Effective Methods in Algebraic Geometry

Table of Contents

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   Book Overview
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   Chapter 1 On Lack of Effectiveness in Semi-algebraic Geometry
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   Chapter 2 A simple constructive proof of Canonical Resolution of Singularities
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   Chapter 3 Local Membership Problems for Polynomial Ideals
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   Chapter 4 Un Algorithme pour le Calcul des Résultants
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   Chapter 5 On algorithms for real algebraic plane curves
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   Chapter 6 Duality methods for the membership problem
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   Chapter 7 Exemples d’ensembles de Points en Position Uniforme
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   Chapter 8 Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets
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    Chapter 9 Noetherian Properties and Growth of some Associative Algebras
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    Chapter 10 Codes and Elliptic Curves
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    Chapter 11 Algorithmes – disons rapides – pour la décomposition d’une variété algébrique en composantes irréductibles et équidimensionnelles
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    Chapter 12 Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators
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    Chapter 13 Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals
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    Chapter 14 On the Complexity of Zero-dimensional Algebraic Systems
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    Chapter 15 A Single Exponential Bound on the Complexity of Computing Gröbner Bases of Zero Dimensional Ideals
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    Chapter 16 Algorithms for a Multiple Algebraic Extension
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    Chapter 17 Elementary constructive theory of ordered fields
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    Chapter 18 Effective real Nullstellensatz and variants
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    Chapter 19 Algorithms for the Solution of Systems of Linear Equations in Commutative Rings
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    Chapter 20 Une conjecture sur les anneaux de Chow A ( G , Z ) renforcée par un calcul formel
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    Chapter 21 Construction de courbes de genre 2 à partir de leurs modules
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    Chapter 22 Computing Syzygies à la Gauß-Jordan
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    Chapter 23 The non-scalar Model of Complexity in Computational Geometry
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    Chapter 24 Géométrie et Interpretations Génériques un Algorithme
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    Chapter 25 Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms
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    Chapter 26 The tangent cone algorithm and some applications to local algebraic geometry
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    Chapter 27 Effective Methods for Systems of Algebraic Partial Differential Equations
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    Chapter 28 Finding roots of equations involving functions defined by first order algebraic differential equations
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    Chapter 29 Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties
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    Chapter 30 Sign determination on zero dimensional sets
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    Chapter 31 A Classification of Finite-dimensional Monomial Algebras
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    Chapter 32 An Algorithm related to Compactifications of adjoint Groups
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    Chapter 33 Deciding Consistency of Systems of Polynomial in Exponent Inequalities in Subexponential Time