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Algorithmische Zahlentheorie
Das Buch gibt eine Einführung in die elementare Zahlentheorie bis hin zu den quadratischen Zahlkörpern. Damit der Leser die Algorithmen auf seinem PC auch konkret testen kann, werden auf der beigelegten Diskette der pascalähnliche Multipräzisions-Interpreter ARIBAS sowie die Quelltexte aller im Buch besprochenen Algorithmen mitgeliefert.
322 pages, Paperback
First published October 1, 1996
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September 26, 2020
What a little gem this book is! This book provides an introduction to elementary number theory and to computer algebra. It starts out on a very elementary level, introducing in detail the natural numbers and their arithmetic, and modular arithmetic. But later on, the reader is expected to have some familiarity with groups, rings and fields.
For the most part, the explanations are elementary and step-by-step, so it's quite easy to follow. Only in the later chapters did they occasionally feel rushed.
Many algorithms are presented in a much clearer way than I found in other books, for example Euklid's extended algorithm, or the Fast Fourier Transform (which is shown here over arbitrary rings that admit roots of unity). The main focus is on factorisation algorithms, for which many different methods are shown (p-1, p+1, Pollard-Rho, elliptic curves, ideal classes). As this is an introductory book, the complexity analysis of algorithms is somewhat cursory, and for more involved algorithms is omitted altogether.
Somewhat unfortunately, the algorithms are presented in ARIBAS, a programming language developed by the author himself, whose source code is no longer available on the internet. It serves as a decent pseudo-code, though, but sometimes relies on built-in methods that are lost with the source code.
For the most part, the explanations are elementary and step-by-step, so it's quite easy to follow. Only in the later chapters did they occasionally feel rushed.
Many algorithms are presented in a much clearer way than I found in other books, for example Euklid's extended algorithm, or the Fast Fourier Transform (which is shown here over arbitrary rings that admit roots of unity). The main focus is on factorisation algorithms, for which many different methods are shown (p-1, p+1, Pollard-Rho, elliptic curves, ideal classes). As this is an introductory book, the complexity analysis of algorithms is somewhat cursory, and for more involved algorithms is omitted altogether.
Somewhat unfortunately, the algorithms are presented in ARIBAS, a programming language developed by the author himself, whose source code is no longer available on the internet. It serves as a decent pseudo-code, though, but sometimes relies on built-in methods that are lost with the source code.
Displaying 1 of 1 review