SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS

Polynomials in one variable Grobner bases of zero-dimensional ideals Bernstein's theorem and fewnomials Resultants Primary decomposition Polynomial systems in economics Sums of squares Polynomial systems in statistics Tropical algebraic geometry Linear partial differential equations with constant coefficients Bibliography Index.

[1]  Erratum zu: Über die lösung algebraischer gleichungssysteme durch hypergeometrische funktionen , 1936 .

[2]  Karl Mayr,et al.  Über die Lösung algebraischer Gleichungssysteme durch hypergeometrische Funktionen , 1936 .

[3]  W. Gröbner,et al.  Über eine neue idealtheoretische Grundlegung der algebraischen Geometrie , 1938 .

[4]  W. Gröbner,et al.  Über die algebraischen Eigenschaften der Integrale von linearen Differentialgleichungen mit konstanten Koeffizienten , 1939 .

[5]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[6]  C. E. Lemke,et al.  Equilibrium Points of Bimatrix Games , 1964 .

[7]  George M. Bergman,et al.  The logarithmic limit-set of an algebraic variety , 1971 .

[8]  A. Iarrobino,et al.  Reducibility of the families of 0-dimensional schemes on a variety , 1972 .

[9]  Herbert E. Scarf,et al.  The Computation of Economic Equilibria , 1974 .

[10]  I. Shafarevich Basic algebraic geometry , 1974 .

[11]  G. Stengle A nullstellensatz and a positivstellensatz in semialgebraic geometry , 1974 .

[12]  Jan-Erik Björk,et al.  Rings of differential operators , 1979 .

[13]  R. Bieri,et al.  The geometry of the set of characters iduced by valuations. , 1984 .

[14]  E. Allgower,et al.  Numerical Continuation Methods , 1990 .

[15]  J. Risler,et al.  Real algebraic and semi-algebraic sets , 1990 .

[16]  Eugene L. Allgower,et al.  Numerical continuation methods - an introduction , 1990, Springer series in computational mathematics.

[17]  Joe Harris,et al.  The Geometry Of Schemes , 1992 .

[18]  N. V. Ilyushechkin Discriminant of the characteristic polynomial of a normal matrix , 1992 .

[19]  David A. Cox,et al.  Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics) , 2007 .

[20]  Bernd Sturmfels,et al.  Product formulas for resultants and Chow forms , 1993 .

[21]  W. Fulton Introduction to Toric Varieties. , 1993 .

[22]  Bernd Sturmfels,et al.  On the Newton Polytope of the Resultant , 1994 .

[23]  B. Sturmfels,et al.  Binomial Ideals , 1994, alg-geom/9401001.

[24]  B. Sturmfels,et al.  Multigraded Resultants of Sylvester Type , 1994 .

[25]  D. Eisenbud Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .

[26]  B. Sturmfels Gröbner bases and convex polytopes , 1995 .

[27]  John K. McDonald Fiber polytopes and fractional power series , 1995 .

[28]  Bernd Sturmfels,et al.  Initial Complexes of Prime Ideals , 1995 .

[29]  Maria Grazia Marinari,et al.  ON MULTIPLICITIES IN POLYNOMIAL SYSTEM SOLVING , 1996 .

[30]  Jeffrey C. Lagarias,et al.  Multivariate descartes rule of signs and sturmfels’s challenge problem , 1997 .

[31]  Gerhard Pfister,et al.  Primary Decomposition: Algorithms and Comparisons , 1997, Algorithmic Algebra and Number Theory.

[32]  J. Duistermaat,et al.  Constant terms of powers of a Laurent polynomial , 1998 .

[33]  Tien Yien Li,et al.  Numerical solution of multivariate polynomial systems by homotopy continuation methods , 1997, Acta Numerica.

[34]  Andrew McLennan,et al.  The Maximal Number of Regular Totally Mixed Nash Equilibria , 1997 .

[35]  Bernd Sturmfels,et al.  Lattice Walks and Primary Decomposition , 1998 .

[36]  P. Diaconis,et al.  Algebraic algorithms for sampling from conditional distributions , 1998 .

[37]  P. Lax On the discriminant of real symmetric matrices , 1998 .

[38]  N. Shor Nondifferentiable Optimization and Polynomial Problems , 1998 .

[39]  David A. Cox,et al.  Using Algebraic Geometry , 1998 .

[40]  Ulrich Oberst,et al.  The Construction of Noetherian Operators , 1999 .

[41]  Bernhard von Stengel,et al.  New Maximal Numbers of Equilibria in Bimatrix Games , 1999, Discret. Comput. Geom..

[42]  Yang Yu The Permanent Rank of a Matrix , 1999, J. Comb. Theory, Ser. A.

[43]  Fabrice Rouillier,et al.  Solving Zero-Dimensional Systems Through the Rational Univariate Representation , 1999, Applicable Algebra in Engineering, Communication and Computing.

[44]  H. Wynn,et al.  Algebraic Statistics: Computational Commutative Algebra in Statistics , 2000 .

[45]  Serkan Hosten,et al.  Primary Decomposition of Lattice Basis Ideals , 2000, J. Symb. Comput..

[46]  Bernd Sturmfels,et al.  Solving algebraic equations in terms of A-hypergeometric series , 2000, Discret. Math..

[47]  Reinhard C. Laubenbacher,et al.  Permanental Ideals , 2000, J. Symb. Comput..

[48]  Mikael Passare,et al.  Laurent determinants and arrangements of hyperplane amoebas , 2000 .

[49]  S E Fienberg,et al.  INAUGURAL ARTICLE by a Recently Elected Academy Member:Bounds for cell entries in contingency tables given marginal totals and decomposable graphs , 2000 .

[50]  P. Parrilo Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[51]  Martin Kreuzer,et al.  Computational Commutative Algebra 1 , 2000 .

[52]  John F. Canny,et al.  A subdivision-based algorithm for the sparse resultant , 2000, JACM.

[53]  B. Sturmfels,et al.  Grbner Deformations of Hypergeometric Differential Equations , 2000 .

[55]  Michael L. Littman,et al.  Graphical Models for Game Theory , 2001, UAI.

[56]  David Eisenbud,et al.  Resultants and Chow forms via exterior syzygies , 2001, math/0111040.

[57]  Andrew J. Sommese,et al.  Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components , 2000, SIAM J. Numer. Anal..

[58]  Pablo A. Parrilo,et al.  Minimizing Polynomial Functions , 2001, Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science.

[59]  Xing Li,et al.  Finding Mixed Cells in the Mixed Volume Computation , 2001, Found. Comput. Math..

[60]  G. Greuel,et al.  A Singular Introduction to Commutative Algebra , 2002 .

[61]  Amit Khetan Determinantal formula for the chow form of a toric surface , 2002, ISSAC '02.

[62]  J. McDonald Fractional Power Series Solutions for Systems of Equations , 2002, Discret. Comput. Geom..