Aho, A.V., Hopcroft, J.E., Ullman, J.D., The Design and Analysis of Computer Algorithms, Addison–Wesley (1974).
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.
Ampère, A.-M., Fonctions Interpolaires, Annales de M. Gergonne (1826).
Arnaudiès, J.M., Valibouze, A., Résolventes de Lagrange, Report LIPT 93.61 (1993),
Arnaudiès, J.M., Valibouze, A., Lagrange resolvents, J. Pure Appl. Algebra 117–118 (1996), 23–40.
Aubry, P., Moreno Maza, M., Triangular set for solving polynomial systems: a comparative implementation of four methods, J. Symb. Comp. 28 (1999), 125–154.
Aubry, P., Valibouze, A., Using Galois ideals for computing relative resolvents, J. Symb. Comp. 30 (2000), 635–651.
Aubry, P., Lazard, D., Moreno Maza, M., On the theories of triangular sets, J. Symb. Comp. 28 (1999), 105–124.
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.
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.
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.
Bézout, E., Théorie Generale des Èquations Algébriques, Pierres, Paris (1771).
Bini, D., Pan, V., Polynomial and Matrix Computations, Birkhäuser (1994).
Bostajn, A., Salvy, B., Schost, E., Fast algorithm for zero-dimensional polynomial systems using duality, J. AAECC 14 (2003), 239–272.
Bürgisser, P., Clausen, M., Shorolahi, M.A., Algebraic Complexity Theory, Springer (1997).
Burnside, W., Theory of Groups of Finite Order, Cambridge University Press (1911).
Canny, J., Generalized characteristic polynomials, in L. N. Comp. Sci. 358 (1988), pp. 293–299, Springer.
Canny, J., An effective algorithm for the sparse mixed resultant, in L. N. Comp. Sci. 673 (1993), pp. 89–104, Springer.
Cardinal, J.P., Dualité et algorithms itératifs pour la résolution de systémes polynomiaux, Ph.D.thesis, University of Rennes I (1993).
Cardinal, J.P., Mourrain, B., Algebraic approach of residues and applications, in L. N. Appl. Math. 32 (1999), American Mathematical Society Press.
Cauchy, A., Usage des fonctions interpolaires dans ls determination des fonctions symmetriques des racines d'une équation algébrique donnée, C.R. Acad. Sci. Paris 11 (1840), 933.
Cauchy, A., Oeuvres t. V, Gauthier–Villars, Paris, (1882).
Cayley, A., On the theory of elimination, Camb. Dublin Math. J. III (1848), 116–120.
Cayley, A., Note sur la méthode d'élimination de Bezout, J. Reine Ang. Math. LIII (1857), 366–367.
Cayley, A., A fourth memoir upon quantics, Phil. Trans. Royal Soc. London CXLVIII (1858), 415–427.
Charden, M., Un algorithm pour les calcul des resultants, in Prog. Math. 94 (1990), pp. 47–62, Birkhäuser.
Charden, M., The resultant via a Koszul complex, Prog. Math. 109 (1993), pp. 29–40, Birkhäuser.
Chen, C., Golubitsky, O., Lemaire, F., Moreno Maza, M., Comprehensive triangular decomposition, in Proc. CASC 2007 (2007), pp. 73–101.
Dahan, X., Sur la complexité des représentations des systèmes polynomiaux: triangulation, méthodes modulaires, évaluation dynamique, Ph.D. thesis, École Polytechnique (2006).
Dahan, X., Schost, E., Sharp estimates for triangular sets, in Proc. ISSAC'04 (2004), pp. 103–110, Association for Computing Machinery.
Dahan, X., Moreno Maza, M., Schost, E., Wu, W., Xie, Y., Lifting techniques for triangular decomposition, in Proc. ISSAC'05 (2005), pp. 108–115.
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.
Dixon, A.L., On a form of the eliminant of two quantics, Proc. London Math. Soc. 6 (1908a), 468–478.
Dixon, A.L., The eliminant of three quantics in two independent variables, Proc. London Math. Soc. 7 (1908b), 49–69.
Dixon, A.L., Some results in the theory of elimination, Proc. Roy. Soc. London 82 (1909), 468–478.
Euler, L., Introductio in Analysin Infinitorum, Tom. 2, Lausanne, (1748).
Felszeghy, B., Ráth, B., Rónyai, L., The lex game and some applications, J. Symb. Comp. 41 (2006), 663–681.
Gallo, G., Mishra, B., Effective algorithms and bounds for Wu–Ritt characteristic sets, in Prog. Math. 94 (1990), pp. 119–142, Birkhäuser.
Gallo, G., Mishra, B., A solution to Kronecker's problem, J. AAECC 5 (1994), 343–370.
Gallo, G., Mishra, B., Olivier, F., Some constructions in rings of differential polynomials, in L. N. Comp. Sci. 539 (1991), pp. 171–182, Springer.
Gianni, P., Properties of GrÖbner bases under specialization, in L. N. Comp. Sci. 378 (1987), pp. 293–297, Springer.
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.
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.
Giusti, M., Schost, E., Solving some overdetermined polynomial systems, in Proc. ISSAC'99 (1999), pp. 1–8, Association for Computing Machinery.
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.
Giusti, M., Heintz, J., Hägele, K., Morais, J.E., Pardo, L.M., Montaña, J.M., Lower bounds for diophantine approximation, J. Pure Appl. Algebra 117–118 (1997a), 277–311.
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.
Giusti, M., Heintz, J., Morais, J.E., Morgensten, J., Pardo, L.M., Straight-line programs in geometric elimination theory, J. Pure Appl. Algebra 124 (1998), 101–146.
Giusti, M., Hägele, 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.
Giusti, M., Lecerf, G., Salvy, B., A Gröbner free alternative for polynomial system solving, J. Complexity 17 (2001), 154–211.
Gonzalez-Vega, L., Rouiller, F., Roy, M.-F., Symbolic recipes for polynomial system solving, in Some Tapas of Computer Algebra, ed. A., Cohen, (1997), Springer.
Gunther, N., Sur la forme canonique des systèmes équations homogènes (in Russian)(Journal de l'Institut des Ponts et Chaussées de Russie), Izdanie Inst. In?z. Putej Soob?s?cenija Imp. Al. I. 84 (1913).
Gunther, N., Sur les caractéristiques des systémes d'équations aux dérivées partialles, C.R. Acad. Sci. Paris 156 (1913), 1147–1150.
Gunther, N., Sur la forme canonique des equations algébriques, C.R. Acad. Sci. Paris 157 (1913), 577–80.
Hägele, 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.
Hashemi, A., Structure et Complexité des bases de Gröbner, J. Symb. Comp. 45 (2010), 1330–1340.
Hashemi, A., Lazard, D., Sharper complexity bounds for zero-dimensional Gröbner bases and polynomial system solving, Int. J. Algebra Comp. 21 (2011), 705–713.
Jacobi, C.G.I., De eliminatione variabilis e duabus aequationibus algebraicas, J. Reine Ang. Math. XV (1836) 101–124.
Jouanoulou, J.-P., Le formalisme du résultant, Adv. Math. 90 117–263.
Kalkbrener, M., Solving systems of algebraic equations by using Gröbner bases, in L. N. Comp. Sci. 378 (1987), pp. 282–292, Springer.
Kalkbrener, M., Three contributions to elimination theory, Ph.D. thesis, Linz University (1991).
Kalkbrener, M., A generic euclidean algorithm for computing triangular representations of algebraic varieties, J. Symb. Comp. 15 (1993), 153–167.
Kalkbrener, M., On the stability of Gröbner bases under specialization, J. Symb. Comp. 24 (1997), 51–58.
Kapur, D., Cai, Y., An algorithm for computing a Gröbner basis of a polynomial ideal over a ring with zero divisors, Math. Comput. Sci. 2 (2009), 601–634.
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.
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.
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.
Kapur, D., Saxena, T., Extraneous factors in the Dixon resultant formulation, in Proc. ISSAC 97 (1997), pp. 141–148, Association for Computing Machinery.
Kobayashi, H., Moritsugu, S., Hogan, R.W., On radical zero-dimensional ideals, J. Symb. Comp. 8 (1989), 545–552.
Kratzer, M., Computing the dimension of a polynomial ideal and membership in lowdimensional ideals. Master's thesis, Technische Universität München (2008).
Krick, T., Pardo, L.M., Une approache informatique pour l'approximation diophantienne, C.R. Acad. Sci. Paris 318 (1994), 407–412.
Krick, T., Pardo, L.M., A computational method for Diphantine approximation, in Prog. Math. 143 (1996), pp. 193–254, Birkhäuser.
Lakshman|Y.N., Lazard, D., On the complexity of zero-dimensional algebraic systems, in Prog. Math. 94 (1990), pp. 217–226, Birkhäuser.
Lazard, D., Algèbre linéaire sur K[X1, …, Xn] et élimination, Bull. Soc. Math. France 105 (1977), 165–190.
Lazard, D., Systems of algebraic equations, in L. N. Comp. Sci. 72 (1979), pp. 88–94, Springer.
Lazard, D., Resolution des systemes d'equations algebriques, Theoret. Comput. Sci. 15 (1981), 77–110.
Lazard, D., A new method for solving algebraic systems of positive dimension, Disc. Appl. Math. 33 (1991), 147–160.
Lazard, D., Solving zero-dimensional algebraic systems, J. Symb. Comp. 15 (1992), 117–132.
Lazard, D., Systems of algebraic equations (algorithms and complexity), Symp. Math. 34 (1993), 84–106, Cambridge University Press.
Lazard, D., Resolution of polynomial systems, in Proc. ASCM 2000 (2000), pp. 1–8, World Scientific.
Lazard, D., On the specification for solvers of polynomial systems, in Proc. ASCM 2001 (2001), pp. 1–10, World Scientific.
Lazard, D., Thirty years of polynomial system solving, and now?, J. Symb. Comp. 44 (2009), 222–239.
Lazard, D., Rouillier, F., Solving parametric polynomial systems, J. Symb. Comp. 42 (2007), 636–667.
Lecerf, G., Une alternative aux méthodes de réécriture pour résolution des systémes algébriques, Ph.D. thesis, École Polytechnique (2001).
Lundqvist, S., Complexity of comparing monomials and two improvements of the BMalgorithm, in L. N. Comp. Sci. 5393 (2008), pp. 105–125, Springer.
Lundqvist, S., Vector space bases associated to vanishing ideals of points, J. Pure Appl. Algebra 214 (2010), 309–321.
Macaulay, F. S., Some formulae in elimination, Proc. London Math. Soc. (1) 35 (1903), 3–27.
Macaulay, F. S., The Algebraic Theory of Modular Systems, Cambridge University Press (1916).
Malle, G., Trinks, W., Zur Behandlung algebraischer Gleichungssysteme mit dem Computer, preprint (1985).
Manocha, D., Cannon, J.F., Multipolynomial resultant algorithms, J. Symb. Comp. 15 (1993), 99–122.
Möller, H.M., Systems of algebraic equations solved by means of endomorphisms, in L. N. Comp. Sci. 673 (1993a), pp. 43–56, Springer.
Möller, H.M., On decomposing systems of polynomial equations with finitely many solutions, J. AAECC 4 (1993b), 217–230.
Möller, M., Stetter, H., Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems, Num. Math. 70 (1995), 311–325.
Monico, C., Computing the primary decomposition of zero-dimensional ideals, J. Symb. Comp. 34 (2002), 451–459.
Morais, J.E., Resolución eficaz de systemas de ecuaciones polinomiales, Ph. D. thesis, University of Cantabria, Santander (1997).
Moreno Maza, M., Rioboo, R., Polynomial gcd computation over tower of algebraic extension, in L. N. Comp. Sci. 948 (1995), pp. 365–382, Springer.
Moritzugu, S., Kuriyama, K., On multiple zeros of systems of algebraic equations, in Proc. ISSAC'99 (1999), pp. 23–30, Association for Computing Machinery.
Mourrain, B., Computing the isolated roots by matrix methods, J. Symb. Comp. 26 (1998), 715–738.
Mourrain, B., A new criterion for normal form algorithms, in L. N. Comp. Sci. 1719 (1999), pp. 430–443, Springer.
Mourrain, B., Bezoutian and quotient ring structure, J. Symb. Comp. 39 (2005), 397–415.
Mourrain, B., Pan, Y.V., Multivariate polynomials, duality and structured matrices, J. Complexity 16 (2000), 110–180.
Mourrain, B., Ruatta, O., Relation between roots and coefficients, interpolation and application to system solving, J. Symb. Comp. 33 (2002), 679–699.
Mourrain, B., Trebuchet, P., Solving projective complete intersection faster, in Proc. ISSAC'00 (2000), pp. 234–241, Association for Computing Machinery.
Muir, T., The Theory of Determinants in the Historical Order of Development, MacMillan (1906).
Netto, E., Vorlesungen über Algebra, Zweiter Band Teubner (1900).
Pardo, L.M., How lower and upper complexity bounds meet in elimination, in L. N. Comp. Sci. 948 (1995), pp. 33–69, Springer.
Pierce, R.S., Modules over commutaive regular rings, Mem. A.M.S. 70 (1967).
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.
Poisson, S.D.Mémoire sur l'élimination dans les équations algébriques, J. École Polytechnique t. IV (1802), 199–203.
Rennert, N., Valibouze, A., Calcule de résolventes avec les modules de Cauchy, Exp. Math. 8 (1999), 351–366.
Riordan, J., Combinatorial Identities, Wiley, (1968).
Ritt, J.F., Prime and composite polynomials, Trans. A.M.S. 23 (1922), 51–366.
Ritt, J.F., Differential Equations from the Algebraic Standpoint, A.M.S. Colloquium Publications 14 (1932).
Ritt, J.F., Differential Algebra, A.M.S. Colloquium Publications 33 (1950).
Robinson, L.B., Sur les systémes d'équations aux dérivées partialles, C.R. Acad. Sci. Paris 157 (1913), 106–108.
Rouillier, F., Algorithmes efficaces pour l'étude des zéros réels des systèmes polynomiaux, Ph.D. thesis, University of Rennes I (1996).
Rouillier, F., Solving zero-dimensional systems through the Rational Univariate Representation, J. AAECC 9 (1999), 433–461.
Salmon, G., Lessons Introductory to the Modern Higher Algebra, Fifth Edn., Chelsea (1885).
Sims, C., Computation with Finitely Presented Groups, Cambridge University Press (1994).
Stetter, H., Matrix eigenprobelms are at the heart of polynomial system solving, SIGSAM Bull. 30 (1996), 22–25.
Stetter, H., Numerical Polynomial Algebra, Tutorial Notes at ISSAC'98, Rostock (1998).
Stetter, H., Numerical Polynomial Algebra, SIAM (2004).
Sylvester, J.J., A method of determining by mere inspection the derivatives from two equations of any degree, Phil. Mag. XVI (1840), 132–135.
Sylvester, J.J., Memoir on the dialytic method of elimination. Part I.Phil. Mag. XXXI (1842), 534–539.
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 CXLIII (1853), 407–548.
Trinks, W., über, B.Buchberger Verfahren, Systeme algebraischer Gleichungen zu lösen, J. Numb. Theory 10 (1978), 475–488.
Valibouze, A., Resolutions et functions symmetriques, in Proc. ISSAC'89 (1989), pp. 390–399, Association for Computing Machinery.
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.
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.
Valibouze, A., Théorie de Galois constructive, Mémoir d'Habilitation, Paris (1998).
Wang, D.-M., An elimination method for polynomial systems, J. Symb. Comp. 16 (1993), 83–114.
Wang, D.-M., Decomposing polynomial systems into simple systems, J. Symb. Comp. 25 (1998), 295–314.
Wimmer, H.K., On the history of the Bezoutian and the resultant matrix, Linear Algebra Appl. 128 (1990), 27–34.
Wu, W.-T., On the decision problem and the mechanization of the theorem-proving in elementary geometry, Scinetia Sinica 21 (1978), 159–172.
Wu, W.-T., Basic principles of mechanical theorem proving in elementary geometry, J. Sys. Sci. & Math. Sci. 4 (1984), 207–235.
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.
Wu, W.-T., Some recent advances in mechanical theorem-proving of geometry, (reprinted) in Contemp. Math. 29 (1984), pp. 235–241, American Mathematical Society.
Wu, W.-T., A zero structure theorem for polynomial equations solving, M.M. Research Preprints 1 (1987), 2–12.
Wißmann, D., Anwendung von Rewriting-Techniken in polyzyklischen Gruppen, Dissertation, Kaiserslautern (1989).
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.
Zariski, O., Samuel, P., Commutative Algebra, Van Nostrand (1958).
