Cohen puter Algebra And putation Mathematical Methods (Peters, 2003)( 1568811594)(470S).pdf

文档介绍：Cohen JOEL S. COHEN
Computer Algebra and putation
Computer Algebra and
putation
Mathematical Methods
Mathematical Methods
A K
PETERS
Computer Algebra and putation
Computer Algebra and putation
Mathematical Methods
Joel S. Cohen
Department puter Science
University of Denver
A K Peters
Natick, Massachusetts
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A K Peters, Ltd.
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Natick, MA 01760
Copyright © 2003 by A K Peters, Ltd.
All rights reserved. No part of the material protected by this copyright notice
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Library of Congress Cataloging-in-Publication Data
Cohen, Joel S.
Computer algebra and putation : mathematical methods
/ Joel S. Cohen
p. cm.
Includes bibliographical references and index.
ISBN 1-56881-159-4
1. Algebra–Data processing. I. Title.
.C635 2002
512–dc21 2002024315
Printed in Canada
07 06 05 04 03 10 9 8 7 6 5 4 3 2 1
For my wife Kathryn
vii
Contents
1Preface ix
1 Background Concepts 1
.................... 1
Mathematical Pseudo-Language (MPL) . . . . . . . . . . . . . 2
Automatic Simplification and Expression Structure . . . . . . 5
General Polynomial Expressions . . . . . . . . . . . . . . . . . 11
..................... 12
2 Integers, Rational Numbers, and Fields 17
............................ 17
................... 37
................................ 44
3 Automatic Simplification 63
The Goal of Automatic Simplification . . . . . . . . . . . . . . 63
An Automatic Simplification Algorithm . . . . . . . . . . . . . 91
4 Single Variable Polynomials 111
Elementary Concepts and Polynomial Division . . . . . . . . . 111
mon Divisors in