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100   $a20130321d1993      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 12$aA Course in Computational Algebraic Number Theory /$fby Henri Cohen
205   $a1st ed. 1993.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1993.
215   $a1 online resource (XXI, 536 p.) 
225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v138
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-55640-0 
311   $a3-642-08142-8 
320   $aIncludes bibliographical references and index.
327   $a1. Fundamental Number-Theoretic Algorithms -- 2. Algorithms for Linear Algebra and Lattices -- 3. Algorithms on Polynomials -- 4. Algorithms for Algebraic Number Theory I -- 5. Algorithms for Quadratic Fields -- 6. Algorithms for Algebraic Number Theory II -- 7. Introduction to Elliptic Curves -- 8. Factoring in the Dark Ages -- 9. Modern Primality Tests -- 10. Modern Factoring Methods -- Appendix A. Packages for Number Theory -- Appendix B. Some Useful Tables -- B.1. Table of Class Numbers of Complex Quadratic Fields -- B.2. Table of Class Numbers and Units of Real Quadratic Fields -- B.3. Table of Class Numbers and Units of Complex Cubic Fields -- B.4. Table of Class Numbers and Units of Totally Real Cubic Fields -- B.5. Table of Elliptic Curves.
330   $aWith the advent of powerful computing tools and numerous advances in math­ ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al­ gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli­ cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.
410  0$aGraduate Texts in Mathematics,$x2197-5612 ;$v138
606   $aNumber theory
606   $aAlgebra
606   $aComputer science
606   $aAlgorithms
606   $aComputer science$xMathematics
606   $aNumber Theory
606   $aAlgebra
606   $aTheory of Computation
606   $aAlgorithms
606   $aSymbolic and Algebraic Manipulation
615  0$aNumber theory.
615  0$aAlgebra.
615  0$aComputer science.
615  0$aAlgorithms.
615  0$aComputer science$xMathematics.
615 14$aNumber Theory.
615 24$aAlgebra.
615 24$aTheory of Computation.
615 24$aAlgorithms.
615 24$aSymbolic and Algebraic Manipulation.
676   $a512.7
700   $aCohen$b Henri$4aut$4http://id.loc.gov/vocabulary/relators/aut$060172
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910812157303321
996   $aCourse in computational algebraic number theory$9375632
997   $aUNINA