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A consistent and near complete survey of the important progress
made in the field over the last few years, with the main emphasis
on the rigidity method and its applications. Among others, this
monograph presents the most successful existence theorems known and
construction methods for Galois extensions as well as solutions for
embedding problems combined with a collection of the existing
Galois realizations.
A consistent and near complete survey of the important progress
made in the field over the last few years, with the main emphasis
on the rigidity method and its applications. Among others, this
monograph presents the most successful existence theorems known and
construction methods for Galois extensions as well as solutions for
embedding problems combined with a collection of the existing
Galois realizations.
This book contains 22 lectures presented at the final conference of
the Ger man research program (Schwerpunktprogramm) Algorithmic
Number The ory and Algebra 1991-1997, sponsored by the Deutsche
Forschungsgemein schaft. The purpose of this research program and
of the meeting was to bring together developers of computer algebra
software and researchers using com putational methods to gain
insight into experimental problems and theoret ical questions in
algebra and number theory. The book gives an overview on
algorithmic methods and on results ob tained during this period.
This includes survey articles on the main research projects within
the program: * algorithmic number theory emphasizing class field
theory, constructive Galois theory, computational aspects of
modular forms and of Drinfeld modules * computational algebraic
geometry including real quantifier elimination and real algebraic
geometry, and invariant theory of finite groups * computational
aspects of presentations and representations of groups, especially
finite groups of Lie type and their Heeke algebras, and of the
isomorphism problem in group theory. Some of the articles
illustrate the current state of computer algebra sys tems and
program packages developed with support by the research pro gram,
such as KANT and LiDIA for algebraic number theory, SINGULAR, RED
LOG and INVAR for commutative algebra and invariant theory respec
tively, and GAP, SYSYPHOS and CHEVIE for group theory and
representation theory.
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