메뉴 건너뛰기




Volumn 129, Issue 2, 1998, Pages 173-200

An effective algorithm for quantifier elimination over algebraically closed fields using straight line programs

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032479656     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(97)00068-6     Document Type: Article
Times cited : (11)

References (42)
  • 1
    • 0010072993 scopus 로고
    • Tests d'appartenance d'après un théorème de kollár
    • [1] F. Amoroso, Tests d'appartenance d'après un théorème de Kollár, Acad. Sci. Paris, Serie I Math. 309 (1989) 691-694.
    • (1989) Acad. Sci. Paris, Serie I Math. , vol.309 , pp. 691-694
    • Amoroso, F.1
  • 4
    • 0021388907 scopus 로고
    • On computing the determinant in small parallel time using a small number of processors
    • [4] S.J. Berkowitz, On computing the determinant in small parallel time using a small number of processors, Inform. Process. Lett. 18 (1984) 147-150.
    • (1984) Inform. Process. Lett. , vol.18 , pp. 147-150
    • Berkowitz, S.J.1
  • 5
    • 0000849112 scopus 로고
    • On relating time and space to size and depth
    • [5] A. Borodin, On relating time and space to size and depth, SIAM J. Comput. 6 (1977) 733-744.
    • (1977) SIAM J. Comput. , vol.6 , pp. 733-744
    • Borodin, A.1
  • 7
    • 0001259424 scopus 로고
    • Bounds for the degrees in the nullstellensatz
    • [7] D. Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. Math. 2nd Series, 126 (3) (1987) 577-591.
    • (1987) Ann. Math. 2nd Series , vol.126 , Issue.3 , pp. 577-591
    • Brownawell, D.1
  • 10
    • 0002122321 scopus 로고
    • How to compute the chow form of an unmixed polynomial ideal in single exponential time
    • Springer, Berlin
    • [10] L. Caniglia, How to compute the Chow Form of an unmixed polynomial ideal in single exponential time, AAECC, Springer, Berlin, 1990.
    • (1990) AAECC
    • Caniglia, L.1
  • 11
    • 0001250424 scopus 로고
    • Borne simple exponentielle pour les degrés dans le théorème des zéros sur un corps de caractéristique quelconque
    • Serie I
    • [11] L. Caniglia, A. Galligo, J. Heintz, Borne simple exponentielle pour les degrés dans le théorème des zéros sur un corps de caractéristique quelconque, C.R. Acad. Sci. Paris t. 307, Serie I (1988) 255-258.
    • (1988) C.R. Acad. Sci. Paris T. , vol.307 , pp. 255-258
    • Caniglia, L.1    Galligo, A.2    Heintz, J.3
  • 12
    • 85027644628 scopus 로고
    • Some new effective bounds in computational geometry
    • Proc. 6th Internat. Conf. Applied Algebra, Algebraic Algorithms and Error Correcting Codes, Rome 1988, Springer, Berlin
    • [12] L. Caniglia, A. Galligo, J. Heintz, Some new effective bounds in computational geometry, Proc. 6th Internat. Conf. Applied Algebra, Algebraic Algorithms and Error Correcting Codes, Rome 1988, Lecture Notes in Computer Science, vol. 357, Springer, Berlin, 1989, pp. 131-151.
    • (1989) Lecture Notes in Computer Science , vol.357 , pp. 131-151
    • Caniglia, L.1    Galligo, A.2    Heintz, J.3
  • 13
    • 0042224457 scopus 로고
    • Local membership problems for polynomial ideals
    • T. Mora, C. Traverso (Eds.), Proc. Internat. Conf. Effective Methods in Algebraic Geometry MEGA 90, Castiglioncello 1990, Birkhäuser, Basel
    • [13] L. Caniglia, J. Guccione, J.J. Guccione, Local membership problems for polynomial ideals, in: T. Mora, C. Traverso (Eds.), Proc. Internat. Conf. Effective Methods in Algebraic Geometry MEGA 90, Castiglioncello 1990, Progress in Mathematics, vol. 94, Birkhäuser, Basel, 1991, pp. 31-45.
    • (1991) Progress in Mathematics , vol.94 , pp. 31-45
    • Caniglia, L.1    Guccione, J.2    Guccione, J.J.3
  • 15
    • 85036476335 scopus 로고
    • Complexity of quantifier elimination in the theory of algebraically closed fields
    • Proc. 11th Symp. MFCS 1984, Springer, Berlin
    • [15] A.L. Chistov, D. Yu. Grigor'ev, Complexity of quantifier elimination in the theory of algebraically closed fields, Proc. 11th Symp. MFCS 1984, Lecture Notes in Computer Science, vol. 176, Springer, Berlin, 1984, pp. 17-31.
    • (1984) Lecture Notes in Computer Science , vol.176 , pp. 17-31
    • Chistov, A.L.1    Grigor'ev, D.Yu.2
  • 16
    • 0002981979 scopus 로고
    • Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields
    • [16] N. Fitchas, A. Galligo, J. Morgenstern, Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields, J. Pure Appl. Algebra 67 (1990) 1-14.
    • (1990) J. Pure Appl. Algebra , vol.67 , pp. 1-14
    • Fitchas, N.1    Galligo, A.2    Morgenstern, J.3
  • 18
    • 0000936391 scopus 로고
    • La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial
    • D. Eiseinbud, L. Robbiano (Eds.), Istituto Nazionale di Alta Matematica, Cambridge University Press, Cambridge
    • [18] M. Giusti, J. Heintz, La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial, in: D. Eiseinbud, L. Robbiano (Eds.), Proc. Cortona Conf. on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica, Vol. XXXIV, Istituto Nazionale di Alta Matematica, Cambridge University Press, Cambridge, 1993.
    • (1993) Proc. Cortona Conf. on Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica , vol.34
    • Giusti, M.1    Heintz, J.2
  • 19
    • 0001905196 scopus 로고
    • On the efficiency of effective nullstellensätze
    • [19] M. Giusti, J. Heintz, 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
  • 21
    • 0010188626 scopus 로고
    • The complexity of the decision for the first order theory of algebraically closed fields
    • [21] D. Yu. Grigor'ev, The complexity of the decision for the first order theory of algebraically closed fields, Math. USRR Izvestija 29 (2) (1987) 459-475.
    • (1987) Math. USRR Izvestija , vol.29 , Issue.2 , pp. 459-475
    • Grigor'ev, D.Yu.1
  • 22
    • 0000627865 scopus 로고
    • Definability and fast quantifier elimination over algebraically closed fields
    • [22] J. Heintz, Definability and 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
  • 23
    • 0001365155 scopus 로고
    • On the computational complexity of polynomials and bilinear mappings, a survey
    • L. Huguet, A. Poli (Eds.), Proc. 5th Internat. Conf. Applied Algebra, Algebraic Algorithms and Error Correcting Codes AAECC 5, Menorca, 1987, Springer, Berlin
    • [23] J. Heintz, On the computational complexity of polynomials and bilinear mappings, a survey, in: L. Huguet, A. Poli (Eds.), Proc. 5th Internat. Conf. Applied Algebra, Algebraic Algorithms and Error Correcting Codes AAECC 5, Menorca, 1987, Lecture Notes in Computer Science, vol. 356, Springer, Berlin, 1989, pp. 269-300.
    • (1989) Lecture Notes in Computer Science , vol.356 , pp. 269-300
    • Heintz, J.1
  • 24
    • 0001404855 scopus 로고
    • Testing polynomials which are easy to compute
    • Impr. Kundig, Geneve
    • [24] J. Heintz, C.P. Schnorr, Testing polynomials which are easy to compute, Monographie de l'Enseignement Mathematique, vol. 30, Impr. Kundig, Geneve, 1982, pp. 237-254.
    • (1982) Monographie de L'enseignement Mathematique , vol.30 , pp. 237-254
    • Heintz, J.1    Schnorr, C.P.2
  • 25
    • 0002694831 scopus 로고
    • Absolute primality of polynomials is decidable in random polynomial time in the number of the variables
    • 8th Internat. Colloquium on Automata, Languages and Programming ICALP 81, Springer, Berlin
    • [25] J. Heintz, M. Sieveking, Absolute primality of polynomials is decidable in random polynomial time in the number of the variables, 8th Internat. Colloquium on Automata, Languages and Programming ICALP 81, Lecture Notes in Computer Science, vol. 115, Springer, Berlin, 1981.
    • (1981) Lecture Notes in Computer Science , vol.115
    • Heintz, J.1    Sieveking, M.2
  • 26
    • 0001798490 scopus 로고
    • An efficient quantifier elimination algorithm for algebraically closed fields
    • [26] J. Heintz, R. Wüthrich, An efficient quantifier elimination algorithm for algebraically closed fields, SIGSAM Bull. 9 (1975) 11.
    • (1975) SIGSAM Bull. , vol.9 , pp. 11
    • Heintz, J.1    Wüthrich, R.2
  • 27
    • 0024868428 scopus 로고
    • Quantifier elimination in the theory of an algebraically-closed field
    • [27] D. Ierardi, Quantifier elimination in the theory of an algebraically-closed field, J. ACM (1989) 138-147.
    • (1989) J. ACM , pp. 138-147
    • Ierardi, D.1
  • 28
    • 0023826531 scopus 로고
    • Greatest common divisors of polynomials given by straight line programs
    • [28] E. Kaltofen, Greatest common divisors of polynomials given by straight line programs, J. ACM 35 (1) (1988) 231-264.
    • (1988) J. ACM , vol.35 , Issue.1 , pp. 231-264
    • Kaltofen, E.1
  • 29
    • 84968474102 scopus 로고
    • Sharp effective nullstellensatz
    • [29] J. Kollar, Sharp effective Nullstellensatz, J. AMS 1 (1988) 963-975.
    • (1988) J. AMS , vol.1 , pp. 963-975
    • Kollar, J.1
  • 31
  • 33
    • 0002830129 scopus 로고
    • A fast parallel algorithm to compute the rank of a matrix over an arbitrary field
    • [33] K. Mulmuley, A fast parallel algorithm to compute the rank of a matrix over an arbitrary field, Proc. 18th ACM Symp. Theory of Computing, 1986, pp. 338-339.
    • (1986) Proc. 18th ACM Symp. Theory of Computing , pp. 338-339
    • Mulmuley, K.1
  • 34
    • 84936242145 scopus 로고
    • Estimates for the orders of zeros of functions of a certain class and applications in the theory of trascendental numbers
    • [34] Yu. V. Nesterenko, Estimates for the orders of zeros of functions of a certain class and applications in the theory of trascendental numbers, Math. USSR Izvestija, 11 (2) (1977) Izvestia Akad. Nauk. SSR Set-Mat. Tom 41 (2) (1977).
    • (1977) Math. USSR Izvestija , vol.11 , Issue.2
    • Nesterenko, Y.V.1
  • 35
    • 84936242145 scopus 로고
    • [34] Yu. V. Nesterenko, Estimates for the orders of zeros of functions of a certain class and applications in the theory of trascendental numbers, Math. USSR Izvestija, 11 (2) (1977) Izvestia Akad. Nauk. SSR Set-Mat. Tom 41 (2) (1977).
    • (1977) Izvestia Akad. Nauk. SSR Set-Mat. Tom , vol.41 , Issue.2
  • 37
    • 0001572510 scopus 로고
    • On the computational complexity and geometry of the first-order theory of the reals
    • [36] J. Renegar, On the computational complexity and geometry of the first-order theory of the reals, J. Symbol. Comput. 13 (1992) 253-352.
    • (1992) J. Symbol. Comput. , vol.13 , pp. 253-352
    • Renegar, J.1
  • 38
    • 0024639793 scopus 로고
    • On the representation of rational functions of bounded complexity
    • [37] H.J. Stoss, On the representation of rational functions of bounded complexity, Theoret. Comput. Sci. 64 (1989) 1-13.
    • (1989) Theoret. Comput. Sci. , vol.64 , pp. 1-13
    • Stoss, H.J.1
  • 39
    • 0015491022 scopus 로고
    • Berechnung und programm I
    • [38] V. Strassen, Berechnung und Programm I, Acta Inform. 1 (1972) 320-334.
    • (1972) Acta Inform. , vol.1 , pp. 320-334
    • Strassen, V.1
  • 41
    • 84957621752 scopus 로고
    • Parallel arithmetic computations: A survey
    • Proc. 13th Symp. MFCS 1986, Springer, Berlin
    • [40] J. von zur Gathen, Parallel arithmetic computations: a survey, Proc. 13th Symp. MFCS 1986, Lecture Notes in Computer Science, vol. 233, Springer, Berlin, 1986, pp. 93-112.
    • (1986) Lecture Notes in Computer Science , vol.233 , pp. 93-112
    • Von Zur Gathen, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.