Pohst M., Zassenhaus H. Algorithmic Algebraic Number Theory

Cambridge University Press, 1993. — 478 p. — (Encyclopedia of Mathematics and its Applications, 30). — ISBN: 0-521-33060, 978-0511661952.This classic book gives a thorough introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. It also provides a comprehensive look at recent research. For experimental number theoreticians, the authors developed new methods and obtained new results of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.List of symbols used in the texBasics of constructive algebraic number theoryThe main task of constructive algebra
On the construction of overmodules and overrings
The ring of an equation
The Gaussian integer ring Z
Factorial monoids and divisor cascadesThe group of an equation
Splitting rings
The fixed subring of the permutation automorphisms
Symmetric polynomials
Indecomposable splitting rings 6
Finite fields
The main theorem of Galois theory
Minimal splitting fields
The Lagrange resolvent
The group of an equation
How to determine the group of a separable equation over a field
The cyclotomic equation
Normal basesMethods from the geometry of numbersFree modules over principal entire rings
Lattices and basis reduction
Minkowski's convex body theoremEmbedding of commutative orders into the maximal orderThe algebraic background
Valuation theory
Eisenstein polynomials
Dedekind rings and orders
Embedding algorithmUnits in algebraic number fieldsThe Dirichlet theorem
On solving norm equations I
Computation of roots of unity
Computation of independent units
Regulator bounds and index estimates
Computation of fundamental units
Remarks on computerizationThe class group of algebraic number fieldsThe ring oF of algebraic integers as a Dedekind ring
Ideal calculus
On solving norm equations II
Computation of the class groupAppendix: Numerical tablesReferences
IndexФайл: отскан. стр. (b/w 600 dpi) + OCR + закладки.