Algorithmic Algebra and Number Theory

by Matzat, B. Heinrich; Greuel, Gert-Martin; Hiss, Gerhard

• ISBN13: 9783540646709
• ISBN10: 3540646701
• Format: Paperback
• Copyright: 1998-10-01
• Publisher: Springer Verlag

Summary

Presents 22 lectures given at the final conference of the German research program - Algorithmic # Theory and Algebra 1991-1997 - sponsored by the Deutsche Forschungsgemeinschaft. Designed to bring together developers & researchers using computational methods to gain insight into experimental problems & theoretical questions in algebra & number theory. Paper.

Table of Contents

Part A: Algorithmic Algebraic Number Theory
Sieving Methods for Class Group Computation	3	(8)
J. Buchmann
M.J. Jacobson, Jr.
S. Neis
P. Theobald
D. Weber
Arithmetic of Modular Curves and Applications	11	(38)
G. Frey
M. Muller
Local and Global Ramification Properties of Elliptic Curves in Characteristics Two and Three	49	(16)
E.-U. Gekeler
Techniques for the Computation of Galois Groups	65	(14)
A. Hulpke
Fortschritte in der inversen Galoistheorie	79	(24)
B. H. Matzat
From Class Groups to Class Fields	103	(18)
M. E. Pohst
A Gross-Zagier Formula for Function Fields	121	(18)
H.-G. Ruck
U. Tipp
Extremal Lattices	139	(34)
R. Scharlau
R. Schulze-Pillot
Part B: Algorithmic Commutative Algebra and Algebraic Geometry
On the Real Nullstellensatz	173	(14)
E. Becker
J. Schmid
Primary Decomposition: Algorithms and Comparisons	187	(34)
W. Decker
G.-M. Greuel
G. Pfister
Real Quantifier Elimination in Practice	221	(28)
A. Dolzmann
T. Sturm
V. Weispfenning
Hilbert Series and Degree Bounds in Invariant Theory	249	(16)
G. Kemper
Invariant Rings and Fields of Finite Groups	265	(18)
G. Kemper
G. Malle
Computing Versal Deformations with SINGULAR	283	(12)
B. Martin
Algorithms for the Computation of Free Resolutions	295	(18)
T. Siebert
Part C: Algorithmic Group and Representation Theory
Computational Aspects of the Isomorphism Problem	313	(18)
F. M. Bleher
W. Kimmerle
K. W. Roggenkamp
M. Wursthorn
Representations of Hecke Algebras and Finite Groups of Lie Type	331	(48)
R. Dipper
M. Geck
G. Hiss
G. Malle
The Groups of Order 512	379	(2)
B. Eick
E. A. O'Brien
Computational Aspects of Representation Theory of Finite Groups II	381	(18)
K. Lux
H. Pahlings
High Performance Computations in Group Representation Theory	399	(18)
G. O. Michler
The Structure of Maximal Finite Primitive Matrix Groups	417	(6)
G. Nebe
Presentations and Representations of Groups	423
W. Plesken