Computational Number Theory : Proceedings of the Colloquium on Computational Number Theory Held at Kossuth Lajos University, Debrecen (Hungary), September 4-9, 1989

This professional book presents the history, controversy, and negotiations that have resulted in worldwide agreement on a set of principles that will underlie the cataloguing practices for the digital age. The Statement of International Cataloguing Principles (ICP) provides the fundamental principles, objectives, and basic rules for cataloguing throughout the world among the world's rule makers and national cataloguing experts. These principles will be useful for all types of institutions and organizations that deal with bibliographic resources. Preface List of contributors Table of contents On the construction of primitive elements and primitive normal bases in a finite field A numerical method for the determination of the cyclotomic polynomial coefficients Number systems Fast converging series representations of real numbers and their implementations in digital processing On a polynomial transformation and its application to the construction of a public key cryptosystem Number-theoretic transforms and a theorem of Sylvester-Kronecker- Zsigmondy A probabilistic class group and regulator algorithm and its implementation Prime-producing quadratic polynomials and class numbers of quadratic orders Applications of a new class number two criterion for real quadratic fields On a solution of a class number two problem for a family of real quadratic fields Cubic number fields with exceptional units Enumeration of totally complex quartic fields of small discriminant Class number computation by cyclotomic or elliptic units Computing fundamental units from independent units A note on index divisors Computation of independent units in number fields by a combination of the methods of Buchmann / Pethö and Pohst / Zassenhaus Hecke actions on classes of ternary quadratic forms Computation of singular moduli by multi-valued modular equations Congruent numbers and elliptic curves The rank of elliptic curves upon quadratic extension On the resolution of some diophantine equations Index form equations in cubic number fields On the practical solution of the Thue-Mahler equation Some results on Thue equations and Thue-Mahler equations On the solution of the diophantine equation Gn = P(x) with sieve algorithm On Thue equations associated with certain quartic number fields KANT - a tool for computations in algebraic number fields SIMATH - a computer algebra system Devoted to the interaction of modern scientific computation and classical number theory, covering subjects from effective finiteness results to efficient algorithms in elementary, analytical and algebraic number theory, these papers provide a broad review of methods and results in the area. The purpose of this survey is to present some recent results of the authors on finding fast algorithms for the construction of primitive elements, normal bases and primitive normal bases in a finite field.