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Referencias:

• Bank, B., Giusti, M., Heintz, J., Mbakop, G.M., Polar varieties, real equation solving and data structures: The hypersurface case (1997) J. Complexity, 13, pp. 5-27
• Bank, B., Giusti, M., Heintz, J., Mbakop, G.M., Polar varieties and efficient real elimination (2001) Math. Z., 238, pp. 115-144
• Bank, B., Giusti, M., Heintz, J., Pardo, L.M., Generalized polar varieties and an efficient real elimination procedure (2004) Kybernetika (Prague), 40, pp. 519-550
• Bank, B., Giusti, M., Heintz, J., Pardo, L.M., Generalized polar varieties: Geometry and algorithms (2005) J. Complexity, 21, pp. 377-412
• Bank, B., Giusti, M., Heintz, J., Safey El Din, M., Schost, E., On the geometry of polar varieties (2010) Appl. Algebra Engrg. Comm. Comput., 21, pp. 33-83
• Basu, S., Pollack, R., Roy, M.-F., On the combinatorial and algebraic complexity of quantifier elimination (1996) J. ACM, 43, pp. 1002-1045
• Brasselet, J.P., Milnor classes via polar varieties, AMS (2000) Contemp. Math., 266, pp. 181-187
• Bürgisser, P., Clausen, M., Shokrollahi, M.A., (1997) Algebraic complexity theory. With the collaboration of Thomas Lickteig, , [B] Grundlehren der Mathematischen Wissenschaften 315, Springer-Verlag, Berlin
• Canny, J.F., Some Algebraic and Geometric Computations in PSPACE (1988) Proc. 20th ACM Symp. on Theory of Computing, pp. 460-467
• Castro, D., Giusti, M., Heintz, J., Matera, G., Pardo, L.M., The hardness of polynomial equation solving (2003) Found. Comput. Math., 3, pp. 347-420
• Giusti, M., Heintz, J., Kronecker's smart, little black boxes (2001) Foundations of Computational Mathematics, Conf, 284, pp. 69-104. , R.A. DeVore, A. Iserles, E. Süli (eds.), Oxford 1999, Cambridge University Press, Lond. Math. Soc. Lect. Note Ser
• Grigor'ev, D., Vorobjov, N., Solving systems of polynomial inequalities in subexponential time (1988) J. Symb. Comput., 5, pp. 37-64
• Heintz, J., Kuijpers, B., Constraint databases, data structures and efficient query evaluation (2004) Constraint databases, Proceedings of the First international symposium, pp. 1-24. , B. Kuijpers et al. (eds.), CDB 2004, Paris (France), June 12-13 2004, Lecture Notes in Computer Science 3074, Springer-Verlag, Berlin
• Henry, J.P.G., Merle, M., Limites d'espaces tangents et transversalité de variétés polaires (1982) Algebraic geometry, Proc. int. Conf., 961, pp. 189-199. , La Rabida (Spain) 1981 Lect. Notes Math
• Heintz, J., Roy, M.-F., Solernó, P., On the complexity of semialgebraic sets (1989) IFIP Information Processing 89, pp. 293-298. , G.X. Ritter (ed.), Elsevier
• Heintz, J., Roy, M.-F., Solernó, P., Sur la complexité du principe de Tarski-Seidenberg (1990) Bull. Soc. Math. Fr., 118, pp. 101-126
• Lê, D.T., Teissier, B., Variétés polaires locales et classes de Chern des variétés singuli'eres (1981) Ann. Math., 114 (2), pp. 457-491
• Mumford, D., Fogarty, J., Kirwan, F., (1994) Geometric Invariant Theory, , Springer-Verlag, Berlin
• Piene, R., Polar classes of singular varieties (1978) Ann. Scient. éc. Norm. Sup. 4. Sér., 11, pp. 247-276
• Renegar, J., A faster PSPACE algorithm for deciding the existential theory of the reals (1988) Proceedings of the 29th Annual Symposium on Foundations of Computer Science, pp. 291-295
• Renegar, J., On the computational complexity and geometry of the first-order theory of the reals. I. Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals (1992) J. Symbolic Comput., 13 (3), pp. 255-299
• Renegar, J., On the computational complexity and geometry of the first-order theory of the reals. II. The general decision problem. Preliminaries for quantifier elimination (1992) J. Symbolic Comput., 13 (3), pp. 301-327
• Renegar, J., On the computational complexity and geometry of the first-order theory of the reals. III. Quantifier elimination (1992) J. Symbolic Comput., 13 (3), pp. 329-352
• Room, T.G., (1938) The Geometry of Determinantal Loci, , Cambridge University Press, London
• Rouillier, F., Roy, M.-F., Safey El Din, M., Finding at least one point in each connected component of a real algebraic set defined by a single equation (2000) J. Complexity, 16, pp. 716-750
• Safey El Din, M., Schost, E., Polar varieties and computation of one point in each connected component of a smooth real algebraic set (2003) Proceedings of ISSAC 2003, pp. 224-231. , J. Rafael (ed.), ACM Press
• Safey El Din, M., Schost, E., Properness defects of projections and computation of at least one point in each connected component of a real algebraic set (2004) J. Discrete and Comput. Geom., 32, pp. 417-430
• Safey El Din, M., (2005) Finding sampling points on real hypersurfaces is easier in singular situations, , preprint
• Teissier, B., Variétes polaires. II. Multiplicités polaires, sections planes, et conditions de Whitney (1982) Algebraic geometry, Proc. Int. Conf., 961, pp. 314-491. , La Rabida (Spain) 1981, Lect. Notes Math
• Teissier, B., (1988) Quelques points de l'histoire des variétés polaires, de Poncelet 'a nos jours, p. 4. , Sémin. Anal., Univ. Blaise Pascal 1987-1988

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