Overview

This text contains 22 lectures presented at the final conference of the German research programme ""Algorithmic Number Theory and Algebra 1991-1997"", sponsored by the Deutsche Forschungsgemeinschaft. The purpose of this research programme and the meeting was to bring together developers of computer algebra software and researchers using computational methods to gain insight into experimental problems and theoretical questions in algebra and number theory. The book gives an overview on algorithmic methods and results obtained during this period mainly in algebraic geometry, and group and representation theory. Some of the articles illustrate the current state of the computer algebra systems developed with support from the research programme, for example KANT and LIDiA for algebraic number theory, SINGULAR, REDLONG and INVAR for commutative algebra and invariant theory respectively, and GAP, SYSYPHOS and CHEVIE for group and representation theory.

Full Product Details

Author:   B.Heinrich Matzat ,  Gert-Martin Greuel ,  Gerhard Hiss
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1999
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.680kg
ISBN:  

9783540646709

ISBN 10:   3540646701
Pages:   434
Publication Date:   20 October 1998
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Table of Contents/Inhaltsverzeichnis Chapter 1: Algorithmic Algebraic Number Theory J.Buchmann, M.J.Jacobson Jr., S.Neis, P.Theobald and D.Weber: Sieving Methods for Class Group Computation G. Frey and M. M'uller: Arithmetic of Modular Curves and Applications E.-U. Gekeler: Local and Global Ramification Properties of Elliptic Curves in Characteristics two and three A. Hulpke: Techniques for the Computation of Galois Groups B. H. Matzat: Fortschritte in der inversen Galoistheorie M. E. Pohst: From Class Groups to Class Fields H.-G. R'uck and U. Tipp: A. Gross-Zagier formula for function fields R. Scharlau and R. Schulze-Pillot: Extremal lattices Chapter 2: Algorithmic Commutative Algebra and Algebraic Geometry E. Becker and J. Schmid: On the Real Nullstellensatz W. Decker, G.-M. Greuel and G. Pfister: Primary Decompositions: Algorithms and Comparisons A. Dolzmann, Th. Sturm and V. Weispfenning: Real Quantifier Elimination in Practice G. Kemper: Hilbert Series and Degree Bounds in Invariant Theory G. Kemper and G. Malle: Invariant rings and fields of finite groups B. Martin: Computing Versal Deformations with SINGULAR Th. Siebert: Algorithms for the computation of free resolutions Chapter 3: Algorithmic Group and Representation Theory F. M. Bleher, W. Kimmerle, K. W. Roggenkamp and M. Wursthorn: Computational Aspects of the Isomorphism Problem R. Dipper, M. Geck, G. Hiss and G. Malle: Representations of Hecke algebras and finite groups of Lie type B. Eick and E. A. Orien: The groups of order 512 K. Lux and H. Pahlings: Computational aspects of representation theory of finite groups II G. O. Michler: High Performance Computations in Group Representation Theory G. Nebe: The structure of maximal finite primitive matrix groups W. Plesken: Presentations and representations of groups ' Chapter 2: Algorithmic Commutative Algebra and Algebraic Geometry p.177 E. Becker and J. Schmid: p.179 On the Real Nullstellensatz W. Decker, G.-M. Greuel and G. Pfister: p.193 Primary Decompositions: Algorithms and Comparisons A. Dolzmann, Th. Sturm and V. Weispfenning: p.227 Real Quantifier Elimination in Practice G. Kemper: p.255 Hilbert Series and Degree Bounds in Invariant Theory G. Kemper and G. Malle: p.271 Invariant rings and fields of finite groups B. Martin: p.289 Computing Versal Deformations with SINGULAR Th. Siebert: p.301 Algorithms for the computation of free resolutions Chapter 3: Algorithmic Group and Representation Theory p.319 F. M. Bleher, W. Kimmerle, K. W. Roggenkamp and M. Wursthorn: p.321 Computational Aspects of the Isomorphism Problem R. Dipper, M. Geck, G. Hiss and G. Malle: p.339 Representations of Hecke algebras and finite groups of Lie type B. Eick and E. A. Orien: p.387 The groups of order 512 K. Lux and H. Pahlings: p.389 Computational aspects of representation theory of finite groups II G. O. Michler: p.407 High Performance Computations in Group Representation Theory G. Nebe: p.425 The structure of maximal finite primitive matrix groups W. Plesken: p.431 Presentations and representations of groups '

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