Effective Methods in Algebraic Geometry

1. Front Matter

   Pages i-xiv

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2. On Lack of Effectiveness in Semi-algebraic Geometry

   • Riccardo Benedetti

   Pages 1-10

3. A simple constructive proof of Canonical Resolution of Singularities

   • Edward Bierstone, Pierre D. Milman

   Pages 11-30

4. Local Membership Problems for Polynomial Ideals

   • Leandro Caniglia, Jorge A. Guccione, Juan J. Guccione

   Pages 31-45

5. Un Algorithme pour le Calcul des Résultants

   • Marc Chardin

   Pages 47-62

6. On algorithms for real algebraic plane curves

   • Felipe Cucker, Laureano González Vega, Francesc Rossello

   Pages 63-87

7. Duality methods for the membership problem

   • Alicia Dickenstein, Carmen Sessa

   Pages 89-103

8. Exemples d’ensembles de Points en Position Uniforme

   • André Galligo

   Pages 105-117

9. Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets

   • Giovanni Gallo, Bhubaneswar Mishra

   Pages 119-142

10. Noetherian Properties and Growth of some Associative Algebras

    • Tatiana Gateva-Ivanova

    Pages 143-158

11. Codes and Elliptic Curves

    • Gerard van der Geer

    Pages 159-168

12. Algorithmes – disons rapides – pour la décomposition d’une variété algébrique en composantes irréductibles et équidimensionnelles

    • Marc Giusti, Joos Heintz

    Pages 169-194

13. Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators

    • Dimitri Yu. Grigor’ev

    Pages 195-202

14. Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals

    • Teresa Krick, Alessandro Logar

    Pages 203-216

15. On the Complexity of Zero-dimensional Algebraic Systems

    • Y. N. Lakshman, Daniel Lazard

    Pages 217-225

16. A Single Exponential Bound on the Complexity of Computing Gröbner Bases of Zero Dimensional Ideals

    • Y. N. Lakshman

    Pages 227-234

17. Algorithms for a Multiple Algebraic Extension

    • Lars Langemyr

    Pages 235-248

18. Elementary constructive theory of ordered fields

    • Henri Lombardi, Marie-Françoise Roy

    Pages 249-262

19. Effective real Nullstellensatz and variants

    • Henri Lombardi

    Pages 263-288

20. Algorithms for the Solution of Systems of Linear Equations in Commutative Rings

    • Gennadi I. Malashonok

    Pages 289-298

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").

• Dimension
• Mathematica
• algebraic geometry
• algebraic number theory
• average
• commutative algebra
• commutative property
• complexity
• differential algebra
• differential topology
• geometry
• group
• group theory
• number theory
• topology

• Dipartimento de Matematica, Università di Genova, Genova, Italy

  Teo Mora

• Dipartimento de Matematica, Università di Pisa, Pisa, Italy

  Carlo Traverso

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