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Volumn 28, Issue 1-2, 1999, Pages 225-242

Recent advances on determining the number of real roots of parametric polynomials

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EID: 0010223906     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1998.0274     Document Type: Article
Times cited : (133)

References (20)
  • 1
    • 0024123851 scopus 로고
    • Geometric reasoning with logic and algebra
    • Arnon, D.S. (1988). Geometric reasoning with logic and algebra. Artif. Intell., 37, 37-60.
    • (1988) Artif. Intell. , vol.37 , pp. 37-60
    • Arnon, D.S.1
  • 2
    • 84992258804 scopus 로고
    • On mechanical quantifier elimination for elementary algebra and geometry
    • Arnon, D.S., Mignotte, M. (1988). On mechanical quantifier elimination for elementary algebra and geometry. J. Symb. Comput., 5, 237-260.
    • (1988) J. Symb. Comput. , vol.5 , pp. 237-260
    • Arnon, D.S.1    Mignotte, M.2
  • 3
    • 1542454362 scopus 로고
    • Towards a mechanical solution of the Kahan ellipse problem I
    • LNCS New York, Springer
    • Arnon, D.S., Smith, S. (1983). Towards a mechanical solution of the Kahan ellipse problem I. In Proceedings of EUROCAL'83, LNCS 162, pp. 36-44. New York, Springer.
    • (1983) Proceedings of EUROCAL'83 , vol.162 , pp. 36-44
    • Arnon, D.S.1    Smith, S.2
  • 5
    • 80052985571 scopus 로고
    • Partial cylindrical algebraic decomposition for quantifier elimination
    • Collins, G.E., Hong, H. (1991). Partial cylindrical algebraic decomposition for quantifier elimination. J. Symb. Comput., 12, 299-328.
    • (1991) J. Symb. Comput. , vol.12 , pp. 299-328
    • Collins, G.E.1    Hong, H.2
  • 6
    • 0003538307 scopus 로고
    • New York, Chelsea Publishing Company
    • Gantmacher, F.R. (1959). Matrix Theory. New York, Chelsea Publishing Company.
    • (1959) Matrix Theory
    • Gantmacher, F.R.1
  • 7
    • 0041913269 scopus 로고    scopus 로고
    • A combinatorial algorithm solving some quantifier elimination problems
    • Caviness, B. F. and Johnson, J. R., eds, New York, Springer
    • Gonzalez-Vega, L. (1998). A combinatorial algorithm solving some quantifier elimination problems. In Caviness, B. F. and Johnson, J. R., eds, Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 365-375. New York, Springer.
    • (1998) Quantifier Elimination and Cylindrical Algebraic Decomposition , pp. 365-375
    • Gonzalez-Vega, L.1
  • 9
    • 0042414340 scopus 로고    scopus 로고
    • Sturm-Habicht sequence, determinants and real roots of univariate polynomials
    • Caviness, B. F. and Johnson, J. R., eds, New York, Springer
    • Gonzalez-Vega, L., Recio, T., Lombardi, H., Roy, M.-F. (1998). Sturm-Habicht sequence, determinants and real roots of univariate polynomials. In Caviness, B. F. and Johnson, J. R., eds, Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 300-316. New York, Springer.
    • (1998) Quantifier Elimination and Cylindrical Algebraic Decomposition , pp. 300-316
    • Gonzalez-Vega, L.1    Recio, T.2    Lombardi, H.3    Roy, M.-F.4
  • 10
    • 51249194297 scopus 로고
    • Eine Verallgemeinerung des Sturmschen Wurzelzählverfahrens
    • Habicht, W. (1948). Eine Verallgemeinerung des Sturmschen Wurzelzählverfahrens. Comm. Math. Helv., 21, 99-116.
    • (1948) Comm. Math. Helv. , vol.21 , pp. 99-116
    • Habicht, W.1
  • 11
    • 0000176380 scopus 로고
    • Quantifier elimination: Optimal solution for two classical examples
    • Lazard, D. (1988). Quantifier elimination: optimal solution for two classical examples. J. Symb. Comput., 5, 261-266.
    • (1988) J. Symb. Comput. , vol.5 , pp. 261-266
    • Lazard, D.1
  • 12
    • 0041732982 scopus 로고    scopus 로고
    • A complete discrimination system for polynomials with complex coeffi-cients and its automatic generation
    • To appear
    • Liang, S.X., Zhang, J.Z. (1999) A complete discrimination system for polynomials with complex coeffi-cients and its automatic generation. Sci. China E, 42. To appear.
    • (1999) Sci. China E , vol.42
    • Liang, S.X.1    Zhang, J.Z.2
  • 13
    • 0003062680 scopus 로고
    • Generalized polynomial remainder sequence
    • Buchberger, B. et al., eds, New York, Springer
    • Loos, R. (1983). Generalized polynomial remainder sequence. In Buchberger, B. et al., eds, Computer Algebra: Symbolic and Algebraic Computation, pp. 115-137. New York, Springer.
    • (1983) Computer Algebra: Symbolic and Algebraic Computation , pp. 115-137
    • Loos, R.1
  • 14
    • 0002172421 scopus 로고    scopus 로고
    • Basic algorithms in real geometry and their complexity: From Sturm's theorem to the existential theory of reals
    • Broglia, F., ed., De Gruyter Expositions in Mathematics Walter De Gruyter
    • Roy, M.-F. (1996). Basic algorithms in real geometry and their complexity: from Sturm's theorem to the existential theory of reals. In Broglia, F., ed., Lectures in Real Geometry, De Gruyter Expositions in Mathematics 23, pp. 1-68. Walter De Gruyter.
    • (1996) Lectures in Real Geometry , vol.23 , pp. 1-68
    • Roy, M.-F.1
  • 15
    • 85013246813 scopus 로고
    • Quantifier elimination for real algebra - The cubic case
    • New York, ACM Press
    • Weispfenning, V. (1994). Quantifier elimination for real algebra - the cubic case. In Proceedings of IS-SAC'94, pp. 258-263. New York, ACM Press.
    • (1994) Proceedings of IS-SAC'94 , pp. 258-263
    • Weispfenning, V.1
  • 16
    • 9144241844 scopus 로고
    • On problems involving inequalities
    • Wu, W.T. (1992). On problems involving inequalities. MM Research Preprints, 7, 1-13.
    • (1992) MM Research Preprints , vol.7 , pp. 1-13
    • Wu, W.T.1
  • 17
    • 1542787296 scopus 로고    scopus 로고
    • A complete discrimination system for polynomials
    • Yang, L., Hou, X.R., Zeng, Z.B. (1996). A complete discrimination system for polynomials. Sci. China E, 39, 628-646.
    • (1996) Sci. China E , vol.39 , pp. 628-646
    • Yang, L.1    Hou, X.R.2    Zeng, Z.B.3
  • 18
    • 0013249602 scopus 로고    scopus 로고
    • Explicit criterion to determine the number of positive roots of a polynomial
    • Yang, L., Xia, B.C. (1997). Explicit criterion to determine the number of positive roots of a polynomial. MM Research Preprints, 15, 134-145.
    • (1997) MM Research Preprints , vol.15 , pp. 134-145
    • Yang, L.1    Xia, B.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.