Computer Algebra in Scientific Computing CASC’99: Proceedings of the Second Workshop on Computer Algebra in Scientific Computing, Munich, May 31 – June 4, 1999

506 Pages·1999·20.81 MB·English

by  Gerd Baumann (auth.)

Ganzha . Mayr . Vorozhtsov (Eds.)
Computer Algebra in Scientific Computing
Springer
Berlin
Heidelberg
New York
Barcelona
Hong Kong
London
Milan
Paris
Singapore
Tokyo
Victor G. Ganzha Ernst W. Mayr
Evgenii V. Vorozhtsov (Eds.)
Computer Algebra
in Scientific Computing
CASC'99
Proceedings of the Second Workshop on
Computer Algebra in Scientific Computing,
Munich, May 31- June 4, 1999
t
Springer
Editors
Victor G. Ganzha
Ernst W. Mayr
Institut fUr Informatik
Technische Universitat
D-80290 Miinchen, Germany
Evgenii V. Vorozhtsov
Institute of Theoretical and Applied Mathematics
Russian Academy of Sciences
Novosibirsk 630090, Russia
Mathematics Subject Classification (1991): 68Q40, 65Mo6, 13PlO,12Yo5, 34A25, 20C40, 34D2o, 68T35
Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek -CIP-Einheitsaufnahme
Computer algebra in scientific computing I CASC '99, Proceedings of the Second Workshop on Computer Algebra
in Scientific Computing, Munich, May 31-June 4,1999. V. G. Ganzha ... (ed.). -Berlin; Heidelberg; New York; Barcelona;
Hong Kong; London; Paris; Singapore; Tokyo: Springer, 1999
ISBN-13:978-3-S40-66047-7
ISBN-13:978-3-S40-66047 -7 e-ISBN-13:978-3-642-60218-4
DOl: 10.1007/978-3-642-60218-4
ISBN-13:978-3-S40-66047-7
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Preface
The development of powerful computer algebra systems has considerably ex
tended the scope of problems of scientific computing which can now be solved
successfully with the aid of computers. However, as the field of applications of
computer algebra in scientific computing becomes broader and more complex,
there is a danger of separation between theory, systems, and applications. For
this reason, we felt the need to bring together the researchers who now ap
ply the tools of computer algebra for the solution of problems in scientific
computing, in order to foster new and closer interactions.
CASC'99 is the second conference devoted to applications of computer al
gebra in scientific computing. The first conference in this sequence, CASC'98,
was held 20-24 April 1998 in St. Petersburg, Russia.
This volume contains revised versions of the papers submitted by the par
ticipants and accepted by the program committee after a thorough reviewing
process. The collection of papers included in the proceedings covers various
topics of computer algebra methods, algorithms and software applied to scien
tific computing: symbolic-numeric analysis and solving differential equations,
efficient computations with polynomials, groups, matrices and other related
objects, special purpose programming environments, application to physics,
mechanics, optics and to other areas.
In particular, a significant group of papers deals with applications of com
puter algebra methods for the solution of current problems in group theory,
which mostly arise in mathematical physics.
Another important trend which may be seen from the present collection
of papers, is the application of computer algebra methods to the development
of new efficient analytic and numerical solvers, both for ordinary and partial
differential equations.
A number of papers deals with algorithmic and software aspects associ
ated with the implementation of computer algebra methods. Other papers
study the stability of satellite and mechanical systems, or the application of
computer algebra to the solution of problems in technology (e.g., aerodynam
ics).
In addition to the accepted submissions, this proceedings volume also in
cludes two invited papers. In the paper by W. Seiler (University of Mannheim)
various indices used for numerical analysis of differential algebraic equations
are studied and geometrically interpreted within the framework of the formal
theory of differential equations. This provides, in particular, the theoreti
cal estimation of the indices in view of completion of differential systems to
involution which is the key concept of the formal theory.
The paper by G. Gonnet (ETH Zurich) deals with the problem how to
generate many fix-point iterators of the form Xi+l = F(Xi) in order to solve
vi
a given non-linear equation. Such methods are suitable only for computer
algebra systems where the equations to be solved can be manipulated in
symbolic form.
The CASC'99 workshop was supported financially by a generous grant
from the Deutsche Forschungsgemeinschaft (DFG) and ADDITIVE GmbH.
We are grateful to M. Mnuk for his technical help in the preparation of
the camera ready manuscript for this volume. We also thank the people at
Springer Verlag for their support in preparing these proceedings, and the Bil
dungsstatte des Bayerischen Bauernverbandes in Herrsching for hosting the
workshop.
Munich, April 1999
V.G. Ganzha
E.W. Mayr
E.V. Vorozhtsov
VII
Workshop Organization
Workshop Chairs
Vladimir Gerdt, JINR, Dubna, Russia
Ernst W. Mayr, TU Munchen, Germany
Program Committee Chairs
Victor Ganzha, TU Munchen, Germany
Evgenii Vorozhtsov, ITAM, Novosibirsk, Russia
Program Committee
Victor Edneral, Moscow State University, Moscow, Russia
Marc Gaetano, INRIA, Sophia, France
Richard Liska, Czech Technical University in Prague, Czech Republic
Roman Maeder, MathConsult, Wollerau, Switzerland
Yuri Matiyasevich, EIMI, St. Petersburg, Russia
Stanly Steinberg, University of New Mexico, Albuquerque, USA
Nikolay Vassiliev, EIMI, St. Petersburg, Russia
Paul Wang, Kent State Univer'sity, Kent, USA
Volker Weispfenning, Universitiit Passau, Passau, Germany
Christoph Zenger, TU Munchen, Germany
Local Organizing Committee
Victor Ganzha, TU Munchen, Germany
Herbert Fischer, TU Munchen, Germany
Ernst W. Mayr, TU Munchen, Germany - chair
Michal Mnuk, TU Munchen, Germany - secretary
Table of Contents
Solution of Ordinary Differential Equations with MathLie . . . . . . . . . . . . 1
Gerd Baumann
Analysis of Stability of Rational Approximations through
Computer Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
Massimo Cafaro, Beatrice Paternoster
An Automatic Symbolic-Numeric Taylor Series ODE Solver. . . . . . . . .. 37
Brian J. Dupee, James H. Davenport
About Normal Form Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51
Victor F. Edneral
Computer Algebra Investigation of Equivalence in 4-node Plane
Stress/Strain Finite Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67
Anders Eriksson, Yunhua Luo, Costin Pacoste
Symmetry Theorems for the Newtonian 4- and 5-body Problems
with Equal Masses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81
J ean-Charles Faugere and !lias K otsireas
Symbolic Derivation of Different Class of High-order Compact
Schemes for Partial Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . .. 93
Michel Fournie
Implementation of Aerodynamic Computations with Mathematica .... 101
Victor G. Ganzha, Evgenii V. Vorozhtsov
Completion of Linear Differential Systems to Involution ............. 115
Vladimir P. Gerdt
Constrained Hamiltonian Systems and Grabner Bases ............... 139
Vladimir P. Gerdt, Soso A. Gogilidze
Construction of Involutive Monomial Sets for Different Involutive
Divisions ....................................................... 147
Vladimir P. Gerdt, Vladimir V. Kornyak, Matthias Berth,
Gunter Czichowski
Partial Inverse Heuristic for the Approximate Solution of
Non-linear Equations ............................................ 159
Gaston H. Gonnet, Allan Bonadio
x
Computing Co cycles on Simplicial Complexes 177
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Rocio Gonzalez-Diaz, Pedro Real
Bifurcations of Maps in the Software Package CONTENT 191
0 0 0 0 0 0 0 0 0 0 0 0
W. Govaerts, YUo Ao Kuznetsov and Bo Sijnave
Extending a Java Based Framework for Scientific
Software-Components 207
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Manfred Gobel, Wolfgang Kuchlin, Stefan Muller, and
Andreas Weber
Symbolic-numeric Investigations for Stability Analysis of Satellite
Systems 223
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Sergey AoGutnik
Quantization by Presentation: The Nambu-Goto String in
1+ 3 Dimensions 229
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Gerrit Handrich
One Algorithm of Finding Solutions for the Systems with First
Integrals 233
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Valentin Irtegov, Tatyana Titorenko
Cohomology of Lie Superalgebras of Hamiltonian Vector Fields:
Computer Analysis 241
0000000000000000000000000000000000000000000000
Vladimir Vo K ornyak
Computer Algebra Tools in Construction of Renormgroup Symmetries 251
0
Vladimir Fo K ovalev
Where Numerics Can Benefit from Computer Algebra in Finite
Difference Modelling of Fluid Flows 269
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Richard Liska, Burton WendrofJ
Effectively Computation of Some Radicals of Submodules of Free
Modules 287
0000000000000000000000000000000000000000000000000000 000
Agustin Marcelo, Felix Marcelo, Cesar Rodriguez
Computations on Character Tables of Association Schemeso 293
0 0 0 0 0 0 0 0 0 0
Edgar M artinez-M oro
Investigation of Subgroup Embeddings by the Computer Algebra
Package GAP 309
00000000000000000000000000000000000000000000000000
Vol. Mysovskikh
An Investigation into Stability of Conservative Mechanical Systems
Using Analytic Calculations 317
0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 000 0 0 0 0 000 0 0 0 0 0 0 0 0 0
MoAo Novickov
Xl
Superfast Computations with Singular Structured Matrices over
Abstract Fields ................................................. 323
V. Y. Pan, A. Zheng, M. Abu Tabanjeh, Z. Chen,
S. Providence
From Modeling to Simulation with Symbolic Computation:
An Application to Design and Performance Analysis of Complex
Optical Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Yves A. Papegay
A Symbolic Numeric Environment for Analyzing Measurement
Data in Multi-Model Settings (Extended Abstract) ................. 343
Christoph Richard and Andreas Weber
Geometric Interpretation of Strong Inconsistency in Knowledge
Based Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
E. Roanes-Lozano, E. Roanes-Macias, L. M. Laita
Indices and Solvability for General Systems of Differential Equations .. 365
Werner M. Seiler
Decomposing Systems of Polynomial Equations ..................... 387
Rainer Steinwandt
Polynomials with Coefficients of Limited Accuracy .................. 409
Hans J. Stetter
Localization of Roots of a Polynomial not Represented in
Canonical Form ................................................. 431
Alexei Yu. Uteshev
On Normalization of a Class of Polynomial Hamiltonians:
From Ordinary and Inverse Points of View ......................... 441
Yoshio Uwano, Nikolai Chekanov, Vitaly Rostovtsev, Sergue
Vinitsky
On Multivariate Polynomial Decomposition ........................ 463
Joachim von zur Gathen, Jaime Gutierrez, Rosario Rubio
Complexity of Monomial Evaluations and Duality ................... 479
Nikolai N. Vassiliev
On the Simplification of Nonlinear DAE Systems in Analog Circuit
Design ......................................................... 485
Tim Wichmann, Ral! Popp, Walter" Hartong, Lars Hedrich
Symbolic Analysis of Computational Algorithms with SYDNA " " " " .. " " 499
Radu Zapotinschi