Algorithmic Algebra and Number Theory (eBook, PDF)

Selected Papers From a Conference Held at the University of Heidelberg in October 1997
Redaktion: Matzat, B. Heinrich; Hiss, Gerhard; Greuel, Gert-Martin

• Format: PDF

Produktbeschreibung

This book contains 22 lectures presented at the final conference of the German research program "Algorithmic Number Theory and Algebra 1991-1997", sponsored by the Deutsche Forschungsgemeinschaft. The purpose of this research program 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 number theory, commutative algebra and 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 program, for example KANT and LiDIA for algebraic number theory, SINGULAR, REDLOG and INVAR for commutative algebra and invariant theory respectively, and GAP, SYSYPHOS and CHEVIE for group and representation theory.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 434
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642599323
• Artikelnr.: 53088920

Inhaltsangabe

Algorithmic Algebraic Number Theory.- Sieving Methods for Class Group Computation.- Arithmetic of Modular Curves and Applications.- Local and Global Ramification Properties of Elliptic Curvesin Characteristics Two and Three.- Techniques for the Computation of Galois Groups.- Fortschritte in der inversen Galoistheorie.- From Class Groups to Class Fields.- A Gross-Zagier Formula for Function Fields.- Extremal Lattices.- AlgorithmicCommutative Algebra andAlgebraic Geometry.- On the Real Nullstellensatz.- Primary Decomposition: Algorithms and Comparisons.- Real Quantifier Elimination in Practice.- Hilbert Series and Degree Bounds in Invariant Theory.- Invariant Rings and Fields of Finite Groups.- Computing Versal Deformations with Singular.- Algorithms for the Computation of Free Resolutions.- Algorithmic Group andRepresentation Theory.- Computational Aspects of the Isomorphism Problem.- Representations of Heeke Algebras and Finite Groups of Lie Type.- The Groups of Order 512.- Computational Aspects of Representation Theory of Finite Groups II.- High Performance Computations in Group Representation Theory.- The Structure of Maximal Finite Primitive Matrix Groups.- Presentations and Representations of Groups.