Symbolic_Computation-ed_Grossman.pdf

Frontiers in Applied Mathematics

Managing Editors

for Practical Computing Series

W.M. Coughran, Jr.

Eric Grosse

AT&T Bell Laboratories

Murray Hill, New Jersey

Frontiers in Applied Mathematics is a series that presents new mathe-

matical or computational approaches to significant scientific problems.

Beginning with Volume 4, the series reflects a change in both philosophy

and format. Each volume focuses on a broad application of general interest

to applied mathematicians as well as engineers and other scientists.

This unique series will advance the development of applied mathemat-

ics through the rapid publication of short, inexpensive books that lie on the

cutting edge of research.

Frontiers in Applied Mathematics

Vol. 1

Ewing, Richard E., The Mathematics of Reservoir Simulation

Vol. 2

Buckmaster, John D., The Mathematics of Combustion

Vol. 3

McCormick, Stephen F., Multigrid Methods

Vol. 4

Coleman, Thomas F. and Van Loan, Charles, Handbook for Matrix

Computations

Vol. 5

Grossman, Robert, Symbolic Computation: Applications to Scientific

Computing

Symbolic Computation

Applications to

Scientific Computing

Edited by Robert Grossman

University of Illinois at Chicago

Society for Industrial and Applied Mathematics

Philadelphia 1989

siam

Library of Congress Cataloging-in-Publication Data

Symbolic computation: applications to scientific computing / [edited

by] Robert Grossman.

p. cm. — (Frontiers in applied mathematics ; 5)

The outgrowth of talks at the NASA-Ames Workshop on the Use of

Symbolic Methods to Solve Algebraic and Geometric Problems Arising

in Engineering, which took place on January 15 and 16,1987, at the

NASA-Ames Research Center in Moffett Field, California"-Pref.

Includes bibliographical references.

ISBN 0-89871-239-4

1. Engineering mathematics—Data processing—Congresses.

2. Object-oriented programming—Congresses. I. Grossman, Robert,

1957- . II. Society for Industrial and Applied Mathematics.

III. Ames Research Center. IV. Series.

TA331.S95 1989

620'.001'51~dc20

89-19701

CIP

duced, stored, or transmitted in any manner without the written permission of the Publisher.

For information, write the Society for Industrial and Applied Mathematics, 3600 University

City Science Center, Philadelphia, Pennsylvania 19104-2688.

Contents

ix Preface

1 Chapter 1 Computer Algebra and Operators

Richard Fateman and Robert Grossman

15 Chapter 2 The Dynamicist's Workbench: I,

Automatic Preparation of Numerical Experiments

Harold Abelson and Gerald Jay Sussman

53 Chapter 3 Symbolic Computations in Differential

Geometry Applied to Nonlinear Control Systems

O. Akhrifand G. L. Blankenship

77 Chapter 4 Vector Fields and Nilpotent Lie Algebras

Matthew Grayson and Robert Grossman

97 Chapter 5 FIDIL: A Language for Scientific

Programming

Paul N. Hilfinger and Philip Colella

139 Chapter 6 Perturbation Methods and Computer

Algebra

Richard H. Rand

153 Chapter 7 Multibody Simulation in an Object

Oriented Programming Environment

N. Sreenath and P. S. Krishnaprasad

181 Index

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