Ebook: Effective Methods in Algebraic Geometry

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").

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Content:
Front Matter....Pages i-xiv
On Lack of Effectiveness in Semi-algebraic Geometry....Pages 1-10
A simple constructive proof of Canonical Resolution of Singularities....Pages 11-30
Local Membership Problems for Polynomial Ideals....Pages 31-45
Un Algorithme pour le Calcul des R?sultants....Pages 47-62
On algorithms for real algebraic plane curves....Pages 63-87
Duality methods for the membership problem....Pages 89-103
Exemples d’ensembles de Points en Position Uniforme....Pages 105-117
Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets....Pages 119-142
Noetherian Properties and Growth of some Associative Algebras....Pages 143-158
Codes and Elliptic Curves....Pages 159-168
Algorithmes – disons rapides – pour la d?composition d’une vari?t? alg?brique en composantes irr?ductibles et ?quidimensionnelles....Pages 169-194
Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators....Pages 195-202
Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals....Pages 203-216
On the Complexity of Zero-dimensional Algebraic Systems....Pages 217-225
A Single Exponential Bound on the Complexity of Computing Gr?bner Bases of Zero Dimensional Ideals....Pages 227-234
Algorithms for a Multiple Algebraic Extension....Pages 235-248
Elementary constructive theory of ordered fields....Pages 249-262
Effective real Nullstellensatz and variants....Pages 263-288
Algorithms for the Solution of Systems of Linear Equations in Commutative Rings....Pages 289-298
Une conjecture sur les anneaux de Chow A(G, Z) renforc?e par un calcul formel....Pages 299-311
Construction de courbes de genre 2 ? partir de leurs modules....Pages 313-334
Computing Syzygies ? la Gau?-Jordan....Pages 335-345
The non-scalar Model of Complexity in Computational Geometry....Pages 347-361
G?om?trie et Interpretations G?n?riques un Algorithme....Pages 363-377
Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms....Pages 379-400
The tangent cone algorithm and some applications to local algebraic geometry....Pages 401-409
Effective Methods for Systems of Algebraic Partial Differential Equations....Pages 411-426
Finding roots of equations involving functions defined by first order algebraic differential equations....Pages 427-440
Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties....Pages 441-455
Sign determination on zero dimensional sets....Pages 457-468
A Classification of Finite-dimensional Monomial Algebras....Pages 469-481
An Algorithm related to Compactifications of adjoint Groups....Pages 483-489
Deciding Consistency of Systems of Polynomial in Exponent Inequalities in Subexponential Time....Pages 491-500

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Content:
Front Matter....Pages i-xiv
On Lack of Effectiveness in Semi-algebraic Geometry....Pages 1-10
A simple constructive proof of Canonical Resolution of Singularities....Pages 11-30
Local Membership Problems for Polynomial Ideals....Pages 31-45
Un Algorithme pour le Calcul des R?sultants....Pages 47-62
On algorithms for real algebraic plane curves....Pages 63-87
Duality methods for the membership problem....Pages 89-103
Exemples d’ensembles de Points en Position Uniforme....Pages 105-117
Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets....Pages 119-142
Noetherian Properties and Growth of some Associative Algebras....Pages 143-158
Codes and Elliptic Curves....Pages 159-168
Algorithmes – disons rapides – pour la d?composition d’une vari?t? alg?brique en composantes irr?ductibles et ?quidimensionnelles....Pages 169-194
Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators....Pages 195-202
Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals....Pages 203-216
On the Complexity of Zero-dimensional Algebraic Systems....Pages 217-225
A Single Exponential Bound on the Complexity of Computing Gr?bner Bases of Zero Dimensional Ideals....Pages 227-234
Algorithms for a Multiple Algebraic Extension....Pages 235-248
Elementary constructive theory of ordered fields....Pages 249-262
Effective real Nullstellensatz and variants....Pages 263-288
Algorithms for the Solution of Systems of Linear Equations in Commutative Rings....Pages 289-298
Une conjecture sur les anneaux de Chow A(G, Z) renforc?e par un calcul formel....Pages 299-311
Construction de courbes de genre 2 ? partir de leurs modules....Pages 313-334
Computing Syzygies ? la Gau?-Jordan....Pages 335-345
The non-scalar Model of Complexity in Computational Geometry....Pages 347-361
G?om?trie et Interpretations G?n?riques un Algorithme....Pages 363-377
Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms....Pages 379-400
The tangent cone algorithm and some applications to local algebraic geometry....Pages 401-409
Effective Methods for Systems of Algebraic Partial Differential Equations....Pages 411-426
Finding roots of equations involving functions defined by first order algebraic differential equations....Pages 427-440
Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties....Pages 441-455
Sign determination on zero dimensional sets....Pages 457-468
A Classification of Finite-dimensional Monomial Algebras....Pages 469-481
An Algorithm related to Compactifications of adjoint Groups....Pages 483-489
Deciding Consistency of Systems of Polynomial in Exponent Inequalities in Subexponential Time....Pages 491-500
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