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Volumn 117-118, Issue , 1997, Pages 277-317

Lower bounds for diophantine approximations

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EID: 0031142051     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(97)00015-7     Document Type: Article
Times cited : (84)

References (59)
  • 6
    • 0021388907 scopus 로고
    • On computing the determinant in small parallel time using a small number of processors
    • S.J. Berkowitz, On computing the determinant in small parallel time using a small number of processors, Inf. Proc. Lett. 18 (1984) 147-150.
    • (1984) Inf. Proc. Lett. , vol.18 , pp. 147-150
    • Berkowitz, S.J.1
  • 10
    • 0001259424 scopus 로고
    • Bounds for the degree in the Nullstellensatz
    • D.W. Brownawell, Bounds for the degree in the Nullstellensatz, Ann. Math. 126 (1987) 577-591.
    • (1987) Ann. Math. , vol.126 , pp. 577-591
    • Brownawell, D.W.1
  • 12
    • 0001250424 scopus 로고
    • Borne simplement exponentielle pour les degrés dans le théorème des zéros sur un corps de caractéristique quelconque
    • L. Caniglia, A. Galligo and J. Heintz, Borne simplement exponentielle pour les degrés dans le théorème des zéros sur un corps de caractéristique quelconque, C.R. Acad. Sci. Paris, Série I, Math. 307 (1988) 255-258.
    • (1988) C.R. Acad. Sci. Paris, Série I, Math. , vol.307 , pp. 255-258
    • Caniglia, L.1    Galligo, A.2    Heintz, J.3
  • 16
    • 0000538288 scopus 로고
    • Fast parallel matrix inversion algorithms
    • L. Csanky, Fast parallel matrix inversion algorithms, SIAM J. Comp. 5 (1976) 618-623.
    • (1976) SIAM J. Comp. , vol.5 , pp. 618-623
    • Csanky, L.1
  • 19
    • 0000608946 scopus 로고
    • Bornes pour le degré et les hauteurs dans le problème de division
    • M. Elkadi, Bornes pour le degré et les hauteurs dans le problème de division, Michigan Math. J. 40 (1993) 609-618.
    • (1993) Michigan Math. J. , vol.40 , pp. 609-618
    • Elkadi, M.1
  • 21
    • 0000252436 scopus 로고
    • Diophantine approximation on abelian varieties
    • G. Fallings, Diophantine approximation on abelian varieties, Ann. Math. 133 (1991) 549-576.
    • (1991) Ann. Math. , vol.133 , pp. 549-576
    • Fallings, G.1
  • 23
    • 85034753633 scopus 로고
    • Algebraic solution of systems of polynomial equations using Gröbner bases
    • Springer, Berlin
    • P. Gianni and T. Mora, Algebraic solution of systems of polynomial equations using Gröbner bases, in: Proc. AAECC-5, LNCS, Vol. 356 (Springer, Berlin, 1989) 247-257.
    • (1989) Proc. AAECC-5, LNCS , vol.356 , pp. 247-257
    • Gianni, P.1    Mora, T.2
  • 24
    • 0000936391 scopus 로고
    • La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial
    • D. Eisenbud and L. Robbiano, Eds. Computational Algebraic Geometry and Commutative Algebra, Istituto Nazionale di Alta Matematica (Cambridge Univ. Press, Cambridge)
    • M. Giusti and J. Heintz, La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial, in: D. Eisenbud and L. Robbiano, Eds., Computational Algebraic Geometry and Commutative Algebra, Proc. Cortona Conf. on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica, vol. XXXIV, Istituto Nazionale di Alta Matematica (Cambridge Univ. Press, Cambridge, 1993).
    • (1993) Proc. Cortona Conf. on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica , vol.34
    • Giusti, M.1    Heintz, J.2
  • 26
    • 84955611783 scopus 로고
    • When polynomial equation systems can be "solved" fast?
    • G. Cohen, M. Giusti and T. Mora, Eds., Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, Paris 1995. (Springer, Berlin)
    • M. Giusti, J. Heintz, J.E. Morais and L.M. Pardo, When polynomial equation systems can be "solved" fast? in: G. Cohen, M. Giusti and T. Mora, Eds., Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, Paris 1995, Lecture Notes in Computer Science, Vol. 948 (Springer, Berlin, 1995) 205-231.
    • (1995) Lecture Notes in Computer Science , vol.948 , pp. 205-231
    • Giusti, M.1    Heintz, J.2    Morais, J.E.3    Pardo, L.M.4
  • 27
    • 0001905196 scopus 로고
    • On the efficiency of effective Nullstellensätze
    • M. Giusti, J. Heintz and J. Sabia, On the efficiency of effective Nullstellensätze, Comput. Complexity 3 (1993) 56-95.
    • (1993) Comput. Complexity , vol.3 , pp. 56-95
    • Giusti, M.1    Heintz, J.2    Sabia, J.3
  • 28
    • 0000627865 scopus 로고
    • Fast quantifier elimination over algebraically closed fields
    • J. Heintz, Fast quantifier elimination over algebraically closed fields, Theoret. Comput. Sci. 24 (1983) 239-277.
    • (1983) Theoret. Comput. Sci. , vol.24 , pp. 239-277
    • Heintz, J.1
  • 31
    • 0001197574 scopus 로고
    • On the intrinsic complexity of elimination theory
    • J. Heintz and J. Morgenstern, On the intrinsic complexity of elimination theory, J. Complexity 9 (1993) 471-498.
    • (1993) J. Complexity , vol.9 , pp. 471-498
    • Heintz, J.1    Morgenstern, J.2
  • 32
    • 84944060784 scopus 로고
    • Testing polynomials which are easy to compute
    • J. Heintz and C.P. Schnorr, Testing polynomials which are easy to compute, Proc. 12th Ann. ACM Symp. on Computing (1980) 262-268; also in Logic and Algorithmic. An Internat. Symp. held in Honour of Ernst Specker, Monographie No. 30 de l'Enseignement de Mathématiques, Genève (1982) 237-254.
    • (1980) Proc. 12th Ann. ACM Symp. on Computing , pp. 262-268
    • Heintz, J.1    Schnorr, C.P.2
  • 33
    • 85119635775 scopus 로고
    • An Internat. Symp. held in Honour of Ernst Specker, Monographie No. 30 de l'Enseignement de Mathématiques, Genève
    • J. Heintz and C.P. Schnorr, Testing polynomials which are easy to compute, Proc. 12th Ann. ACM Symp. on Computing (1980) 262-268; also in Logic and Algorithmic. An Internat. Symp. held in Honour of Ernst Specker, Monographie No. 30 de l'Enseignement de Mathématiques, Genève (1982) 237-254.
    • (1982) Logic and Algorithmic , pp. 237-254
  • 34
    • 84968474102 scopus 로고
    • Sharp Effective Nullstellensatz
    • J. Kollár, Sharp Effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988) 963-975.
    • (1988) J. Amer. Math. Soc. , vol.1 , pp. 963-975
    • Kollár, J.1
  • 35
    • 0000697864 scopus 로고    scopus 로고
    • A computational method for diophantine approximation
    • L. González and T. Recio, eds. (Birkhäuser, Basel)
    • T. Krick and L.M. Pardo, A computational method for diophantine approximation, in: L. González and T. Recio, eds., Algorithms in Algebraic Geometry and Applications, Progress in Mathematics, Vol. 142 (Birkhäuser, Basel, 1996) 193-254.
    • (1996) Algorithms in Algebraic Geometry and Applications, Progress in Mathematics , vol.142 , pp. 193-254
    • Krick, T.1    Pardo, L.M.2
  • 36
    • 0001379976 scopus 로고
    • Une approche informatique pour l'approximation diophantienne
    • Série I
    • T. Krick and L.M. Pardo, Une approche informatique pour l'approximation diophantienne, C.R. Acad. Sci. Paris, t. 318, Série I (5) (1994) 407-412.
    • (1994) C.R. Acad. Sci. Paris , vol.318 , Issue.5 , pp. 407-412
    • Krick, T.1    Pardo, L.M.2
  • 39
    • 0003242570 scopus 로고
    • Generic Local Structure of the Morphisms in Commutative Algebra
    • Springer, Berlin
    • B. Iversen, Generic Local Structure of the Morphisms in Commutative Algebra, Lecture Notes in Computer Science, Vol. 310 (Springer, Berlin, 1973).
    • (1973) Lecture Notes in Computer Science , vol.310
    • Iversen, B.1
  • 43
    • 84936242145 scopus 로고
    • Estimates for the order of zero o functions of a certain class and applications in the theory of transcendental numbers
    • Yu.V. Nesterenko, Estimates for the order of zero o functions of a certain class and applications in the theory of transcendental numbers. Math. USSR Izvestija 11 (2) (1977) 239-270.
    • (1977) Math. USSR Izvestija , vol.11 , Issue.2 , pp. 239-270
    • Nesterenko, Yu.V.1
  • 44
    • 0000789663 scopus 로고
    • On a measure of the algebraic independence of the values of certain functions
    • Yu.V. Nesterenko, On a measure of the algebraic independence of the values of certain functions. Math. USSR Sbornik 56 (1987) 545-567.
    • (1987) Math. USSR Sbornik , vol.56 , pp. 545-567
    • Nesterenko, Yu.V.1
  • 45
    • 84955604612 scopus 로고
    • How lower and upper complexity bounds meet in elimination theory
    • G. Cohen, M. Giusti and T. Mora, Eds., Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error- Correcting Codes, AAECC-11, Paris 1995. (Springer, Berlin)
    • L.M. Pardo, How lower and upper complexity bounds meet in elimination theory, in: G. Cohen, M. Giusti and T. Mora, Eds., Proc. 11th Internat. Symp. Applied Algebra, Algebraic Algorithms and Error- Correcting Codes, AAECC-11, Paris 1995, Lecture Notes in Computer Science, Vol. 948 (Springer, Berlin, 1995) 33-69.
    • (1995) Lecture Notes in Computer Science , vol.948 , pp. 33-69
    • Pardo, L.M.1
  • 46
    • 51249177761 scopus 로고
    • Critères pour l'independence algébrique
    • P. Philippon, Critères pour l'independence algébrique, Pub. Math. de l'IHFS 64 (1987) 5-52.
    • (1987) Pub. Math. de l'IHFS , vol.64 , pp. 5-52
    • Philippon, P.1
  • 47
    • 0000572440 scopus 로고
    • Sur des hauteurs alternatives, I
    • P. Philippon, Sur des hauteurs alternatives, I, Math. Ann. 289 (1991) 255-283.
    • (1991) Math. Ann. , vol.289 , pp. 255-283
    • Philippon, P.1
  • 48
    • 0000924409 scopus 로고
    • Sur des hauteurs alternatives, II
    • P. Philippon, Sur des hauteurs alternatives, II, Ann. Inst. Fourier, Grenoble, 44 (2) (1994) 1043-1065.
    • (1994) Ann. Inst. Fourier, Grenoble , vol.44 , Issue.2 , pp. 1043-1065
    • Philippon, P.1
  • 49
    • 0000801815 scopus 로고
    • Sur des hauteurs alternatives, III
    • P. Philippon, Sur des hauteurs alternatives, III, J. Math. Pures Appl. 74 (1995) 345-365.
    • (1995) J. Math. Pures Appl. , vol.74 , pp. 345-365
    • Philippon, P.1
  • 50
    • 0000874914 scopus 로고    scopus 로고
    • Bounds for traces in complete intersections and degrees in the Nullstellensatz
    • J. Sabia and P, Solernó, Bounds for traces in complete intersections and degrees in the Nullstellensatz, Appl. Algebra in Eng. Commun. Comput. (AAECC J.) 6 (1996) 353-376.
    • (1996) Appl. Algebra in Eng. Commun. Comput. (AAECC J.) , vol.6 , pp. 353-376
    • Sabia, J.1    Solernó, P.2
  • 52
    • 84968505377 scopus 로고
    • Complexity of Bezout's theorem I: Geometric aspects
    • M. Shub and S. Smale, Complexity of Bezout's theorem I: Geometric aspects, J. Amer. Math. Soc. 6 (1993) 459-501.
    • (1993) J. Amer. Math. Soc. , vol.6 , pp. 459-501
    • Shub, M.1    Smale, S.2
  • 53
    • 0000537756 scopus 로고
    • Complexity of Bezout's theorem II: Volumes and probabilities
    • F. Eyssette and A. Galligo, eds. (Birkhäuser, Basel)
    • M. Shub and S. Smale, Complexity of Bezout's theorem II: Volumes and probabilities, in: F. Eyssette and A. Galligo, eds., Computational Algebraic Geometry, Progress in Mathematics, Vol. 109 (Birkhäuser, Basel, 1993) 267-285.
    • (1993) Computational Algebraic Geometry, Progress in Mathematics , vol.109 , pp. 267-285
    • Shub, M.1    Smale, S.2
  • 54
    • 0002102930 scopus 로고
    • Complexity of Bezout's theorem III: Condition number and packing
    • M. Shub and S. Smale, Complexity of Bezout's theorem III: condition number and packing, J. Complexity 9 (1993) 4-14.
    • (1993) J. Complexity , vol.9 , pp. 4-14
    • Shub, M.1    Smale, S.2
  • 55
    • 0028516294 scopus 로고    scopus 로고
    • Complexity of Bezout's theorem V: Polynomial time
    • M. Shub and S. Smale, Complexity of Bezout's theorem V: polynomial time, Theoret. Comput. Sci. 133 (1994).
    • Theoret. Comput. Sci. , vol.133 , Issue.1994
    • Shub, M.1    Smale, S.2
  • 56
    • 0011037169 scopus 로고
    • On the intractability of Hubert's Nullstellensatz and an algebraic version of NP ≠ P?
    • Yorktown Heights
    • M. Shub and S. Smale, On the intractability of Hubert's Nullstellensatz and an algebraic version of NP ≠ P?, IBM Research Report, Yorktown Heights (1994).
    • (1994) IBM Research Report
    • Shub, M.1    Smale, S.2
  • 57
    • 0000675799 scopus 로고    scopus 로고
    • Complexity of Bezout's theorem IV: Probability of success, extensions
    • to appear
    • M. Shub and S. Smale, Complexity of Bezout's theorem IV: probability of success, extensions, SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal.
    • Shub, M.1    Smale, S.2
  • 58
    • 0010951612 scopus 로고    scopus 로고
    • Personal communication
    • C. Soulé, Personal communication.
    • Soulé, C.1


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