現(xiàn)代計(jì)算機(jī)代數(shù)(英文版)

內(nèi)容概要

Modern Computer Algebra Computer algebra systems are gaining more and more importance in all areasof science and engineering. This textbook gives a thorough introduction to thealgorithmic basis of the mathematical engine in computer algebra systems. It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority make it also an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). Some of this material has never appeared before in book form. Finally, a great deal of historical information and illustration enlivens the text. Joachim yon zur Gathen has a PhD from Universitat Ztirich, taught at University of Toronto from 1981 to 1994, and is now at Universitat Paderbom. Jtirgen Gerhard is completing his PhD and is wissenschaftlicher Mitarbeiter at Universitat Paderborn.

書籍目錄

Introduction   1 Cyclohexane， cryptography， codes， and computer algebra     1.1 Cyclohexane conformations     1.2 The RSA cryptosystem     1.3 Distributed data structures     1.4 Computer algebra systems I Euclid   2 Fundamental algorithms     2.1 Representation and addition of numbers     2.2 Representation and addition of polynomials     2.3 Multiplication     2.4 Division with remainder     Notes     Exercises   3 The Euclidean Algorithm     3.1 Euclidean domains     3.2 The Extended Euclidean Algorithm     3.3 Cost analysis for Z and F[x]     Notes     Exercises   4 Applications of the Euclidean Algorithm    4.1 Modular arithmetic    4.2 Modualr inverses via Euclid     4.3 Repeated squaring    4.4 Modular inverses via Fermat    4.5 Linear Diophantine equations    ……  5 Modualr algorithms and interpolation  6 The resultant and gcd computaion  7 Application:Decoding BCH codesⅡ Newton  8 Fast multiplication  9 Newton iteration  10 Fast polynomial evalution and interpoation  11 Fast Euclidean Algorithm  12 Fast Linear algebra  13 Fourier Transform and image compressionⅢ GauB  14 Factoring polynomials over finite fields  15 Hensel lifting and factoring polynomials  16 Short vectors in lattices  17 Applications of basis reductionⅣ Fermat  18 Primality testing  19 Factoring integers  20 Application:Public key cryptographyⅤ Hibert  21 Grobner bases  22 Symbolic integration  23 Symbolic Summation  24 Applications Appendix  25 Fundamental conceptsSources of illustrationsSources of quotaionsList of algorithmsLsit of figureds and tablesReferencesList of notationIndex

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