 10.1007/PL00004896
Generalized polar varieties and an efficient real elimination procedure, Kybernetika, vol.40, pp.519-550, 2004. ,
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
On the geometry of polar varieties, Applicable Algebra in Engineering, Communication and Computing, vol.43, issue.2, pp.33-83, 2010. ,
DOI : 10.1007/s00200-009-0117-1
URL : https://hal.archives-ouvertes.fr/hal-01148162
Point searching in real singular complete intersection varieties -algorithms of intrinsic complexity, 2012. ,
Degeneracy loci and polynomial equation solving, eprint arXiv1306 ,
DOI : 10.1007/s10208-014-9214-z
URL : http://arxiv.org/abs/1306.3390
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
Algorithms in real algebraic geometry, 2006. ,
DOI : 10.1007/978-3-662-05355-3
URL : https://hal.archives-ouvertes.fr/hal-01083587
Certified relaxation for polynomial optimization on semi-algebraic sets, 2013. ,
Algebraic complexity theory, with the collaboration of Thomas Lickteig, Grundlehren der Mathematischen Wissenschaften, vol.315, 1997. ,
Fast computation of a rational point of a variety over a finite field, Mathematics of Computation, vol.75, issue.256, pp.2049-2085, 2006. ,
DOI : 10.1090/S0025-5718-06-01878-3
Some algebraic and geometric computations in PSPACE, Proceedings of the twentieth annual ACM symposium on Theory of computing , STOC '88, pp.460-467, 1988. ,
DOI : 10.1145/62212.62257
Thom's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets, Journal of Symbolic Computation, vol.5, issue.1-2, pp.121-129, 1988. ,
DOI : 10.1016/S0747-7171(88)80008-7
NC algorithms for real algebraic numbers, Applicable Algebra in Engineering, Communication and Computing, vol.10, issue.2, pp.79-98, 1992. ,
DOI : 10.1007/BF01387193
Catastrophes et bifurcations, 1989. ,
Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals, Journal of Pure and Applied Algebra, vol.209, issue.1, pp.189-200, 2007. ,
DOI : 10.1016/j.jpaa.2006.05.028
A concise proof of the Kronecker polynomial system solver from scratch, Expositiones Mathematicae, vol.26, issue.2, pp.101-139, 2008. ,
DOI : 10.1016/j.exmath.2007.07.001
URL : https://hal.archives-ouvertes.fr/hal-00682083
Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge 2, 1998. ,
Lower bounds for diophantine approximations, Journal of Pure and Applied Algebra, vol.117, issue.118, pp.118-277, 1997. ,
DOI : 10.1016/S0022-4049(97)00015-7
Straight-line programs in geometric elimination theory, Journal of Pure and Applied Algebra, vol.124, issue.1-3, pp.101-146, 1998. ,
DOI : 10.1016/S0022-4049(96)00099-0
A Gr??bner Free Alternative for Polynomial System Solving, Journal of Complexity, vol.17, issue.1, pp.154-211, 2001. ,
DOI : 10.1006/jcom.2000.0571
Optimisation globale algébrique et variétés: théorie, algorithmes et implantations, 2013. ,
Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set, SIAM Journal on Optimization, vol.24, issue.3, 2013. ,
DOI : 10.1137/130931308
URL : https://hal.archives-ouvertes.fr/hal-00849523
Deciding reachability of the infimum of a multivariate polynomial, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, 2011. ,
DOI : 10.1145/1993886.1993910
URL : https://hal.archives-ouvertes.fr/hal-00744469
Global optimization of polynomials restricted to a smooth variety using sums of squares, Journal of Symbolic Computation, vol.47, issue.5, pp.47-883, 2012. ,
DOI : 10.1016/j.jsc.2011.12.003
URL : https://hal.archives-ouvertes.fr/hal-00744605
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
Solving polynomial optimization problems via the truncated tangency variety and sums of squares, J. Pure Appl. Algebra, vol.213, issue.11, pp.2167-2176, 2009. ,
Definability and fast quantifier elimination in algebraically closed fields, Theoretical Computer Science, vol.24, issue.3, pp.239-277, 1983. ,
DOI : 10.1016/0304-3975(83)90002-6
On the Time-Space Complexity of Geometric Elimination Procedures, Applicable Algebra in Engineering, Communication and Computing, vol.11, issue.4, pp.239-296, 2001. ,
DOI : 10.1007/s002000000046
On the complexity of semialgebraic sets, IFIP Information Processing 89, pp.293-298, 1989. ,
On the Minimum of a Polynomial Function on a Basic Closed Semialgebraic Set and Applications, SIAM Journal on Optimization, vol.23, issue.1, 2011. ,
DOI : 10.1137/110857751
URL : https://hal.archives-ouvertes.fr/hal-00776280
A Probabilistic Symbolic Algorithm to Find the Minimum of a Polynomial Function on a Basic Closed Semialgebraic Set, Discrete & Computational Geometry, vol.17, issue.3, 2013. ,
DOI : 10.1007/s00454-014-9619-0
Global Optimization with Polynomials and the Problem of Moments, SIAM Journal on Optimization, vol.11, issue.3, pp.796-817, 2001. ,
DOI : 10.1137/S1052623400366802
Kronecker software package ,
Safey El Din, On the practical computation of one point in each connected component of a semi-algebraic set defined by a polynomial system of equations and non-strict inequalities, INRIA Rapport de recherche, vol.5079, 2004. ,
The red book of varieties and schemes, Lecture Notes in Mathematics, 1358. ,
Commutative ring theory, (transl, Paperback Cambridge Studies in Advanced Mathematics, 1989. ,
An exact Jacobian SDP relaxation for polynomial optimization, Mathematical Programming, vol.207, issue.3, pp.225-255, 2013. ,
DOI : 10.1007/s10107-011-0489-4
Counting real zeroes in the multivariate case, Computational algebraic geometry, Eyssette et Galligo Progress in Mathematics 109, pp.203-224, 1993. ,
A faster PSPACE algorithm for deciding the existential theory of the reals, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, pp.291-295, 1988. ,
DOI : 10.1109/SFCS.1988.21945
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.255-352, 1992. ,
DOI : 10.1016/S0747-7171(10)80003-3
Complexity of computation on real algebraic numbers, Journal of Symbolic Computation, vol.10, issue.1, pp.39-51, 1990. ,
DOI : 10.1016/S0747-7171(08)80035-1
Polar varieties and computation of one point in each connected component of a smooth real algebraic set, Proceedings of the 2003 international symposium on Symbolic and algebraic computation , ISSAC '03, pp.224-231, 2003. ,
DOI : 10.1145/860854.860901
URL : https://hal.archives-ouvertes.fr/inria-00099649
Computing the global optimum of a multivariate polynomial over the reals, Austria (Hagenberg), 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-01305635
Practical and Theoretical Issues for the Computation of Generalized Critical Values of a Polynomial Mapping, Lecture Notes in Computer Science, vol.5081, 2007. ,
DOI : 10.1007/978-3-540-87827-8_4
URL : https://hal.archives-ouvertes.fr/hal-01305664
Basic algebraic geometry. 1: Varieties in projective space, 1994. ,
DOI : 10.1007/978-3-642-37956-7
Lectures on results on Bézout's theorem. Notes by D, P. Patil, Lectures on Mathematics and Physics Mathematics Tata Institute of Fundamental Research, vol.74, 1984. ,