Generalized polar varieties and an efficient real elimination
Bernd Bank; Marc Giusti; Joos Heintz; Luis M. Pardo
Kybernetika (2004)
- Volume: 40, Issue: 5, page [519]-550
- ISSN: 0023-5954
Access Full Article
topAbstract
topHow to cite
topReferences
top- Aubry P., Rouillier, F., Din M. Safey El, 10.1006/jsco.2002.0563, J. Symb. Computation 34 (2002), 6, 543–560 MR1943042DOI10.1006/jsco.2002.0563
- Bank B., Giusti M., Heintz, J., Pardo L. M., Generalized polar varieties: Geometry and algorithms, Manuscript. Humboldt Universität zu Berlin, Institut für Mathematik 2003. Submitted to J. Complexity Zbl1085.14047MR2152713
- Bank B., Giusti M., Heintz, J., Mbakop G. M., 10.1007/PL00004896, Math.Z. 238 (2001), 115–144. Digital Object Identifier (DOI) 10.1007/s002090100248 Zbl1073.14554MR1860738DOI10.1007/PL00004896
- Bank B., Giusti M., Heintz, J., Mbakop G. M., 10.1006/jcom.1997.0432, J. Complexity 13 (1997), 1, 5–27. Best Paper Award J. Complexity 1997 (1997) Zbl0872.68066MR1449757DOI10.1006/jcom.1997.0432
- Basu S., Pollack, R., Roy M.-F., 10.1145/235809.235813, J.ACM 43 (1996), 6, 1002–1045 (1996) Zbl0885.68070MR1434910DOI10.1145/235809.235813
- Basu S., Pollack, R., Roy M.-F., Complexity of computing semi-algebraic descriptions of the connected components of a semialgebraic set, In: Proc. ISSAC’98, (XXX. Gloor and XXX. Oliver, eds.), Rostock 1998, pp. 13–15. ACM Press. (1998), 25–29 (1998) Zbl0960.14033MR1805168
- Bochnak J., Coste, M., Roy M.–F., Géométrie algébrique réelle, Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer, Berlin – Heidelberg – New York 1987 Zbl0633.14016MR0949442
- Bruns W., Vetter U., Determinantal Rings, (Lecture Notes in Mathematics 1327), Springer, Berlin 1988 Zbl1079.14533MR0953963
- Bürgisser P., Clausen, M., Shokrollahi M. A., Algebraic complexity theory, With the collaboration of Thomas Lickteig. (Grundlehren der Mathematischen Wissenschaften 315), Springer, Berlin 1997 Zbl1087.68568MR1440179
- Canny J. F., Some algebraic and geometric computations in PSPACE, In: Proc. 20th ACM Symp. on Theory of Computing 1988, pp. 460–467 (1988)
- Canny J. F., Emiris I. Z., 10.1006/jsco.1995.1041, J. Symb. Comput. 20 (1995), 2, 117–149 (1995) Zbl0843.68036MR1374227DOI10.1006/jsco.1995.1041
- Castro D., Giusti M., Heintz J., Matera, G., Pardo L. M., 10.1007/s10208-002-0065-7, Found. Comput. Math. 3, (2003), 4, 347–420 MR2009683DOI10.1007/s10208-002-0065-7
- Castro D., Hägele K., Morais J. E., Pardo L. M., 10.1006/jcom.2000.0572, J. Complexity 17 (2001), 1, 212–303 MR1817613DOI10.1006/jcom.2000.0572
- Coste M., Roy M.-F., 10.1016/S0747-7171(88)80008-7, J. Symbolic Comput. 5 (1988), 121–130 (1988) MR0949115DOI10.1016/S0747-7171(88)80008-7
- Cucker F., Smale S., 10.1145/300515.300519, J. ACM 46 (1999), 1, 113–184 (1999) MR1692497DOI10.1145/300515.300519
- Demazure M., Catastrophes et bifurcations, Ellipses, Paris 1989 Zbl0907.58002
- Eagon J. A., Northcott D. G., 10.1098/rspa.1962.0170, Proc. R. Soc. Lond., Ser. A 269 (1962), 188–204 (1962) Zbl0106.25603MR0142592DOI10.1098/rspa.1962.0170
- Eagon J. A., Hochster M., R–sequences and indeterminates, O.J. Math., Oxf. II. Ser. 25 (1974), 61–71 (1974) Zbl0278.13008MR0337934
- Eisenbud D., Commutative Algebra with a View Toward Algebraic Geometry, Springer, New York 1995 Zbl0819.13001MR1322960
- Fulton W., Intersection Theory, (Ergebnisse der Mathematik und ihrer Grenzgebiete 3), Springer, Berlin 1984 Zbl0935.00036MR0732620
- Gathen J. von zur, Parallel linear algebra, In: Synthesis of Parallel Algorithmns (J. Reif, ed.), Morgan Kaufmann 1993
- Giusti M., Heintz J., 10.1017/CBO9781107360198.005, Foundations of Computational Mathematics (R. A. DeVore, A. Iserles, and E. Süli, eds.), Cambridge Univ. Press 284 (2001), 69–104 Zbl0978.65043MR1836615DOI10.1017/CBO9781107360198.005
- Giusti M., Heintz J., Morais J. E., Morgenstern, J., Pardo L. M., 10.1016/S0022-4049(96)00099-0, J. Pure Appl. Algebra 124 (1998), 1 – 3, 101–146 (1998) Zbl0944.12004MR1600277DOI10.1016/S0022-4049(96)00099-0
- Giusti M., Heintz J., Hägele K., Morais J. E., Montaña J. L., Pardo L. M., 10.1016/S0022-4049(97)00015-7, J. Pure and Applied Alg. 117, 118 (1997), 277–317 (1997) Zbl0871.68101MR1457843DOI10.1016/S0022-4049(97)00015-7
- Giusti M., Lecerf, G., Salvy B., 10.1006/jcom.2000.0571, J. Complexity 17 (2001), 1, 154–211 Zbl1003.12005MR1817612DOI10.1006/jcom.2000.0571
- Grigor’ev D., Vorobjov N., 10.1016/S0747-7171(88)80005-1, J. Symb. Comput. 5 (1998), 1/2, 37–64 (1998) MR0949112DOI10.1016/S0747-7171(88)80005-1
- Heintz J., 10.1016/0304-3975(83)90002-6, Theoret. Comp. Sci. 24 (1983), 239–277 (1983) MR0716823DOI10.1016/0304-3975(83)90002-6
- Heintz J., Matera, G., Waissbein A., 10.1007/s002000000046, Appl. Algebra Engrg. Comm. Comput. 11 (2001), 4, 239–296 Zbl0977.68101MR1818975DOI10.1007/s002000000046
- Heintz J., Roy, M.–F., Solernó P., Complexité du principe de Tarski–Seidenberg, CRAS, t. 309, Série I, Paris 1989, pp. 825–830 (1989) Zbl0704.03013MR1055203
- Heintz J., Roy,, M–F., Solernó P., Sur la complexité du principe de Tarski–Seidenberg, Bull. Soc. Math. France 18 (1990), 101–126 (1990) Zbl0767.03017MR1077090
- Heintz J., Schnorr C. P., Testing polynomials which are easy to compute, In: Proc. 12th Ann. ACM Symp. on Computing, 1980, pp. 262–268, also in: Logic and Algorithmic: An Int. Symposium held in Honour of Ernst Specker, Monographie No.30 de l’Enseignement de Mathématiques, Genève 1982, pp. 237–254 (1980) MR0648305
- Krick T., Pardo L. M., A computational method for diophantine approximation, In: Proc. MEGA’94, Algorithms in Algebraic Geometry and Applications, (L. Gonzales-Vega and T. Recio, eds.), (Progress in Mathematics 143), Birkhäuser, Basel 1996, pp. 193-254 (1996) Zbl0878.11043MR1414452
- Kunz E., Kähler Differentials, Advanced Lectures in Mathematics. Vieweg, Braunschweig – Wiesbaden 1986 Zbl0587.13014MR0864975
- Lê D. T., Teissier B., 10.2307/1971299, Annals of Mathematics 114 (1981), 457–491 (1981) Zbl0488.32004MR0634426DOI10.2307/1971299
- Lecerf G., Une alternative aux méthodes de réécriture pour la résolution des systèmes algébriques, Thèse. École Polytechnique 2001
- Lecerf G., 10.1007/s102080010026, Found. Comput. Math. 2 (2002), 3, 247–293 MR1907381DOI10.1007/s102080010026
- Lehmann L., Waissbein A., Wavelets and semi–algebraic sets, In: WAIT 2001, (M. Frias and J. Heintz eds.), Anales JAIIO 30 (2001), 139–155
- Matera G., 10.1007/s002000050115, Appl. Algebra Engrg. Commun. Comput. 9 (1999), 6, 463–520 (1999) Zbl0934.68122MR1706433DOI10.1007/s002000050115
- Matsumura H., Commutative Ring Theory, (Cambridge Studies in Adv. Math. 8), Cambridge Univ. Press, Cambridge 1986 Zbl0666.13002MR0879273
- Piene R., Polar classes of singular varieties, Ann. Scient. Éc. Norm. Sup. 4. Série, t. 11 (1978), 247–276 (1978) Zbl0401.14007MR0510551
- Renegar J., A faster PSPACE algorithm for the existential theory of the reals, In: Proc. 29th Annual IEEE Symposium on the Foundation of Computer Science 1988, pp. 291–295 (1988)
- Renegar J., On the computational complexity and geometry of the first order theory of the reals, J. Symbolic Comput. 13 (1992), 3, 255–352 (1992) Zbl0798.68073MR1156882
- Din M. Safey El, Résolution réelle des systèmes polynomiaux en dimension positive, Thèse. Université Paris VI 2001
- Din M. Safey El, Schost E., Polar varieties and computation of one point in each connected component of a smooth real algebraic set, In: Proc. 2003 International Symposium on Symbolic and Algebraic Computation (ISSAC 2003), ACM Press 2003, pp. 224–231 MR2035216
- Spivak M., Calculus on Manifolds, A Modern Approach to Classical Theorems of Calculus. W. A. Benjamin, Inc., New York – Amsterdam 1965 Zbl0381.58003MR0209411
- Teissier B., Variétés Polaires, II. Multiplicités polaires, sections planes et conditions de Whitney. Algebraic geometry (La Rábida, 1981), (J. M. Aroca, R. Buchweitz, M. Giusti and M. Merle eds.), pp. 314–491, (Lecture Notes in Math. 961) Springer, Berlin 1982, pp. 314–491 (1981) Zbl0572.14002MR0708342
- Vogel W., Lectures on Results on Bézout’s Theorem, Springer, Berlin 1984 Zbl0553.14022MR0743265