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Volumn , Issue , 2015, Pages 1-275

Solving polynomial equation systems III

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EID: 84952660465     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book
Times cited : (33)

References (141)
  • 2
    • 0001906678 scopus 로고    scopus 로고
    • Multiplicities and idempotents for zero dimensional systems
    • Birkhäuser
    • Alonso M.E., Becker E., Roy M.-F., Wörmann T. Zeroes, multiplicities and idempotents for zero dimensional systems, in Prog. Math. 143 (1996), pp. 1-16, Birkhäuser.
    • (1996) Prog. Math , vol.143 , pp. 1-16
    • Alonso, M.E.1    Becker, E.2    Roy, M.-F.3    Zeroes, W.T.4
  • 6
    • 0000631665 scopus 로고    scopus 로고
    • Triangular set for solving polynomial systems: A comparative implementation of four methods
    • Aubry P., Moreno Maza M., Triangular set for solving polynomial systems: a comparative implementation of four methods, J. Symb. Comp. 28 (1999), 125-154.
    • (1999) J. Symb. Comp , vol.28 , pp. 125-154
    • Aubry, P.1    Moreno Maza, M.2
  • 7
    • 0346109328 scopus 로고    scopus 로고
    • Using galois ideals for computing relative resolvents
    • Aubry P., Valibouze A., Using Galois ideals for computing relative resolvents, J. Symb. Comp. 30 (2000), 635-651.
    • (2000) J. Symb. Comp , vol.30 , pp. 635-651
    • Aubry, P.1    Valibouze, A.2
  • 9
    • 0002783070 scopus 로고
    • An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations
    • Birkhäuser
    • Auzinger W., Stetter H.J., An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, in I.S.N.M. 86 (1988), pp. 11-30, Birkhäuser.
    • (1988) I.S.N.M , vol.86 , pp. 11-30
    • Auzinger, W.1    Stetter, H.J.2
  • 10
    • 0000197849 scopus 로고    scopus 로고
    • Multivariate bezoutians, kronecker symbol and eisenbud-levin formula
    • Birkhäuser
    • Becker E., Cardinal J.-P., Roy M.-F., Szafraniec Z., Multivariate Bezoutians, Kronecker symbol and Eisenbud-Levin formula, in Prog. Math. 143 (1996), pp. 79-104, Birkhäuser.
    • (1996) Prog. Math , vol.143 , pp. 79-104
    • Becker, E.1    Cardinal, J.-P.2    Roy, M.-F.3    Szafraniec, Z.4
  • 11
    • 0002884078 scopus 로고
    • Recherches sur le degré des équations résultantes de l’évanouissement des inconnues, et sur les moyens qu’il convient d’employer pour trouver ses équations
    • Bézout E., Recherches sur le degré des équations résultantes de l’évanouissement des inconnues, et sur les moyens qu’il convient d’employer pour trouver ses équations, Mém. Acad. Roy. Sci. Paris (1764), 288-233.
    • (1764) Mém. Acad. Roy. Sci. Paris , pp. 233-288
    • Bézout, E.1
  • 14
    • 0346885832 scopus 로고    scopus 로고
    • Fast algorithm for zero-dimensional polynomial systems using duality
    • Bostajn A., Salvy B., Schost E., Fast algorithm for zero-dimensional polynomial systems using duality, J. AAECC 14 (2003), 239-272.
    • (2003) J. AAECC , vol.14 , pp. 239-272
    • Bostajn, A.1    Salvy, B.2    Schost, E.3
  • 17
    • 85032875512 scopus 로고
    • Generalized characteristic polynomials
    • Springer
    • Canny J., Generalized characteristic polynomials, in L. N. Comp. Sci. 358 (1988), pp. 293-299, Springer.
    • (1988) L. N. Comp. Sci , vol.358 , pp. 293-299
    • Canny, J.1
  • 18
    • 85010519644 scopus 로고
    • An effective algorithm for the sparse mixed resultant
    • Springer
    • Canny J., An effective algorithm for the sparse mixed resultant, in L. N. Comp. Sci. 673 (1993), pp. 89-104, Springer.
    • (1993) L. N. Comp. Sci , vol.673 , pp. 89-104
    • Canny, J.1
  • 20
    • 0001675230 scopus 로고    scopus 로고
    • Algebraic approach of residues and applications
    • American Mathematical Society Press
    • Cardinal J.P., Mourrain B., Algebraic approach of residues and applications, in L. N. Appl. Math. 32 (1999), American Mathematical Society Press.
    • (1999) L. N. Appl. Math , vol.32
    • Cardinal, J.P.1    Mourrain, B.2
  • 21
    • 84952713592 scopus 로고
    • Usage des fonctions interpolaires dans ls determination des fonctions sym-metriques des racines d’une équation algébrique donnée
    • Cauchy A., Usage des fonctions interpolaires dans ls determination des fonctions sym-metriques des racines d’une équation algébrique donnée, C.R. Acad. Sci. Paris 11 (1840), 933.
    • (1840) C.R. Acad. Sci. Paris , vol.11 , pp. 933
    • Cauchy, A.1
  • 22
    • 84952662328 scopus 로고
    • T. V, Gauthier-Villars, Paris
    • Cauchy A., Oeuvres T. V, Gauthier-Villars, Paris, (1882).
    • (1882) Oeuvres
    • Cauchy, A.1
  • 23
    • 0001713268 scopus 로고
    • On the theory of elimination
    • Cayley A., On the theory of elimination, Camb. Dublin Math. J. 3 (1848), 116-120.
    • (1848) Camb. Dublin Math. J , vol.3 , pp. 116-120
    • Cayley, A.1
  • 24
    • 0011401763 scopus 로고
    • Note sur la méthode d’élimination de bezout
    • Cayley A., Note sur la méthode d’élimination de Bezout, J. Reine Ang. Math. 53 (1857), 366-367
    • (1857) J. Reine Ang. Math , vol.53 , pp. 366-367
    • Cayley, A.1
  • 25
    • 77951154009 scopus 로고
    • A fourth memoir upon quantics
    • Cayley, A., A fourth memoir upon quantics, Phil. Trans. Royal Soc. London 168 (1858), 415-427.
    • (1858) Phil. Trans. Royal Soc. London , vol.168 , pp. 415-427
    • Cayley, A.1
  • 26
    • 84952671363 scopus 로고
    • Un algorithm pour les calcul des resultants
    • Birkhäuser
    • Charden M., Un algorithm pour les calcul des resultants, in Prog. Math. 94 (1990), pp. 47-62, Birkhäuser.
    • (1990) Prog. Math , vol.94 , pp. 47-62
    • Charden, M.1
  • 27
    • 0002912359 scopus 로고
    • The resultant via a koszul complex
    • Birkhäuser
    • Charden M., The resultant via a Koszul complex, Prog. Math. 109 (1993), pp. 29-40, Birkhäuser.
    • (1993) Prog. Math , vol.109 , pp. 29-40
    • Charden, M.1
  • 30
    • 27644512413 scopus 로고    scopus 로고
    • Sharp estimates for triangular sets
    • Association for Computing Machinery
    • Dahan X., Schost E., Sharp estimates for triangular sets, in Proc. ISSAC’04 (2004), pp. 103-110, Association for Computing Machinery.
    • (2004) Proc. ISSAC’04 , pp. 103-110
    • Dahan, X.1    Schost, E.2
  • 32
    • 84952713593 scopus 로고
    • Sur les systèmes algébriques et leurs relations avec certains systèmes d’equations aux dérivées partielles
    • Delassus E., Sur les systèmes algébriques et leurs relations avec certains systèmes d’equations aux dérivées partielles. Ann. Éc. Norm. 3e série 14 (1897), 21-44.
    • (1897) e série , vol.14 , pp. 21-44
    • Delassus, E.1
  • 33
    • 84960585591 scopus 로고
    • On a form of the eliminant of two quantics
    • Dixon, A.L., On a form of the eliminant of two quantics, Proc. London Math. Soc. 6 (1908a), 468-478.
    • (1908) Proc. London Math. Soc , vol.6 , pp. 468-478
    • Dixon, A.L.1
  • 34
    • 84960589566 scopus 로고
    • The eliminant of three quantics in two independent variables
    • Dixon, A.L., The eliminant of three quantics in two independent variables, Proc. London Math. Soc. 7 (1908b), 49-69.
    • (1908) Proc. London Math. Soc , vol.7 , pp. 49-69
    • Dixon, A.L.1
  • 35
    • 84952713594 scopus 로고
    • Some results in the theory of elimination
    • Dixon, A.L., Some results in the theory of elimination, Proc. Roy. Soc. London 82 (1909), 468-478.
    • (1909) Proc. Roy. Soc. London , vol.82 , pp. 468-478
    • Dixon, A.L.1
  • 37
    • 33645987866 scopus 로고    scopus 로고
    • The lex game and some applications
    • Felszeghy B., Rath B., Ronyai L., The lex game and some applications, J. Symb. Comp. 41 (2006), 663-681.
    • (2006) J. Symb. Comp , vol.41 , pp. 663-681
    • Felszeghy, B.1    Rath, B.2    Ronyai, L.3
  • 38
    • 0010070016 scopus 로고
    • Effective algorithms and bounds for wu-ritt characteristic sets
    • Birkhäuser
    • Gallo G., Mishra B., Effective algorithms and bounds for Wu-Ritt characteristic sets, in Prog. Math. 94 (1990), pp. 119-142, Birkhäuser.
    • (1990) Prog. Math , vol.94 , pp. 119-142
    • Gallo, G.1    Mishra, B.2
  • 39
    • 0011417325 scopus 로고
    • A solution to kronecker’s problem
    • Gallo G., Mishra, B., A solution to Kronecker’s problem, J. AAECC 5 (1994), 343-370.
    • (1994) J. AAECC , vol.5 , pp. 343-370
    • Gallo, G.1    Mishra, B.2
  • 40
    • 84955591390 scopus 로고
    • Some constructions in rings of differential polynomials
    • Springer
    • Gallo G., Mishra, B., Olivier F., Some constructions in rings of differential polynomials, in L. N. Comp. Sci. 539 (1991), pp. 171-182, Springer.
    • (1991) L. N. Comp. Sci , vol.539 , pp. 171-182
    • Gallo, G.1    Mishra, B.2    Olivier, F.3
  • 41
    • 85033721578 scopus 로고
    • Properties of gröbner bases under specialization
    • Springer
    • Gianni P., Properties of Gröbner bases under specialization, in L. N. Comp. Sci. 378 (1987), pp. 293-297, Springer.
    • (1987) L. N. Comp. Sci , vol.378 , pp. 293-297
    • Gianni, P.1
  • 42
    • 0000750175 scopus 로고
    • Algorithmes-disons rapides-pour la décomposition d’une variété algébrique en composantes irréductibles
    • Birkhäuser
    • Giusti M., Heintz J., Algorithmes-disons rapides-pour la décomposition d’une variété algébrique en composantes irréductibles, in Prog. Math. 94 (1990), pp. 169-194, Birkhäuser.
    • (1990) Prog. Math , vol.94 , pp. 169-194
    • Giusti, M.1    Heintz, J.2
  • 43
    • 0000936391 scopus 로고
    • La detérmination des point isolés et de la dimension d’une variété algébrique peut se faire en temps polynomial
    • Cambridge University Press
    • Giusti M., Heintz J., La detérmination des point isolés et de la dimension d’une variété algébrique peut se faire en temps polynomial, in Symp. Math. 34 (1993), pp. 216-256, Cambridge University Press.
    • (1993) Symp. Math , vol.34 , pp. 216-256
    • Giusti, M.1    Heintz, J.2
  • 44
    • 85139861192 scopus 로고    scopus 로고
    • Solving some overdetermined polynomial systems
    • Association for Computing Machinery
    • Giusti M., Schost E., Solving some overdetermined polynomial systems, in Proc. ISSAC’99 (1999), pp. 1-8, Association for Computing Machinery.
    • (1999) Proc. ISSAC’99 , pp. 1-8
    • Giusti, M.1    Schost, E.2
  • 45
    • 84955611783 scopus 로고
    • When polynomial equation systems can be “solved” fast?
    • Springer
    • Giusti M., Heintz J., Morais J.E., Pardo L.M., When polynomial equation systems can be “solved” fast?, in L. N. Comp. Sci. 948 (1995), pp. 205-231, Springer.
    • (1995) L. N. Comp. Sci , vol.948 , pp. 205-231
    • Giusti, M.1    Heintz, J.2    Morais, J.E.3    Pardo, L.M.4
  • 47
    • 0031539424 scopus 로고    scopus 로고
    • Le rôle des structures de données dans les problèmes d’élimination
    • Giusti M., Heintz J., Morais J.E., Pardo L.M., Le rôle des structures de données dans les problèmes d’élimination, C.R. Acad. Sci. Paris 325 (1997b), 1223-1228.
    • (1997) C.R. Acad. Sci. Paris , vol.325 , pp. 1223-1228
    • Giusti, M.1    Heintz, J.2    Morais, J.E.3    Pardo, L.M.4
  • 49
    • 0034259150 scopus 로고    scopus 로고
    • The projective noether maple package: Computing the dimension of a projective variety
    • Giusti M., Hagele K., Lecerf G., Marchand J., Salvy B., The projective Noether maple package: computing the dimension of a projective variety, J. Symb. Comp. 30 (2000), 291-307.
    • (2000) J. Symb. Comp , vol.30 , pp. 291-307
    • Giusti, M.1    Hagele, K.2    Lecerf, G.3    Marchand, J.4    Salvy, B.5
  • 50
    • 0035294718 scopus 로고    scopus 로고
    • A grobner free alternative for polynomial system solving
    • Giusti M., Lecerf G., Salvy B., A Grobner free alternative for polynomial system solving, J. Complexity 17 (2001), 154-211.
    • (2001) J. Complexity , vol.17 , pp. 154-211
    • Giusti, M.1    Lecerf, G.2    Salvy, B.3
  • 53
    • 84952642114 scopus 로고
    • Sur les caractéristiques des systèmes d’équations aux dérivées partialles
    • Gunther N., Sur les caractéristiques des systèmes d’équations aux dérivées partialles, C.R. Acad. Sci. Paris 156 (1913), 1147-1150.
    • (1913) C.R. Acad. Sci. Paris , vol.156 , pp. 1147-1150
    • Gunther, N.1
  • 54
    • 84918831557 scopus 로고
    • Sur la forme canonique des equations algébriques
    • Gunther N., Sur la forme canonique des equations algébriques, C.R. Acad. Sci. Paris 157 (1913), 577-80.
    • (1913) C.R. Acad. Sci. Paris , vol.157 , pp. 577-580
    • Gunther, N.1
  • 55
    • 0034695774 scopus 로고    scopus 로고
    • On the intrinsic complexity of the arithmetic nullstellensatz
    • Hagele K., Morais J.E., Pardo L.M., Sombra M., On the intrinsic complexity of the arithmetic Nullstellensatz, J. Pure Appl. Algebra 146 (2000), 103-183.
    • (2000) J. Pure Appl. Algebra , vol.146 , pp. 103-183
    • Hagele, K.1    Morais, J.E.2    Pardo, L.M.3    Sombra, M.4
  • 56
    • 77957277141 scopus 로고    scopus 로고
    • Structure et complexité des bases de grobner
    • Hashemi A., Structure et Complexité des bases de Grobner, J. Symb. Comp. 45 (2010), 1330-1340.
    • (2010) J. Symb. Comp , vol.45 , pp. 1330-1340
    • Hashemi, A.1
  • 57
    • 80051767567 scopus 로고    scopus 로고
    • Sharper complexity bounds for zero-dimensional grobner bases and polynomial system solving
    • Hashemi A., Lazard D., Sharper complexity bounds for zero-dimensional Grobner bases and polynomial system solving, Int. J. Algebra Comp. 21 (2011), 705-713.
    • (2011) Int. J. Algebra Comp , vol.21 , pp. 705-713
    • Hashemi, A.1    Lazard, D.2
  • 58
    • 0013416339 scopus 로고
    • De eliminatione variabilis e duabus aequationibus algebraicas
    • Jacobi C.G.I., De eliminatione variabilis e duabus aequationibus algebraicas, J. Reine Ang. Math. 15 (1836) 101-124.
    • (1836) J. Reine Ang. Math , vol.15 , pp. 101-124
    • Jacobi, C.1
  • 59
    • 38149144730 scopus 로고    scopus 로고
    • Le formalisme du résultant
    • Jouanoulou J.-P., Le formalisme du résultant, Adv. Math. 90 117-263.
    • Adv. Math , vol.90 , pp. 117-263
    • Jouanoulou, J.-P.1
  • 60
    • 85033676092 scopus 로고
    • Solving systems of algebraic equations by using grobner bases
    • Springer
    • Kalkbrener M., Solving systems of algebraic equations by using Grobner bases, in L. N. Comp. Sci. 378 (1987), pp. 282-292, Springer.
    • (1987) N. Comp. Sci , vol.378 , pp. 282-292
    • Kalkbrener, M.1
  • 62
    • 38249006658 scopus 로고
    • A generic euclidean algorithm for computing triangular representations of algebraic varieties
    • Kalkbrener M., A generic euclidean algorithm for computing triangular representations of algebraic varieties, J. Symb. Comp. 15 (1993), 153-167.
    • (1993) J. Symb. Comp , vol.15 , pp. 153-167
    • Kalkbrener, M.1
  • 63
    • 0031185293 scopus 로고    scopus 로고
    • On the stability of grobner bases under specialization
    • Kalkbrener M., On the stability of Grobner bases under specialization, J. Symb. Comp. 24 (1997), 51-58.
    • (1997) J. Symb. Comp , vol.24 , pp. 51-58
    • Kalkbrener, M.1
  • 64
    • 72149099072 scopus 로고    scopus 로고
    • An algorithm for computing a grobner basis of a polynomial ideal over a ring with zero divisors
    • Kapur D., Cai Y., An algorithm for computing a Grobner basis of a polynomial ideal over a ring with zero divisors, Math. Comput. Sci. 2 (2009), 601-634.
    • (2009) Math. Comput. Sci , vol.2 , pp. 601-634
    • Kapur, D.1    Cai, Y.2
  • 65
    • 0033645331 scopus 로고    scopus 로고
    • Conditions for exact resultants using the dixon resultant formulation
    • Association for Computing Machinery
    • Kapur D., Chtcherba A.D., Conditions for exact resultants using the Dixon resultant formulation, in Proc. ISSAC 2000 (2000), pp. 62-70, Association for Computing Machinery.
    • (2000) Proc. ISSAC , vol.2000 , pp. 62-70
    • Kapur, D.1    Chtcherba, A.D.2
  • 66
    • 0036042386 scopus 로고    scopus 로고
    • On the efficiency and optimality of dixon-based resultant method
    • Association for Computing Machinery
    • Kapur D., Chtcherba A.D., On the efficiency and optimality of Dixon-based resultant method, in Proc. ISSAC 2002 (2002), pp. 29-36, Association for Computing Machinery.
    • (2002) Proc. ISSAC , vol.2002 , pp. 29-36
    • Kapur, D.1    Chtcherba, A.D.2
  • 67
    • 85020527472 scopus 로고
    • Algebraic and geometric reasoning using dixon resultants
    • Association for Computing Machinery
    • Kapur D., Saxena T., Yang, L., Algebraic and geometric reasoning using Dixon resultants, in Proc. ISSAC 94 (1994), pp. 99-136, Association for Computing Machinery.
    • (1994) Proc. ISSAC , vol.94 , pp. 99-136
    • Kapur, D.1    Saxena, T.2    Yang, L.3
  • 68
    • 0030659943 scopus 로고    scopus 로고
    • Extraneous factors in the dixon resultant formulation
    • Association for Computing Machinery
    • Kapur D., Saxena T., Extraneous factors in the Dixon resultant formulation, in Proc. ISSAC 97 (1997), pp. 141-148, Association for Computing Machinery.
    • (1997) Proc. ISSAC , vol.97 , pp. 141-214
    • Kapur, D.1    Saxena, T.2
  • 71
    • 0001379976 scopus 로고
    • Une approache informatique pour l’approximation diophantienne
    • Krick T., Pardo L.M., Une approache informatique pour l’approximation diophantienne, C.R. Acad. Sci. Paris 318 (1994), 407-412.
    • (1994) C.R. Acad. Sci. Paris , vol.318 , pp. 407-412
    • Krick, T.1    Pardo, L.M.2
  • 72
    • 0000697864 scopus 로고    scopus 로고
    • A computational method for diphantine approximation
    • Birkhäuser
    • Krick T., Pardo L.M., A computational method for Diphantine approximation, in Prog. Math. 143 (1996), pp. 193-254, Birkhäuser.
    • (1996) Prog. Math , vol.143 , pp. 193-254
    • Krick, T.1    Pardo, L.M.2
  • 73
    • 0003367986 scopus 로고
    • On the complexity of zero-dimensional algebraic systems
    • Birkhäuser
    • Lakshman Y.N., Lazard D., On the complexity of zero-dimensional algebraic systems, in Prog. Math. 94 (1990), pp. 217-226, Birkhäuser.
    • (1990) Prog. Math , vol.94 , pp. 217-226
    • Lakshman, Y.N.1    Lazard, D.2
  • 74
    • 0000713722 scopus 로고
    • Algèbre linéaire sur k[ap…, xn] et élimination
    • Lazard D., Algèbre linéaire sur K[Ap…, Xn] et élimination, Bull. Soc. Math. France 105 (1977), 165-190.
    • (1977) Bull. Soc. Math. France , vol.105 , pp. 165-190
    • Lazard, D.1
  • 75
    • 85034863243 scopus 로고
    • Systems of algebraic equations
    • Springer
    • Lazard D., Systems of algebraic equations, in L. N. Comp. Sci. 72 (1979), pp. 88-94, Springer.
    • (1979) L. N. Comp. Sci , vol.72 , pp. 88-94
    • Lazard, D.1
  • 76
    • 0002548511 scopus 로고
    • Resolution des systemes d’equations algebriques
    • Lazard, D., Resolution des systemes d’equations algebriques, Theoret. Comput. Sci. 15 (1981), 77-110.
    • (1981) Theoret. Comput. Sci , vol.15 , pp. 77-110
    • Lazard, D.1
  • 77
    • 0000069912 scopus 로고
    • A new method for solving algebraic systems of positive dimension
    • Lazard, D., A new method for solving algebraic systems of positive dimension, Disc. Appl. Math. 33 (1991), 147-160.
    • (1991) Disc. Appl. Math , vol.33 , pp. 147-160
    • Lazard, D.1
  • 78
    • 0000167385 scopus 로고
    • Solving zero-dimensional algebraic systems
    • Lazard D., Solving zero-dimensional algebraic systems, J. Symb. Comp. 15 (1992), 117-132.
    • (1992) J. Symb. Comp , vol.15 , pp. 117-132
    • Lazard, D.1
  • 79
    • 33645954818 scopus 로고
    • Systems of algebraic equations (Algorithms and complexity)
    • Cambridge University Press
    • Lazard D., Systems of algebraic equations (algorithms and complexity), Symp. Math. 34 (1993), 84-106, Cambridge University Press.
    • (1993) Symp. Math , vol.34 , pp. 84-106
    • Lazard, D.1
  • 80
    • 84865533115 scopus 로고    scopus 로고
    • Resolution of polynomial systems
    • World Scientific
    • Lazard D., Resolution of polynomial systems, in Proc. ASCM 2000 (2000), pp. 1-8, World Scientific.
    • (2000) Proc. ASCM , vol.2000 , pp. 1-8
    • Lazard, D.1
  • 81
    • 84952671742 scopus 로고    scopus 로고
    • On the specification for solvers of polynomial systems
    • World Scientific
    • Lazard D., On the specification for solvers of polynomial systems, in Proc. ASCM 2001 (2001), pp. 1-10, World Scientific.
    • (2001) Proc. ASCM , vol.2001 , pp. 1-10
    • Lazard, D.1
  • 82
    • 60549092093 scopus 로고    scopus 로고
    • Thirty years of polynomial system solving, and now?
    • Lazard D., Thirty years of polynomial system solving, and now?, J. Symb. Comp. 44 (2009), 222-239.
    • (2009) J. Symb. Comp , vol.44 , pp. 222-239
    • Lazard, D.1
  • 83
    • 34247632237 scopus 로고    scopus 로고
    • Solving parametric polynomial systems
    • Lazard D., Rouillier F., Solving parametric polynomial systems, J. Symb. Comp. 42 (2007), 636-667.
    • (2007) J. Symb. Comp , vol.42 , pp. 636-667
    • Lazard, D.1    Rouillier, F.2
  • 85
    • 58849106380 scopus 로고    scopus 로고
    • Complexity of comparing monomials and two improvements of the bm-algorithm
    • Springer
    • Lundqvist S., Complexity of comparing monomials and two improvements of the BM-algorithm, in L. N. Comp. Sci. 5393 (2008), pp. 105-125, Springer.
    • (2008) L. N. Comp. Sci , vol.5393 , pp. 105-125
    • Lundqvist, S.1
  • 86
    • 70350604334 scopus 로고    scopus 로고
    • Vector space bases associated to vanishing ideals of points
    • Lundqvist S., Vector space bases associated to vanishing ideals of points, J. Pure Appl. Algebra 214 (2010), 309-321.
    • (2010) J. Pure Appl. Algebra , vol.214 , pp. 309-321
    • Lundqvist, S.1
  • 87
    • 84960556527 scopus 로고
    • Some formulae in elimination
    • Macaulay F. S., Some formulae in elimination, Proc. London Math. Soc. (1) 35 (1903), 3-27.
    • (1903) Proc. London Math. Soc , vol.35 , Issue.1 , pp. 3-27
    • Macaulay, F.S.1
  • 90
    • 0002345405 scopus 로고
    • Multipolynomial resultant algorithms
    • Manocha D., Cannon J.F., Multipolynomial resultant algorithms, J. Symb. Comp. 15 (1993), 99-122.
    • (1993) J. Symb. Comp , vol.15 , pp. 99-122
    • Manocha, D.1    Cannon, J.F.2
  • 91
    • 85027646416 scopus 로고
    • Systems of algebraic equations solved by means of endomorphisms
    • Springer
    • Möller H.M., Systems of algebraic equations solved by means of endomorphisms, in L. N. Comp. Sci. 673 (1993a), pp. 43-56, Springer.
    • (1993) L. N. Comp. Sci , vol.673 , pp. 43-56
    • Möller, H.M.1
  • 92
    • 0001332043 scopus 로고
    • On decomposing systems of polynomial equations with finitely many solutions
    • Möller H.M., On decomposing systems of polynomial equations with finitely many solutions, J. AAECC 4 (1993b), 217-230.
    • (1993) J. AAECC , vol.4 , pp. 217-230
    • Möller, H.M.1
  • 93
    • 21844490170 scopus 로고
    • Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
    • Möller M., Stetter H., Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems, Num. Math. 70 (1995), 311-325.
    • (1995) Num. Math , vol.70 , pp. 311-325
    • Möller, M.1    Stetter, H.2
  • 94
    • 0036851562 scopus 로고    scopus 로고
    • Computing the primary decomposition of zero-dimensional ideals
    • Monico C., Computing the primary decomposition of zero-dimensional ideals, J. Symb. Comp. 34 (2002), 451-459.
    • (2002) J. Symb. Comp , vol.34 , pp. 451-459
    • Monico, C.1
  • 96
    • 84955583152 scopus 로고
    • Polynomial gcd computation over tower of algebraic extension
    • Springer
    • Moreno Maza M., Rioboo R., Polynomial gcd computation over tower of algebraic extension, in L. N. Comp. Sci. 948 (1995), pp. 365-382, Springer.
    • (1995) L. N. Comp. Sci , vol.948 , pp. 365-382
    • Moreno Maza, M.1    Rioboo, R.2
  • 97
    • 0013301023 scopus 로고    scopus 로고
    • On multiple zeros of systems of algebraic equations
    • Association for Computing Machinery
    • Moritzugu S., Kuriyama K., On multiple zeros of systems of algebraic equations, in Proc. ISSAC’99 (1999), pp. 23-30, Association for Computing Machinery.
    • (1999) Proc. ISSAC , vol.99 , pp. 23-30
    • Moritzugu, S.1    Kuriyama, K.2
  • 98
    • 0032349485 scopus 로고    scopus 로고
    • Computing the isolated roots by matrix methods
    • Mourrain B., Computing the isolated roots by matrix methods, J. Symb. Comp. 26 (1998), 715-738.
    • (1998) J. Symb. Comp , vol.26 , pp. 715-738
    • Mourrain, B.1
  • 99
    • 84957631580 scopus 로고    scopus 로고
    • A new criterion for normal form algorithms
    • Springer
    • Mourrain B., A new criterion for normal form algorithms, in L. N. Comp. Sci. 1719 (1999), pp. 430-443, Springer.
    • (1999) L. N. Comp. Sci , vol.1719 , pp. 430-443
    • Mourrain, B.1
  • 100
    • 14944367312 scopus 로고    scopus 로고
    • Bezoutian and quotient ring structure
    • Mourrain B., Bezoutian and quotient ring structure, J. Symb. Comp. 39 (2005), 397-415.
    • (2005) J. Symb. Comp , vol.39 , pp. 397-415
    • Mourrain, B.1
  • 101
    • 0000692349 scopus 로고    scopus 로고
    • Multivariate polynomials, duality and structured matrices
    • Mourrain B., Pan Y.V., Multivariate polynomials, duality and structured matrices, J. Complexity 16 (2000), 110-180.
    • (2000) J. Complexity , vol.16 , pp. 110-180
    • Mourrain, B.1    Pan, Y.V.2
  • 102
    • 0036331164 scopus 로고    scopus 로고
    • Relation between roots and coefficients, interpolation and application to system solving
    • Mourrain B., Ruatta O., Relation between roots and coefficients, interpolation and application to system solving, J. Symb. Comp. 33 (2002), 679-699.
    • (2002) J. Symb. Comp , vol.33 , pp. 679-699
    • Mourrain, B.1    Ruatta, O.2
  • 103
    • 0033650331 scopus 로고    scopus 로고
    • Solving projective complete intersection faster
    • Association for Computing Machinery
    • Mourrain B., Trebuchet P., Solving projective complete intersection faster, in Proc. ISSAC’00 (2000), pp. 234-241, Association for Computing Machinery.
    • (2000) Proc. ISSAC’00 , pp. 234-241
    • Mourrain, B.1    Trebuchet, P.2
  • 106
    • 84955604612 scopus 로고
    • How lower and upper complexity bounds meet in elimination
    • Springer
    • Pardo L.M., How lower and upper complexity bounds meet in elimination, in L. N. Comp. Sci. 948 (1995), pp. 33-69, Springer.
    • (1995) L. N. Comp. Sci , vol.948 , pp. 33-69
    • Pardo, L.M.1
  • 107
    • 0003336859 scopus 로고
    • Modules over commutaive regular rings
    • Pierce R.S., Modules over commutaive regular rings, Mem. A.M.S. 70 (1967).
    • (1967) Mem. A.M.S , pp. 70
    • Pierce, R.S.1
  • 108
    • 84915850913 scopus 로고
    • On solving systems of algebraic equations via ideal bases and elimination
    • Association for Computing Machinery
    • Pohst M., Yun D., On solving systems of algebraic equations via ideal bases and elimination, in Proc. 1981 SymSAC (1981), pp. 206-211, Association for Computing Machinery.
    • (1981) Proc. 1981 Symsac , pp. 206-211
    • Pohst, M.1    Yun, D.2
  • 109
    • 84910798943 scopus 로고
    • Mémoire sur l’élimination dans les équations algébriques
    • Poisson, S.D. Mémoire sur l’élimination dans les équations algébriques, J. École Polytechnique t. 4 (1802), 199-203.
    • (1802) J. École Polytechnique T , vol.4 , pp. 199-203
    • Poisson, S.D.1
  • 110
    • 0033236946 scopus 로고    scopus 로고
    • Calcule de résolventes avec les modules de cauchy
    • Rennert N., Valibouze A., Calcule de résolventes avec les modules de Cauchy, Exp. Math. 8 (1999), 351-366.
    • (1999) Exp. Math , vol.8 , pp. 351-366
    • Rennert, N.1    Valibouze, A.2
  • 112
    • 0002533613 scopus 로고
    • Prime and composite polynomials
    • Ritt J.F., Prime and composite polynomials, Trans. A.M.S. 23 (1922), 51-66.
    • (1922) Trans. A.M.S , vol.23 , pp. 51-66
    • Ritt, J.F.1
  • 114
  • 117
    • 0033131339 scopus 로고    scopus 로고
    • Solving zero-dimensional systems through the rational univariate representation
    • Rouillier F., Solving zero-dimensional systems through the Rational Univariate Representation, J. AAECC 9 (1999), 433-461.
    • (1999) J. AAECC , vol.9 , pp. 433-461
    • Rouillier, F.1
  • 120
    • 0002386546 scopus 로고    scopus 로고
    • Matrix eigenprobelms are at the heart of polynomial system solving
    • Stetter H., Matrix eigenprobelms are at the heart of polynomial system solving, SIGSAM Bull. 30 (1996), 22-25.
    • (1996) SIGSAM Bull , vol.30 , pp. 22-25
    • Stetter, H.1
  • 123
    • 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, Phil. Mag. 16 (1840), 132-135.
    • (1840) Phil. Mag , vol.16 , pp. 132-135
    • Sylvester, J.J.1
  • 124
    • 0038052673 scopus 로고
    • Memoir on the dialytic method of elimination. Part i
    • Sylvester J.J., Memoir on the dialytic method of elimination. Part I. Phil. Mag. 26 (1842), 534-539.
    • (1842) Phil. Mag , vol.26 , pp. 534-539
    • Sylvester, J.J.1
  • 125
    • 0001453534 scopus 로고
    • On a theory of the syzygietic relations of two rational integral functions, comprising an application to the theory of sturm’s functions, and that of the greatest algebraic common measure
    • Sylvester J.J., On a theory of the syzygietic relations of two rational integral functions, comprising an application to the theory of Sturm’s functions, and that of the greatest algebraic common measure, Phil. Trans. Royal Soc. London 163 (1853), 407-548.
    • (1853) Phil. Trans. Royal Soc. London , vol.163 , pp. 407-548
    • Sylvester, J.J.1
  • 126
    • 0001277020 scopus 로고
    • Systeme algebraischer gleichungen zu lösen
    • Trinks W., Über B., Buchberger Verfahren, Systeme algebraischer Gleichungen zu lösen, J. Numb. Theory 10 (1978), 475-488.
    • (1978) J. Numb. Theory , vol.10 , pp. 475-488
    • Trinks, W.1    Über Verfahren, B.B.2
  • 127
    • 84952713600 scopus 로고
    • Resolutions et functions symmetriques
    • Association for Computing Machinery
    • Valibouze A., Resolutions et functions symmetriques, in Proc. ISSAC’89 (1989), pp. 390-399, Association for Computing Machinery.
    • (1989) Proc. ISSAC’89 , pp. 390-399
    • Valibouze, A.1
  • 128
    • 84955619805 scopus 로고
    • Computation of the galois groups of the resolvent factors for the direct and inverse galois problems
    • Springer
    • Valibouze A., Computation of the Galois groups of the resolvent factors for the direct and inverse Galois problems, in L. N. Comp. Sci. 948 (1995), pp. 456-468, Springer.
    • (1995) L. N. Comp. Sci , vol.948 , pp. 456-468
    • Valibouze, A.1
  • 129
    • 0009097352 scopus 로고    scopus 로고
    • Étude des relations algébriques entre les racines d’un polynôme d’une variable
    • Valibouze A., Étude des relations algébriques entre les racines d’un polynôme d’une variable, Bull. Belg. Math. Soc. Simon Stevin 6 (1999), 507-535.
    • (1999) Bull. Belg. Math. Soc. Simon Stevin , vol.6 , pp. 507-535
    • Valibouze, A.1
  • 131
    • 0003161187 scopus 로고
    • An elimination method for polynomial systems
    • Wang D.-M., An elimination method for polynomial systems, J. Symb. Comp. 16 (1993), 83-114.
    • (1993) J. Symb. Comp , vol.16 , pp. 83-114
    • Wang, D.-M.1
  • 132
    • 0032016328 scopus 로고    scopus 로고
    • Decomposing polynomial systems into simple systems
    • Wang D.-M., Decomposing polynomial systems into simple systems, J. Symb. Comp. 25 (1998), 295-314.
    • (1998) J. Symb. Comp , vol.25 , pp. 295-314
    • Wang, D.-M.1
  • 133
    • 0011405387 scopus 로고
    • On the history of the bezoutian and the resultant matrix
    • Wimmer H.K., On the history of the Bezoutian and the resultant matrix, Linear Algebra Appl. 128 (1990), 27-34.
    • (1990) Linear Algebra Appl , vol.128 , pp. 27-34
    • Wimmer, H.K.1
  • 134
    • 0003343439 scopus 로고
    • On the decision problem and the mechanization of the theorem-proving in elementary geometry
    • Wu W.-T., On the decision problem and the mechanization of the theorem-proving in elementary geometry, Scinetia Sinica 21 (1978), 159-172.
    • (1978) Scinetia Sinica , vol.21 , pp. 159-172
    • Wu, W.-T.1
  • 135
    • 0000060015 scopus 로고
    • Basic principles of mechanical theorem proving in elementary geometry
    • Wu W.-T., Basic principles of mechanical theorem proving in elementary geometry, J. Sys. Sci. & Math. Sci. 4 (1984), 207-235.
    • (1984) J. Sys. Sci. & Math. Sci , vol.4 , pp. 207-235
    • Wu, W.-T.1
  • 136
    • 0038256188 scopus 로고
    • On the decision problem and the mechanization of the theorem-proving in elementary geometry
    • American Mathematical Society
    • Wu W.-T., On the decision problem and the mechanization of the theorem-proving in elementary geometry, in Contemp. Math. 29 (1984), pp. 213-234, American Mathematical Society.
    • (1984) Contemp. Math , vol.29 , pp. 213-234
    • Wu, W.-T.1
  • 137
    • 0037580578 scopus 로고
    • Some recent advances in mechanical theorem-proving of geometry
    • American Mathematical Society
    • Wu W.-T., Some recent advances in mechanical theorem-proving of geometry, (reprinted) in Contemp. Math. 29 (1984), pp. 235-241, American Mathematical Society.
    • (1984) Contemp. Math , vol.29 , pp. 235-241
    • Wu, W.-T.1
  • 138
    • 0002971341 scopus 로고
    • A zero structure theorem for polynomial equations solving
    • Wu W.-T., A zero structure theorem for polynomial equations solving, M.M. Research Preprints 1 (1987), 2-12.
    • (1987) M.M. Research Preprints , vol.1 , pp. 2-12
    • Wu, W.-T.1
  • 140
    • 38249010304 scopus 로고
    • Solutions of systems of algebraic equations and linear maps on residue class rings
    • Yokoyama K., Noro M., Takeshima T., Solutions of systems of algebraic equations and linear maps on residue class rings, J. Symb. Comp. 14 (1992), 399-417.
    • (1992) J. Symb. Comp , vol.14 , pp. 399-417
    • Yokoyama, K.1    Noro, M.2    Takeshima, T.3


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