How Lower and Upper Complexity Bounds Meet in Elimination Theory

[1]  Patrizia M. Gianni,et al.  Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases , 1987, AAECC.

[2]  Teresa Krick,et al.  UNE APPROCHE INFORMATIQUE POUR L'APPROXIMATION DIOPHANTIENNE , 1994 .

[3]  David E. Muller,et al.  Restructuring of Arithmetic Expressions For Parallel Evaluation , 1976, JACM.

[4]  Arnold Schönhage,et al.  Fast algorithms - a multitape Turing machine implementation , 1994 .

[5]  Joos Heintz,et al.  Lower Bounds for Polynomials with Algebraic Coefficients , 1980, Theor. Comput. Sci..

[6]  David Mumford,et al.  What Can Be Computed in Algebraic Geometry , 1993, alg-geom/9304003.

[7]  Francisco Santos Leal.  Geometría combinatoria de curvas algebraicas y diagramas de Dalaunay en el plano , 1995 .

[8]  Marie-Françoise Roy,et al.  Multivariate Bezoutians, Kronecker symbol and Eisenbud-Levine formula , 1996 .

[9]  Bernd Sturmfels,et al.  Duality and Minors of Secondary Polyhedra , 1993, J. Comb. Theory, Ser. B.

[10]  Carlos A. Berenstein,et al.  Une formule de Jacobi et ses conséquences , 1991 .

[11]  K. Ramachandra,et al.  Vermeidung von Divisionen. , 1973 .

[12]  Joos Heintz.  On the Computational Complexity of Polynomials and Bilinear Mappings. A Survey , 1987, AAECC.

[13]  Patrice Philippon,et al.  Sur des hauteurs alternatives. I , 1991 .

[14]  Stephen Smale,et al.  Complexity of Bezout's Theorem V: Polynomial Time , 1994, Theor. Comput. Sci..

[15]  Tetsuro Fujise,et al.  Solving Systems of Algebraic Equations by a General Elimination Method , 1988, J. Symb. Comput..

[16]  R. Pollack,et al.  On the number of cells defined by a set of polynomials , 1993 .

[17]  Felipe Cucker,et al.  Separation of Complexity Classes in Koiran's Weak Model , 1994, Theor. Comput. Sci..

[18]  Laureano Gonzalez-Vega.  Determinantal formulae for the solution set of zero-dimensional ideals , 1991 .

[19]  B. Buchberger,et al.  Grobner Bases : An Algorithmic Method in Polynomial Ideal Theory , 1985 .

[20]  A. Meyer,et al.  The complexity of the word problems for commutative semigroups and polynomial ideals , 1982 .

[21]  Volker Strassen,et al.  Algebraic Complexity Theory , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[22]  Oscar H. Ibarra,et al.  Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs , 1983, JACM.

[23]  Joos Heintz,et al.  Algorithmes – disons rapides – pour la décomposition d’une variété algébrique en composantes irréductibles et équidimensionnelles , 1991 .

[24]  Jean-Benoît Bost,et al.  Heights of projective varieties and positive Green forms , 1994 .

[25]  Allan Borodin,et al.  The computational complexity of algebraic and numeric problems , 1975, Elsevier computer science library.

[26]  Bernd Sturmfels,et al.  Some Applications of Affine Gale Diagrams to Polytopes with few Vertices , 1988, SIAM J. Discret. Math..

[27]  Arjen K. Lenstra,et al.  Algorithms in Number Theory , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[28]  W. Dale Brownawell,et al.  Local Diophantine Nullstellen inequalities , 1988 .

[29]  Erich Kaltofen,et al.  Greatest common divisors of polynomials given by straight-line programs , 1988, JACM.

[30]  S. Smale,et al.  On a theory of computation and complexity over the real numbers; np-completeness , 1989 .

[31]  Marc Noy,et al.  Ears of triangulations and Catalan numbers , 1996, Discret. Math..

[32]  Michael Clausen,et al.  Algebraic complexity theory , 1997, Grundlehren der mathematischen Wissenschaften.

[33]  B. Sturmfels.  Gröbner bases of toric varieties , 1991 .

[34]  S. Smale.  On the efficiency of algorithms of analysis , 1985 .

[35]  Joachim von zur Gathen,et al.  Parallel algorithms for algebraic problems , 1983, SIAM J. Comput..

[36]  Stephen Smale,et al.  On the topology of algorithms, I , 1987, J. Complex..

[37]  Walter Baur,et al.  The Complexity of Partial Derivatives , 1983, Theor. Comput. Sci..

[38]  Michael Ben-Or,et al.  Lower bounds for algebraic computation trees , 1983, STOC.

[39]  Guillermo Matera,et al.  Integration of Multivariate Rational Functions Given by Straight-Line Programs , 1995, AAECC.

[40]  James Renegar,et al.  On the worst-case arithmetic complexity of approximating zeros of polynomials , 1987, J. Complex..

[41]  Stuart J. Berkowitz,et al.  On Computing the Determinant in Small Parallel Time Using a Small Number of Processors , 1984, Inf. Process. Lett..

[42]  Oscar H. Ibarra,et al.  Probabilistic Algorithms and Straight-Line Programs for Some Rank Decision Problems , 1981, Information Processing Letters.

[43]  Ernst W. Mayr,et al.  Membership in Plynomial Ideals over Q Is Exponential Space Complete , 1989, STACS.

[44]  David Masser,et al.  Fields of large transcendence degree generated by values of elliptic functions , 1983 .

[45]  André Galligo,et al.  Some New Effectivity Bounds in Computational Geometry , 1988, AAECC.

[46]  Theodor Schneider,et al.  Einführung in die transzendenten Zahlen , 1957 .

[47]  Peter Gritzmann,et al.  Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Basis , 1993, SIAM J. Discret. Math..

[48]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[49]  José L. Balcázar,et al.  Structural Complexity I , 1995, Texts in Theoretical Computer Science An EATCS Series.

[50]  Ming Li,et al.  Kolmogorov Complexity and its Applications , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[51]  Volker Strassen,et al.  Polynomials with Rational Coefficients Which are Hard to Compute , 1974, SIAM J. Comput..

[52]  K. Mulmuley.  A fast parallel algorithm to compute the rank of a matrix over an arbitrary field , 1987, Comb..

[53]  James H. Davenport,et al.  Real Quantifier Elimination is Doubly Exponential , 1988, J. Symb. Comput..

[54]  S. Smale,et al.  Complexity of Bézout’s theorem. I. Geometric aspects , 1993 .

[55]  Grete Hermann,et al.  Die Frage der endlich vielen Schritte in der Theorie der Polynomideale , 1926 .

[56]  David A. Plaisted.  Sparse Complex Polynomials and Polynomial Reducibility , 1977, J. Comput. Syst. Sci..

[57]  Daniel Lazard,et al.  Resolution des Systemes d'Equations Algebriques , 1981, Theor. Comput. Sci..

[58]  Richard Zippel,et al.  Interpolating Polynomials from Their Values , 1990, J. Symb. Comput..

[59]  Allan Borodin,et al.  On Relating Time and Space to Size and Depth , 1977, SIAM J. Comput..

[60]  D. Bayer.  The division algorithm and the hilbert scheme , 1982 .

[61]  Erich Kaltofen,et al.  Factorization of Polynomials Given by Straight-Line Programs , 1989, Adv. Comput. Res..

[62]  H. Riesel.  Prime numbers and computer methods for factorization , 1985 .

[63]  Felipe Cucker,et al.  Time Bounded Computations over the Reals , 1992, Int. J. Algebra Comput..

[64]  Carlos A. Berenstein,et al.  Effective Bezout identities inQ[z1, ...,zn] , 1991 .

[65]  H. T. Kung.  New Algorithms and Lower Bounds for the Parallel Evaluation of Certain Rational Expressions and Recurrences , 1976, JACM.

[66]  Andrew Chi-Chih Yao.  On Parallel Computation for the Knapsack Problem , 1982, JACM.

[67]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[68]  M. Mignotte,et al.  Mathématiques pour le calcul formel , 1989 .

[69]  Joos Heintz,et al.  Corrigendum: Definability and Fast Quantifier Elimination in Algebraically Closed Fields , 1983, Theor. Comput. Sci..

[70]  D. Grigor'ev,et al.  Lower bounds in algebraic computational complexity , 1985 .

[71]  Joos Heintz,et al.  Sur la complexité du principe de Tarski-Seidenberg , 1989 .

[72]  M. Shub,et al.  On The Intractability Of Hilbert's Nullstellensatz And An Algebraic Version Of . . , 1995 .

[73]  J. E. Morais,et al.  When Polynomial Equation Systems Can Be "Solved" Fast? , 1995, AAECC.

[74]  W. Brownawell.  Bounds for the degrees in the Nullstellensatz , 1987 .

[75]  Tomás Recio,et al.  Algorithms in Real Algebraic Geometry and Applications to Computational Geometry , 1990, Discrete and Computational Geometry.

[76]  J. Gathen.  Algebraic complexity theory , 1988 .

[77]  P. Philippon,et al.  Sur des hauteurs alternatives III , 1995 .

[78]  Jean-Benoît Bost,et al.  UN ANALOGUE ARITHMETIQUE DU THEOREME DE BEZOUT , 1991 .

[79]  Joos Heintz,et al.  On the Intrinsic Complexity of Elimination Theory , 1993, J. Complex..

[80]  A. O. Gelʹfond.  Transcendental and Algebraic Numbers , 1960 .

[81]  Joachim von zur Gathen,et al.  Parallel Arithmetic Computations: A Survey , 1986, MFCS.

[82]  Teresa Krick,et al.  A computational method for diophantine approximation , 1996 .

[83]  François Le Lionnais,et al.  Les Grands courants de la pensée mathématique , 1986 .