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Volumn 13, Issue 3, 1997, Pages 303-325

Some complexity results for polynomial ideals

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EID: 0031232452     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.1997.0447     Document Type: Article
Times cited : (45)

References (56)
  • 4
    • 0001890872 scopus 로고
    • Bounds for the degrees in the division problem
    • 4. Berenstein, C., and Yger, A. (1990), Bounds for the degrees in the division problem, Michigan Math. J. 37(1), 25-43.
    • (1990) Michigan Math. J. , vol.37 , Issue.1 , pp. 25-43
    • Berenstein, C.1    Yger, A.2
  • 5
    • 0021388907 scopus 로고
    • On computing the determinant in small parallel time using a small number of processors
    • 5. Berkowitz, S. J. (1984), On computing the determinant in small parallel time using a small number of processors, Inform. Process. Lett. 18(3), 147-150.
    • (1984) Inform. Process. Lett. , vol.18 , Issue.3 , pp. 147-150
    • Berkowitz, S.J.1
  • 6
    • 0000849112 scopus 로고
    • On relating time and space to size and depth
    • 6. Borodin, A. (1977), On relating time and space to size and depth, SIAM J. Comput. 6(4), 733-744.
    • (1977) SIAM J. Comput. , vol.6 , Issue.4 , pp. 733-744
    • Borodin, A.1
  • 8
    • 0001259424 scopus 로고
    • Bounds for the degrees in the Nullstellensatz
    • 8. Brownawell, W. D. (1987), Bounds for the degrees in the Nullstellensatz, Ann. of Math. 126, 577-591.
    • (1987) Ann. of Math. , vol.126 , pp. 577-591
    • Brownawell, W.D.1
  • 10
    • 0002803133 scopus 로고
    • Gröbner bases: An algorithmic method in polynomial ideal theory
    • (N. K. Bose, Ed.) , Reidel, Dordrecht/ Boston/London
    • 10. Buchberger, B. (1985), Gröbner bases: An algorithmic method in polynomial ideal theory, in "Multidimensional Systems Theory" (N. K. Bose, Ed.), pp. 184-232, Reidel, Dordrecht/ Boston/London.
    • (1985) Multidimensional Systems Theory , pp. 184-232
    • Buchberger, B.1
  • 11
    • 85027644628 scopus 로고
    • Some new effectivity bounds in computational geometry
    • Lecture Notes in Computer Science, Springer-Verlag, Berlin/Heidelberg/New York
    • 11. Caniglia, L., Galligo, A., and Heintz, J. (1988), Some new effectivity bounds in computational geometry, in "Proceedings of AAECC-6, Rome, 1988," Lecture Notes in Computer Science, Vol. 357, pp. 131-152, Springer-Verlag, Berlin/Heidelberg/New York.
    • (1988) Proceedings of AAECC-6, Rome, 1988 , vol.357 , pp. 131-152
    • Caniglia, L.1    Galligo, A.2    Heintz, J.3
  • 13
    • 0011049435 scopus 로고
    • Computational complexity of the word problem for commutative semigroups
    • Project MAC, M.I.T.
    • 13. Cardoza, E. W. (1975), "Computational Complexity of the Word Problem for Commutative Semigroups," Tech. Memo. 67, Project MAC, M.I.T.
    • (1975) Tech. Memo. , vol.67
    • Cardoza, E.W.1
  • 15
    • 0000538288 scopus 로고
    • Fast parallel matrix inversion algorithms
    • 15. Csanky, L. (1976), Fast parallel matrix inversion algorithms, SIAM J. Comput. 5(4), 618-623.
    • (1976) SIAM J. Comput. , vol.5 , Issue.4 , pp. 618-623
    • Csanky, L.1
  • 16
    • 0025474826 scopus 로고
    • The structure of polynomial ideals and Gröbner bases
    • 16. Dubé, T. W. (1990), The structure of polynomial ideals and Gröbner bases, SIAM J. Comput. 19, 750-773.
    • (1990) SIAM J. Comput. , vol.19 , pp. 750-773
    • Dubé, T.W.1
  • 17
    • 0010988233 scopus 로고
    • Admissible orderings and bounds for Gröbner Bases Normal Form Algorithms
    • Department of Computer Science, Courant Institute of Mathematical Sciences, New York University
    • 17. Dubé, T. W., Mishra, B., and Yap, C. K. (1986), "Admissible Orderings and Bounds for Gröbner Bases Normal Form Algorithms," Tech. Rep. 258. Department of Computer Science, Courant Institute of Mathematical Sciences, New York University.
    • (1986) Tech. Rep. , vol.258
    • Dubé, T.W.1    Mishra, B.2    Yap, C.K.3
  • 18
    • 0000726083 scopus 로고
    • Rational sets in commutative monoids
    • 18. Eilenberg, S., and Schützenberger, M. P. (1969), Rational sets in commutative monoids, J. Algebra 13, 173-191.
    • (1969) J. Algebra , vol.13 , pp. 173-191
    • Eilenberg, S.1    Schützenberger, M.P.2
  • 21
    • 0002981979 scopus 로고
    • Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields
    • 21. Fitchas, N., Galligo, A., and Morgenstern, J. (1990), Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields, J. Pure Appl. Algebra 67, 1-14.
    • (1990) J. Pure Appl. Algebra , vol.67 , pp. 1-14
    • Fitchas, N.1    Galligo, A.2    Morgenstern, J.3
  • 24
    • 0024302065 scopus 로고
    • Parallel evaluation of the determinant and of the inverse of a matrix
    • 24. Galil, Z., and Pan, V. (1989), Parallel evaluation of the determinant and of the inverse of a matrix, Inform. Process. Lett. 30, 41-45.
    • (1989) Inform. Process. Lett. , vol.30 , pp. 41-45
    • Galil, Z.1    Pan, V.2
  • 25
    • 85034825830 scopus 로고
    • Some effectivity problems in polynomial ideal theory
    • Lecture Notes in Computer Science, (J. Fitch, Ed.) , ACM SIGSAM, SAME/Springer-Verlag, Berlin/Heidelberg/New York
    • 25. Giusti, M. (1984), Some effectivity problems in polynomial ideal theory, in "Proceedings of the 3rd International Symposium on Symbolic and Algebraic Computation EUROSAM 84, Cambridge, July 9-11, 1984," Lecture Notes in Computer Science, Vol. 174 (J. Fitch, Ed.), pp. 159-171, ACM SIGSAM, SAME/Springer-Verlag, Berlin/Heidelberg/New York.
    • (1984) Proceedings of the 3rd International Symposium on Symbolic and Algebraic Computation EUROSAM 84, Cambridge, July 9-11, 1984 , vol.174 , pp. 159-171
    • Giusti, M.1
  • 26
    • 0001905196 scopus 로고
    • On the efficiency of effective Nullstellensätze
    • 26. Giusti, M., Heintz, J., and Sabia, J. (1993), On the efficiency of effective Nullstellensätze. Comput. Complexity 3, 56-95.
    • (1993) Comput. Complexity , vol.3 , pp. 56-95
    • Giusti, M.1    Heintz, J.2    Sabia, J.3
  • 27
    • 34250954644 scopus 로고
    • Die Frage der endlich vielen Schritte in der Theorie der Polynomideale
    • 27. Hermann, G. (1926), Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95, 736-788.
    • (1926) Math. Ann. , vol.95 , pp. 736-788
    • Hermann, G.1
  • 28
    • 0021901851 scopus 로고
    • The complexity of the equivalence problem for commutative semigroups and symmetric vector addition systems
    • ACM Press, New York
    • 28. Huynh, D. T. (1985), The complexity of the equivalence problem for commutative semigroups and symmetric vector addition systems, in "Proceedings of the 17th Ann. ACM Symposium on Theory of Computing, Providence, RI," pp. 405-412, ACM Press, New York.
    • (1985) Proceedings of the 17th Ann. ACM Symposium on Theory of Computing, Providence, RI , pp. 405-412
    • Huynh, D.T.1
  • 29
    • 0022476533 scopus 로고
    • A superexponential lower bound for Gröbner bases and Church-Rosser commutative Thue systems
    • 29. Huynh, D. T. (1986), A superexponential lower bound for Gröbner bases and Church-Rosser commutative Thue systems, Inform. and Control 68(1-3), 196-206.
    • (1986) Inform. and Control , vol.68 , Issue.1-3 , pp. 196-206
    • Huynh, D.T.1
  • 30
    • 0001510808 scopus 로고
    • A note on the parallel complexity of computing the rank of order n matrices
    • 30. Ibarra, O. H., Moran, S., and Rosier, L. E. (1980), A note on the parallel complexity of computing the rank of order n matrices, Inform. Process. Lett. 11, 162.
    • (1980) Inform. Process. Lett. , vol.11 , pp. 162
    • Ibarra, O.H.1    Moran, S.2    Rosier, L.E.3
  • 31
    • 84968474102 scopus 로고
    • Sharp effective Nullstellensatz
    • 31. Kollár, J. (1988), Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1, 963-975.
    • (1988) J. Amer. Math. Soc. , vol.1 , pp. 963-975
    • Kollár, J.1
  • 32
    • 0011023067 scopus 로고
    • The complexity of the boundedness, coverability, and selfcoverability problems for commutative semigroups
    • Institut für Informatik, Technische Universität München
    • 32. Koppenhagen, U., and Mayr, E. W. (1995), "The Complexity of the Boundedness, Coverability, and Selfcoverability Problems for Commutative Semigroups," Tech. Rep. TUM-19518. Institut für Informatik, Technische Universität München.
    • (1995) Tech. Rep. TUM-19518
    • Koppenhagen, U.1    Mayr, E.W.2
  • 33
    • 85030006144 scopus 로고    scopus 로고
    • An Optimal Algorithm for Constructing the Reduced Gröbner Basis of Binomial Ideals
    • Institut für Informatik, Technische Universität München
    • 33. Koppenhagen, U., and Mayr, E. W. (1996), "An Optimal Algorithm for Constructing the Reduced Gröbner Basis of Binomial Ideals," Tech. Rep. TUM-I9605. Institut für Informatik, Technische Universität München.
    • (1996) Tech. Rep. TUM-I9605
    • Koppenhagen, U.1    Mayr, E.W.2
  • 35
    • 85030020621 scopus 로고    scopus 로고
    • Optimal Gröbner Base Algorithms for Binomial Ideals
    • Institut für Informatik, Technische Universität München
    • 35. Koppenhagen, U., and Mayr, E. W. (1996), "Optimal Gröbner Base Algorithms for Binomial Ideals," Tech. Rep. TUM-I9604. Institut für Informatik, Technische Universität München.
    • (1996) Tech. Rep. TUM-I9604
    • Koppenhagen, U.1    Mayr, E.W.2
  • 36
    • 85030010589 scopus 로고    scopus 로고
    • The Complexity of the Equivalence Problem for Commutative Semigroups
    • Institut für Informatik, Technische Universität München
    • 36. Koppenhagen, U., and Mayr, E. W. (1996), "The Complexity of the Equivalence Problem for Commutative Semigroups," Tech. Rep. TUM-I9603. Institut für Informatik, Technische Universität München.
    • (1996) Tech. Rep. TUM-I9603
    • Koppenhagen, U.1    Mayr, E.W.2
  • 37
    • 0009351151 scopus 로고
    • Membership problem, representation problem and the computation of the radical for one-dimensional ideals
    • Progress in Mathematics, Birkhäuser, Boston/Basel/Berlin/Stuttgart
    • 37. Krick, T., and Logar, A. (1991), Membership problem, representation problem and the computation of the radical for one-dimensional ideals, in "Proceedings of Effective Methods in Algebraic Geometry, MEGA'90," Progress in Mathematics, Vol. 94, pp. 203-216, Birkhäuser, Boston/Basel/Berlin/Stuttgart.
    • (1991) Proceedings of Effective Methods in Algebraic Geometry, MEGA'90 , vol.94 , pp. 203-216
    • Krick, T.1    Logar, A.2
  • 38
    • 85030010740 scopus 로고    scopus 로고
    • Exponential space computation of Gröbner bases
    • Institut für Informatik, Technische Universität München
    • 38. Kühnle, K., and Mayr, E. W. (1996), "Exponential space computation of Gröbner bases," Tech. Rep. TUM-I9606. Institut für Informatik, Technische Universität München.
    • (1996) Tech. Rep. TUM-I9606
    • Kühnle, K.1    Mayr, E.W.2
  • 42
    • 85034440461 scopus 로고
    • Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations
    • J. A. van Hulzen, Ed. Lecture Notes in Computer Science, Springer-Verlag, New York/Berlin/Heidelberg
    • 42. Lazard, D. (1983), Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations, in J. A. van Hulzen, Ed., "Proceedings of the European Computer Algebra Conference, Eurocal '83, London, March 1983," Lecture Notes in Computer Science, Vol. 162, pp. 146-156, Springer-Verlag, New York/Berlin/Heidelberg.
    • (1983) Proceedings of the European Computer Algebra Conference, Eurocal '83, London, March 1983 , vol.162 , pp. 146-156
    • Lazard, D.1
  • 43
    • 0000815585 scopus 로고
    • Membership in polynomial ideals over ℚ is exponential space complete
    • Lecture Notes in Computer Science, (B. Monien and R. Cori, Eds.) , Springer-Verlag, Berlin/Heidelberg/New York
    • 43. Mayr, E. W. (1989), Membership in polynomial ideals over ℚ is exponential space complete, in "Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science, Paderborn, Feb. 1989," Lecture Notes in Computer Science, Vol. 349 (B. Monien and R. Cori, Eds.), pp. 400-406, Springer-Verlag, Berlin/Heidelberg/New York.
    • (1989) Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science, Paderborn, Feb. 1989 , vol.349 , pp. 400-406
    • Mayr, E.W.1
  • 45
    • 0001751788 scopus 로고
    • The complexity of the word problems for commutative semigroups and polynomial ideals
    • 45. Mayr, E. W., and Meyer, A. (1982), The complexity of the word problems for commutative semigroups and polynomial ideals, Adv. in Math. 46(3), 305-329.
    • (1982) Adv. in Math. , vol.46 , Issue.3 , pp. 305-329
    • Mayr, E.W.1    Meyer, A.2
  • 47
  • 48
    • 0002830129 scopus 로고
    • A fast parallel algorithm to compute the rank of a matrix over an arbitrary field
    • ACM Press, New York
    • 48. Mulmuley, K. (1986), A fast parallel algorithm to compute the rank of a matrix over an arbitrary field, in "Proceedings of the 18th Annual ACM Symposium on Theory of Computing," pp. 338-339, ACM Press, New York.
    • (1986) Proceedings of the 18th Annual ACM Symposium on Theory of Computing , pp. 338-339
    • Mulmuley, K.1
  • 49
    • 0022122662 scopus 로고
    • Complexity of parallel matrix computations
    • 49. Pan, V (1987), Complexity of parallel matrix computations. Theoret. Comput. Sci. 54(1), 65-85.
    • (1987) Theoret. Comput. Sci. , vol.54 , Issue.1 , pp. 65-85
    • Pan, V.1
  • 50
    • 0002605406 scopus 로고
    • Recursive unsolvability of a problem of Thue
    • 50. Post, E. (1947), Recursive unsolvability of a problem of Thue, J. Symbolic Logic 12, 1-11.
    • (1947) J. Symbolic Logic , vol.12 , pp. 1-11
    • Post, E.1
  • 51
    • 0001189632 scopus 로고
    • An improved parallel processor bound in fast matrix inversion
    • 51. Preparata, F. P., and Sarwate, D. V. (1978), An improved parallel processor bound in fast matrix inversion. Inform. Process. Lett. 7(2), 148-150.
    • (1978) Inform. Process. Lett. , vol.7 , Issue.2 , pp. 148-150
    • Preparata, F.P.1    Sarwate, D.V.2
  • 52
    • 84968497812 scopus 로고
    • Constructive aspects of Noetherian rings
    • 52. Richman, F. (1974), Constructive aspects of Noetherian rings, Proc. Amer. Math. Soc. 44, 436-441.
    • (1974) Proc. Amer. Math. Soc. , vol.44 , pp. 436-441
    • Richman, F.1
  • 54
    • 84968475551 scopus 로고
    • Constructions in algebra
    • 54. Seidenberg, A. (1974), Constructions in algebra, Trans. Amer. Math. Soc. 197, 273-313.
    • (1974) Trans. Amer. Math. Soc. , vol.197 , pp. 273-313
    • Seidenberg, A.1
  • 55
    • 84974574558 scopus 로고
    • A new lower bound construction for commutative Thue systems, with applications
    • 55. Yap, K. (1991), A new lower bound construction for commutative Thue systems, with applications, J. Symbolic Comput. 12, 1-28.
    • (1991) J. Symbolic Comput. , vol.12 , pp. 1-28
    • Yap, K.1
  • 56
    • 0003868126 scopus 로고
    • University Series in Higher Mathematics, Van Nostrand-Reinhold, New York/Cincinnati/Toronto
    • 56. Zariski, O., and Samuel, P. (1958), "Commutative Algebra," Vol. I, University Series in Higher Mathematics, Van Nostrand-Reinhold, New York/Cincinnati/Toronto.
    • (1958) Commutative Algebra , vol.1
    • Zariski, O.1    Samuel, P.2


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