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Algorithmische Zahlentheorie by Otto Forster

Algorithmische Zahlentheorie

by Otto Forster
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Book cover type: Paperback
  • ISBN13: 9783658065393
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 314
  • Original Price: EUR 35.5
  • Language: German
  • Edition: 2., Uberarb. U.
  • Item Weight: 518 grams
  • BISAC Subject(s): Programming / Algorithms

Das Buch gibt eine Einf�hrung in die Zahlentheorie bis hin zu den quadratischen Zahlk�rpern. Dabei wird durchgehend auch der algorithmische Aspekt betrachtet. So werden Existenzs�tze (z.B. f�r die Darstellung von Primzahlen der Form p=4n+1 als Summe von zwei Quadratzahlen) stets durch Algorithmen zur Konstruktion erg�nzt. Neben den klassischen Inhalten der elementaren Zahlentheorie werden in dem Buch u.a. auch die Multiplikation gro er ganzer Zahlen mittels der schnellen Fourier-Transformation sowie Faktorisierung ganzer Zahlen mit elliptischen Kurven behandelt.

F�r die Neuauflage wurden bekannt gewordene Fehler der ersten Auflage korrigiert und an mehreren Stellen Umarbeitungen vorgenommen. Au erdem gibt es neue Abschnitte �ber die Faktorisierung mit dem Quadratischen Sieb, den Diskreten Logarithmus (der in der Kryptographie eine gro e Rolle spielt) sowie �ber den deterministischen AKS-Primzahltest mit polynomialer Laufzeit. Damit der Leser die Algorithmen auf seinem Laptop oder PC auch konkret testen kann, werden die Algorithmen in einem pascal�hnlichen Code f�r den vom Autor entwickelten Multipr�zisions-Interpreter ARIBAS beschrieben, der zum kostenlosen Download zur Verf�gung steht.

Prof. Dr. Otto Forster, Mathematisches Institut der Ludwig-Maximilians-Universität München, ist Autor der bekannten Lehrbücher Analysis 1-3.

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