Machi A. Algebra for Symbolic ...

Machi A. Algebra for Symbolic Computation (Springer, M Mathematics, MA Algebra, MAco Computational algebra

[ Pobierz całość w formacie PDF ]
//-->Algebra for Symbolic ComputationAntonio MachìAlgebra for SymbolicComputationAntonio MachìDepartment of MathematicsUniversity La Sapienza, RomeTranslated from the original Italian version by:Daniele A. GewurzDepartment of Mathematics, University La Sapienza, Rome (Italy)UNITEXT – La Matematica per il 3+2ISSN print edition: 2038-5722ISBN 978-88-470-2396-3DOI 10.1007/978-88-470-2397-0ISSN electronic edition: 2038-5757ISBN 978-88-470-2397-0(eBook)Library of Congress Control Number: 2011945436Springer Milan Heidelberg New York Dordrecht London© Springer-Verlag Italia 2012This work is subject to copyright. All rights are reserved by the Publisher, whether the whole orpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illus-trations, recitation, broadcasting, reproduction on microfilms or in any other physical way, andtransmission or information storage and retrieval, electronic adaptation, computer software, or bysimilar or dissimilar methodology now known or hereafter developed. Exempted from this legalreservation are brief excerpts in connection with reviews or scholarly analysis or material suppliedspecifically for the purpose of being entered and executed on a computer system, for exclusive useby the purchaser of the work. Duplication of this publication or parts thereof is permitted onlyunder the provisions of the Copyright Law of the Publishers location, in its current version, andpermission for use must always be obtained from Springer. Permissions for use may be obtainedthrough RightsLink at the Copyright Clearance Center. Violations are liable to prosecution underthe respective Copyright Law.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are ex-empt from the relevant protective laws and regulations and therefore free for general use.While the advice and information in this book are believed to be true and accurate at the date ofpublication, neither the authors nor the editors nor the publisher can accept any legal responsi-bility for any errors or omissions that may be made. The publisher makes no warranty, express orimplied, with respect to the material contained herein.9 8 7 6 5 4 3 2 1Cover-Design: BeatriceB,MilanoATypesetting with LTEX: PTP-Berlin, Protago TEX-Production GmbH, Germany(www.ptp-berlin.eu)Printing and Binding: Grafiche Porpora, Segrate (MI)Printed in ItalySpringer-Verlag Italia S.r.l., Via Decembrio 28, I-20137 MilanoSpringer is a part of Springer Science+Business Media (www.springer.com)PrefaceThis book arose from a course of lectures given by the author in the univer-sities of Paris VII and Rome “La Sapienza”. It deals with classical topics inAlgebra, some of which have been relegated for a long time to a marginalposition, but have been brought to light by the development of the so-calledsymbolic computation, or computer algebra. I have tried to present them insuch a way as to require only the very basic elements of Algebra, and often noteven those, emphasising their algorithmic aspects. It is clear that a thoroughcomprehension of these subjects would be greatly simplified if it is accompa-nied by exercises at the computer. Many examples of algorithms that may beeasily translated into computer programs are given in the text, others may beeasily deduced from the theory. The literature on the subject is very rich; thebibliography at the end of the book only mentions the texts and the articlesthat I have consulted.The first chapter of the book deals with elementary results like the Eu-clidean algorithm, the Chinese remainder theorem, and polynomial interpola-tion. The second chapter considers thep-adicexpansion of rational and alge-braic numbers and also of rational functions. The resultant of two polynomialsis explained in the third chapter, where many applications are also given (forinstance, augmented and reciprocal roots and Hurwitz polynomials). In thefourth chapter the problem of the polynomial factorisation is discussed; inparticular, the Berlekamp method is studied in greater detail. Finally, in thefifth chapter we consider the Discrete and Fast Fourier Transform, and alsoits interpretation in terms of the representation theory of Abelian groups; thenlogncomplexity is also explained.Every chapter is equipped with exercises, and some results are presented inthis form. The text proper does not make use of them, except when specificallyindicated. [ Pobierz całość w formacie PDF ]

zanotowane.pl

doc.pisz.pl

pdf.pisz.pl

mement.xlx.pl