A course in computational algebraic number theory / Henri Cohen

Auteur: Cohen, Henri (1947-) - AuteurType de document: MonographieCollection: Graduate texts in mathematics ; 138Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, 1993Description: 1 vol. (XXII-534 p.) ; 24 cm ISBN: 9783540556404 ; rel. Note: “A course in computational algebraic number theory” contains 148 algorithms, which were all up-to-date when the book came out. Hence, this book is the source for number theorists wishing to learn about a special method and/or implement an algorithm without studying the theory in greater detail. Among these algorithms, many are new or improved. In most cases, their analysis and their complexity are given (not the complexity of the problem, as stated in the preface) and, most importantly, valuable remarks on implementations. Here one sees the great experience of the author, the founder of the package PARI. The book begins with a chapter devoted to the most important routines from elementary number theory. It is followed by one on algorithms from linear algebra and lattice theory. Especially important are the sections on Hermite and Smith normal forms and lattice basis reduction algorithms. ... (Zentralblatt)Bibliographie: Bibliogr. p. [517]-528. Index. Sujets MSC: 11Rxx Number theory -- Algebraic number theory: global fields
11Y11 Number theory -- Computational number theory -- Primality
11Y05 Number theory -- Computational number theory -- Factorization
11Y16 Number theory -- Computational number theory -- Algorithms; complexity
11Y40 Number theory -- Computational number theory -- Algebraic number theory computations
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“A course in computational algebraic number theory” contains 148 algorithms, which were all up-to-date when the book came out. Hence, this book is the source for number theorists wishing to learn about a special method and/or implement an algorithm without studying the theory in greater detail. Among these algorithms, many are new or improved. In most cases, their analysis and their complexity are given (not the complexity of the problem, as stated in the preface) and, most importantly, valuable remarks on implementations. Here one sees the great experience of the author, the founder of the package PARI.

The book begins with a chapter devoted to the most important routines from elementary number theory. It is followed by one on algorithms from linear algebra and lattice theory. Especially important are the sections on Hermite and Smith normal forms and lattice basis reduction algorithms. ... (Zentralblatt)

Bibliogr. p. [517]-528. Index

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