Computational Algebraic Geometry

ISBN-13: 9781461276524 / Angielski / Miękka / 2011 / 332 str.

Frederic Eyssette; Andre Galligo

Opis

The theory and practice of computation in algebraic geometry and related domains, from a mathematical point of view, has generated an increasing interest both for its rich theoretical possibilities and its usefulness in applications in science and engineering. In fact, it is one of the master keys for future significant improvement of the computer algebra systems (e.g., Reduce, Macsyma, Maple, Mathematica, Axiom, Macaulay, etc.) that have become such useful tools for many scientists in a variety of disciplines. The major themes covered in this volume, arising from papers p- sented at the conference MEGA-92 were: - Effective methods and complexity issues in commutative algebra, projective geometry, real geometry, and algebraic number theory - Algebra-geometric methods in algebraic computing and applica tions. MEGA-92 was the second of a new series of European conferences on the general theme of Effective Methods in Algebraic Geometry. It was held in Nice, France, on April 21-25, 1992 and built on the themes presented at MEGA-90 (Livomo, Italy, April 17-21, 1990). The next conference - MEGA-94 - will be held in Santander, Spain in the spring of 1994. The Organizing committee that initiatiod and supervises this bi enniel conference consists of A. Conte (Torino), J. H. Davenport (Bath), A. Galligo (Nice), D. Yu. Grigoriev (Petersburg), J. Heintz (Buenos Aires), W. Lassner (Leipzig), D. Lazard (paris), H. M. MOller (Hagen), T. Mora (Genova), M. Pohst (DUsseldort), T. Recio (Santander), J. J.

Spis treści

Computation of Real Radicals of Polynomial Ideals.- Semialgebraic geometry of polynomial control problems.- The Resultant via a Koszul Complex.- Gröbner Bases and Standard Monomial Theory.- A Continuous and rational solution to Hubert’s 17th problem and several cases of the Positivstellensatz.- The analytic spread of the ideal of a monomial curve in projective 3-space.- Computational Complexity of Sparse Real Algebraic Function Interpolation.- Shade, Shadow and Shape.- Arrangements of singularities and proper partitions of Dynkin diagrams.- Versal deformations of powers of volume forms.- Computing subfields: Reverse of the primitive element problem.- Applications of Eisenbud-Levine’s theorem to real algebraic geometry.- Applications of Algebraic Geometry to Computer Vision.- Disproving Hibi’s Conjecture with CoCoA or Projective Curves with bad Hilbert Functions.- Counting real zeros in the multivariate case.- Finding the number of distinct real roots of sparse polynomials of the form p(x, xn).- Locally effective objects and algebraic topology.- Decision of Algebra Isomorphisms using Gröbner Bases.- Complexity of Bezout’s Theorem II: Volumes and Probabilities.- A Parametrized Nullstellensatz.- An Elimination Method Based on Seidenberg’s Theory and Its Applications.