Title | Effective Methods in Algebraic Geometry [electronic resource] / edited by Teo Mora, Carlo Traverso |
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Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1991 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-0441-1 |

Descript | XIV, 502 p. online resource |

SUMMARY

The symposium "MEGA-90 - Effective Methods in Algebraic Geomeยญ try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the folยญ lowing: - Effective methods and complexity issues in commutative algebra, proยญ 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 algeยญ 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 varyยญ ing; an average meaning is "Applied Algebra and Error Correcting Codes")

CONTENT

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 Rรฉsultants -- On algorithms for real algebraic plane curves -- Duality methods for the membership problem -- Exemples dโ{128}{153}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 โ{128}{147} disons rapides โ{128}{147} pour la dรฉcomposition dโ{128}{153}une variรฉtรฉ algรฉbrique en composantes irrรฉductibles et รฉquidimensionnelles -- 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 Grรถbner 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, ?) renforcรฉe par un calcul formel -- Construction de courbes de genre 2 ร partir de leurs modules -- Computing Syzygies ร la Gau?-Jordan -- The non-scalar Model of Complexity in Computational Geometry -- Gรฉomรฉtrie et Interpretations Gรฉnรฉriques, 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

Mathematics
Algebraic geometry
Mathematics
Algebraic Geometry