Mora T., Traverso C. (eds.) Effective Methods in Algebraic Geometry

Basel: Birkhäuser, 1991. — 258 p.The symposium "MEGA-90 - Effective Methods in Algebraic Geome­ try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the fol­ lowing: - Effective methods and complexity issues in commutative algebra, pro­ jective geometry, real geometry, algebraic number theory - Algebraic geometric methods in algebraic computing Contributions in related fields (computational aspects of group theory, differential algebra and geometry, algebraic and differential topology, etc.) were also welcome. The origin and the motivation of such a meeting, that is supposed to be the first of a series, deserves to be explained. The subject - the theory and the practice of computation in alge­ braic geometry and related domains from the mathematical viewpoin- has been one of the themes of the symposia organized by SIGSAM (the Special Interest Group for Symbolic and Algebraic Manipulation of the Association for Computing Machinery), SAME (Symbolic and Algebraic Manipulation in Europe), and AAECC (the semantics of the name is vary­ ing; an average meaning is "Applied Algebra and Error Correcting Codes").On Lack of Effectiveness in Semi-algebraic Geometry
A simple constructive proof of Canonical Resolution of Singularities
Local Membership Problems for Polynomial Ideals
Un Algorithme pour le Calcul des Résultants
On algorithms for real algebraic plane curves
Duality methods for the membership problem
Exemples d’ensembles de Points en Position Uniforme
Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets
Noetherian Properties and Growth of some Associative Algebras
Codes and Elliptic Curves
Algorithmes – disons rapides – pour la décomposition d’une variété algébrique en composantes irréductibles et équidimensionnelles
Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators
Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals
On the Complexity of Zero-dimensional Algebraic Systems
A Single Exponential Bound on the Complexity of Computing Gröbner Bases of Zero Dimensional Ideals
Algorithms for a Multiple Algebraic Extension
Elementary constructive theory of ordered fields
Effective real Nullstellensatz and variants
Algorithms for the Solution of Systems of Linear Equations in Commutative Rings
Une conjecture sur les anneaux de Chow A ( G , Z ) renforcée par un calcul formel
Construction de courbes de genre 2 à partir de leurs modules
Computing Syzygies à la Gauß-Jordan
The non-scalar Model of Complexity in Computational Geometry
Géométrie et Interpretations Génériques un Algorithme
Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms
The tangent cone algorithm and some applications to local algebraic geometry
Effective Methods for Systems of Algebraic Partial Differential Equations
Finding roots of equations involving functions defined by first order algebraic differential equations
Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties
Sign determination on zero dimensional sets
A Classification of Finite-dimensional Monomial Algebras
An Algorithm related to Compactifications of adjoint Groups
Deciding Consistency of Systems of Polynomial in Exponent Inequalities in Subexponential Time