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Volumn 297, Issue 1-3, 2003, Pages 199-239

Subresultants revisited

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; LINEAR ALGEBRA; POLYNOMIALS;

EID: 0037282691     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(02)00639-4     Document Type: Conference Paper
Times cited : (39)

References (52)
  • 1
    • 0002884078 scopus 로고
    • Recherches sur le degré des équations résultantes de l'évanouissement des inconnues
    • Summary pp. 88-91
    • É. Bézout, Recherches sur le degré des équations résultantes de l'évanouissement des inconnues, Histoire de l'académie royale des sciences (1764) 288-338 (Summary pp. 88-91).
    • (1764) Histoire de l'Académie Royale des Sciences , pp. 288-338
    • Bézout, É.1
  • 2
    • 0013416477 scopus 로고
    • Über die resultante ganzer functionen
    • Biermann O. Über die Resultante ganzer Functionen. Monatsh. Math. Phys. 2:1891;143-146.
    • (1891) Monatsh. Math. Phys. , vol.2 , pp. 143-146
    • Biermann, O.1
  • 4
    • 0015143623 scopus 로고
    • On Euclid's algorithm and the computation of polynomial greatest common divisors
    • Brown W.S. On Euclid's algorithm and the computation of polynomial greatest common divisors. J. ACM. 18(4):1971;478-504.
    • (1971) J. ACM , vol.18 , Issue.4 , pp. 478-504
    • Brown, W.S.1
  • 5
    • 0018014720 scopus 로고
    • The subresultant PRS algorithm
    • Brown W.S. The subresultant PRS algorithm. ACM Trans. Math. Software. 4(3):1978;237-249.
    • (1978) ACM Trans. Math. Software , vol.4 , Issue.3 , pp. 237-249
    • Brown, W.S.1
  • 6
    • 0015141743 scopus 로고
    • On Euclid's algorithm and the theory of subresultants
    • Brown W.S., Traub J.F. On Euclid's algorithm and the theory of subresultants. J. ACM. 18(4):1971;505-514.
    • (1971) J. ACM , vol.18 , Issue.4 , pp. 505-514
    • Brown, W.S.1    Traub, J.F.2
  • 7
    • 0001705366 scopus 로고
    • Polynomial remainder sequences and determinants
    • Collins G.E. Polynomial remainder sequences and determinants. Amer. Math. Monthly. 73:1966;708-712.
    • (1966) Amer. Math. Monthly , vol.73 , pp. 708-712
    • Collins, G.E.1
  • 8
    • 84945709818 scopus 로고
    • Subresultants and reduced polynomial remainder sequences
    • Collins G.E. Subresultants and reduced polynomial remainder sequences. J. ACM. 14(1):1967;128-142.
    • (1967) J. ACM , vol.14 , Issue.1 , pp. 128-142
    • Collins, G.E.1
  • 9
    • 0015145497 scopus 로고
    • The calculation of multivariate polynomial resultants
    • Collins G.E. The calculation of multivariate polynomial resultants. J. ACM. 18(4):1971;515-532.
    • (1971) J. ACM , vol.18 , Issue.4 , pp. 515-532
    • Collins, G.E.1
  • 10
    • 0000386406 scopus 로고
    • Computer algebra of polynomials and rational functions
    • Collins G.E. Computer algebra of polynomials and rational functions. Amer. Math. Monthly. 80:1973;725-755.
    • (1973) Amer. Math. Monthly , vol.80 , pp. 725-755
    • Collins, G.E.1
  • 12
    • 0034639376 scopus 로고    scopus 로고
    • Optimizations of the subresultant algorithm
    • Ducos L. Optimizations of the subresultant algorithm. J. Pure Appl. Algebra. 145:2000;149-163.
    • (2000) J. Pure Appl. Algebra , vol.145 , pp. 149-163
    • Ducos, L.1
  • 13
    • 0013456696 scopus 로고
    • Démonstration sur le nombre des points où deux lignes des ordres quelconques peuvent se couper
    • (Eneström 148, Opera Omnia, Ser. 1, vol. 26, Orell Füssli, Zürich, 1953, pp. 46-59).
    • L. Euler, Démonstration sur le nombre des points où deux lignes des ordres quelconques peuvent se couper, Mém. Acad. Sci. Berlin 4 (1750) pp. 234-248 (Eneström 148, Opera Omnia, Ser. 1, vol. 26, Orell Füssli, Zürich, 1953, pp. 46-59).
    • (1750) Mém. Acad. Sci. Berlin , vol.4 , pp. 234-248
    • Euler, L.1
  • 14
    • 0021522564 scopus 로고
    • Parallel algorithms for algebraic problems
    • von zur Gathen J. Parallel algorithms for algebraic problems. SIAM J. Comput. 13(4):1984;802-824.
    • (1984) SIAM J. Comput. , vol.13 , Issue.4 , pp. 802-824
    • Von zur Gathen, J.1
  • 18
    • 26044467814 scopus 로고
    • Vorlesungen über invariantentheorie
    • Teubner, Leipzig, (Herausgegeben von Georg Kerschensteiner).
    • P. Gordan, Vorlesungen über Invariantentheorie. Erster Band: Determinanten, Teubner, Leipzig, 1885 (Herausgegeben von Georg Kerschensteiner).
    • (1885) Erster Band: Determinanten
    • Gordan, P.1
  • 19
    • 51249194297 scopus 로고
    • Eine verallgemeinerung des sturmschen wurzelzählverfahrens
    • Habicht W. Eine Verallgemeinerung des Sturmschen Wurzelzählverfahrens. Comment. Math. Helv. 21:1948;99-116.
    • (1948) Comment. Math. Helv. , vol.21 , pp. 99-116
    • Habicht, W.1
  • 21
    • 0029715613 scopus 로고    scopus 로고
    • The Habicht approach to subresultants
    • Ho C.-J., Yap C.K. The Habicht approach to subresultants. J. Symbolic Comput. 21:1996;1-14.
    • (1996) J. Symbolic Comput. , vol.21 , pp. 1-14
    • Ho, C.-J.1    Yap, C.K.2
  • 22
    • 0031123228 scopus 로고    scopus 로고
    • Subresultants under composition
    • Hong H. Subresultants under composition. J. Symbolic Comput. 23(4):1997;355-365.
    • (1997) J. Symbolic Comput. , vol.23 , Issue.4 , pp. 355-365
    • Hong, H.1
  • 23
    • 0013367203 scopus 로고
    • Bigradients and the problem of Routh and Hurwitz
    • (Erratum SIAM Rev. 10(4) (1968) 438)
    • Householder A.S. Bigradients and the problem of Routh and Hurwitz. SIAM Rev. 10(1):1968;56-66. (Erratum SIAM Rev. 10(4) (1968) 438).
    • (1968) SIAM Rev. , vol.10 , Issue.1 , pp. 56-66
    • Householder, A.S.1
  • 25
    • 0013416339 scopus 로고
    • De eliminatione variabilis e duabus aequationibus algebraicis
    • Jacobi C.G.J. De eliminatione variabilis e duabus aequationibus algebraicis. J. Reine Angew. Math. 15:1836;101-124.
    • (1836) J. Reine Angew. Math. , vol.15 , pp. 101-124
    • Jacobi, C.G.J.1
  • 26
    • 84966261439 scopus 로고
    • Johann Faulhaber and sums of powers
    • Knuth D.E. Johann Faulhaber and sums of powers. Math. Comput. 61(203):1993;277-294.
    • (1993) Math. Comput. , vol.61 , Issue.203 , pp. 277-294
    • Knuth, D.E.1
  • 29
    • 0013460590 scopus 로고
    • Zur theorie der elimination einer variabeln aus zwei algebraischen gleichungen
    • Berlin
    • L. Kronecker, Zur Theorie der Elimination einer Variabeln aus zwei algebraischen Gleichungen. Monatsberichte der Königlich Preussischen Akademie der Wissenschaften, Berlin, 1881, pp. 535-600; in: K. Hensel (Ed.), Werke, Zweiter Band, Leipzig, 1897, pp. 113-192 (Reprint by Chelsea Publishing Co., New York, 1968).
    • (1881) Monatsberichte der Königlich Preussischen Akademie der Wissenschaften , pp. 535-600
    • Kronecker, L.1
  • 30
    • 0013460591 scopus 로고
    • Leipzig (Reprint by Chelsea Publishing Co., New York, 1968
    • L. Kronecker, Zur Theorie der Elimination einer Variabeln aus zwei algebraischen Gleichungen. Monatsberichte der Königlich Preussischen Akademie der Wissenschaften, Berlin, 1881, pp. 535-600; in: K. Hensel (Ed.), Werke, Zweiter Band, Leipzig, 1897, pp. 113-192 (Reprint by Chelsea Publishing Co., New York, 1968).
    • (1897) Werke, Zweiter Band , pp. 113-192
    • Hensel, K.1
  • 31
    • 0029704143 scopus 로고    scopus 로고
    • Cauchy index computation
    • Lickteig T., Roy M.-F. Cauchy index computation. Calcolo. 33:1997;331-357.
    • (1997) Calcolo , vol.33 , pp. 331-357
    • Lickteig, T.1    Roy, M.-F.2
  • 32
    • 0000605515 scopus 로고    scopus 로고
    • Sylvester-Habicht sequences and fast Cauchy index computation
    • Lickteig T., Roy M.-F. Sylvester-Habicht sequences and fast Cauchy index computation. J. Symbolic Comput. 31:2001;315-341.
    • (2001) J. Symbolic Comput. , vol.31 , pp. 315-341
    • Lickteig, T.1    Roy, M.-F.2
  • 34
    • 0003062680 scopus 로고
    • Generalized polynomial remainder sequences
    • Loos R. Generalized polynomial remainder sequences. Computing. 4:1982;115-137.
    • (1982) Computing , vol.4 , pp. 115-137
    • Loos, R.1
  • 35
    • 0013453246 scopus 로고    scopus 로고
    • Diplomarbeit, Universität Paderborn
    • T. Lücking, Subresultants, Diplomarbeit, Universität Paderborn, 2000.
    • (2000) Subresultants
    • Lücking, T.1
  • 36
    • 0031191448 scopus 로고    scopus 로고
    • A note on subresultants and the Lazard/Rioboo/Trager formula in rational function integration
    • Mulders T. A note on subresultants and the Lazard/Rioboo/Trager formula in rational function integration. J. Symbolic Comput. 24(1):1997;45-50.
    • (1997) J. Symbolic Comput. , vol.24 , Issue.1 , pp. 45-50
    • Mulders, T.1
  • 37
    • 0013370059 scopus 로고
    • Zur theorie der resultanten
    • Netto E. Zur Theorie der Resultanten. J. Reine Angew. Math. 116:1896;33-49.
    • (1896) J. Reine Angew. Math. , vol.116 , pp. 33-49
    • Netto, E.1
  • 38
    • 0013411460 scopus 로고
    • Zur theorie der resultanten
    • (Nachtrag zu der Abhandlung aus Bd. 116 S. 33-49)
    • Netto E. Zur Theorie der Resultanten. J. Reine Angew. Math. 117:1897;57-71. (Nachtrag zu der Abhandlung aus Bd. 116 S. 33-49).
    • (1897) J. Reine Angew. Math. , vol.117 , pp. 57-71
    • Netto, E.1
  • 39
    • 0013410498 scopus 로고
    • Arithmetica universalis, sive de compositione et resolutione arithmetica liber
    • London
    • I. Newton, Arithmetica Universalis, sive de compositione et resolutione arithmetica liber. J. Senex, London, 1707. (English translation as Universal Arithmetick: or, A Treatise on Arithmetical composition and Resolution, translated by the late Mr. Raphson and revised and corrected by Mr. Cunn, London, 1728, Reprinted in: Derek T. Whiteside, The Mathematical Works of Isaac Newton, Johnson Reprint Co., New York, 1967, p. 4ff).
    • (1707) J. Senex
    • Newton, I.1
  • 40
    • 0011632191 scopus 로고
    • (English translation as Universal Arithmetick: or, A Treatise on Arithmetical composition and Resolution, translated by the late Mr. Raphson and revised and corrected by Mr. Cunn, London, 1728, Reprinted, Johnson Reprint Co., New York, p. 4ff)
    • I. Newton, Arithmetica Universalis, sive de compositione et resolutione arithmetica liber. J. Senex, London, 1707. (English translation as Universal Arithmetick: or, A Treatise on Arithmetical composition and Resolution, translated by the late Mr. Raphson and revised and corrected by Mr. Cunn, London, 1728, Reprinted in: Derek T. Whiteside, The Mathematical Works of Isaac Newton, Johnson Reprint Co., New York, 1967, p. 4ff).
    • (1967) The Mathematical Works of Isaac Newton
    • Whiteside, D.T.1
  • 44
    • 0001977576 scopus 로고
    • The computational complexity of continued fractions
    • Strassen V. The computational complexity of continued fractions. SIAM J. Comput. 12(1):1983;1-27.
    • (1983) SIAM J. Comput. , vol.12 , Issue.1 , pp. 1-27
    • Strassen, V.1
  • 46
    • 0003207762 scopus 로고
    • A method of determining by mere inspection the derivatives from two equations of any degree
    • Sylvester J.J. A method of determining by mere inspection the derivatives from two equations of any degree. Philos. Mag. 16:1840;132-135. (Mathematical Papers, vol. 1, Chelsea Publishing Co., New York, 1973, pp. 54-57).
    • (1840) Philos. Mag. , vol.16 , pp. 132-135
    • Sylvester, J.J.1
  • 47
    • 0013416341 scopus 로고
    • Chelsea Publishing Co., New York
    • Sylvester J.J. A method of determining by mere inspection the derivatives from two equations of any degree. Philos. Mag. 16:1840;132-135. (Mathematical Papers, vol. 1, Chelsea Publishing Co., New York, 1973, pp. 54-57).
    • (1973) Mathematical Papers , vol.1 , pp. 54-57
  • 49
    • 0032066487 scopus 로고    scopus 로고
    • The search for the maximum of a polynomial
    • Uteshev A.Yu., Cherkasov T.M. The search for the maximum of a polynomial. J. Symbolic Comput. 25:1998;587-618.
    • (1998) J. Symbolic Comput. , vol.25 , pp. 587-618
    • Uteshev, A.Yu.1    Cherkasov, T.M.2


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