Other sessions will be announced later

Algebraic Algorithms and Complexity

Session Organizers:

The session will cover various theoretical and practical aspects of synthesis and analysis of algebraic algorithms, in particular various issues of theoretical and practical complexity af algebraic computing. This will include the classical theoretical subject of lower bounds techniques as well as upper estimates for the parameters most important for practical computations, such as computational time, memory space, and computational precision, including both asymptotic estimates and the constants hidden in the "O" notation.

We will focus on the most established fundamental subjects of the solution of polynomial equations and systems of equations and matrix multiplication but will also expose some more recently recognized topics such as computations in finite fields and structured matrices.

Preliminary list of participants

Celestial Mechanics and General Relativity

Session Organizers:

The aim of the session is to provide a forum for discussing new computer algebra algorithms, techniques, software systems and applications in the fields of celestial mechanics and gravitational physics. Although these two research fields are rather different, there are many computer algebra ideas and techniques common to both fields, and it seems to be quite interesting to discuss these questions in such an audience.

Both celestial mechanics and relativistic gravity theories are traditional application fields of computer algebra. Both fields are known for their extremely complicated calculations with many thousands of terms. The complexity of calculations in both research fields forces to develop specialized algorithms and specialized highly optimized software systems. Poisson series processors optimized for typical applications in celestial mechanics and specialized systems for tensorial calculations in relativity play a very important role. However, also general-purpose systems can be successfully used in many cases.

The session is intended to cover the whole spectrum of computer algebra techniques and applications in celestial mechanics and gravitational physics. Session topics include (but are not restricted to):

A.1     Specialized computer algebra systems for celestial mechanics
A.2     Applications of general-purpose computer algebra systems in celestial mechanics
A.3     Algorithm design in celestial mechanics
B.1     Computer algebra systems for gravitational physics
B.2     Algorithms for tensorial computations
B.3     Applications of computer algebra in gravitational physics
AB.1   Computer algebra in teaching celestial mechanics and general relativity
AB.2   Symbolic-numeric interface

Computer Algebra Application to Involutivity and Group Analysis of Differential Equations

Session Organizers:

Symmetry methods developed by Sophus Lie in the later part of the XIX century have become a powerful tool for the reduction and explicit integration of differential equations. Nowadays, special packages and modules implementing Lie symmetry methods are available for most general-purpose computer algebra systems and widely used in many applications. However, the practical applicability of these packages is still rather restricted mainly because of algorithmical difficulties in integrating the linear determining systems for Lie symmetry generators. The most general method of simplification and integration of the determining systems is their completion to involution. Given an involutive form of the determining system one can, in particular, determine the size of the symmetry group and the structure constants of finitely-dimensional Lie symmetry algebra. For nonlinear systems including those containing both differential and algebraic equations, their completion to involution is another general constructi ve approach to analysis and solving. This approach is under intensive algorithmic research over last years. The session aim is to provide a forum for discussing constructive mathematical methods, algorithms, software packages and scientific and engineering applications based on symmetry and involutivity methods for differential and algebraic equations.

Session topics:
a. Lie symmetry analysis of differential equations
b. Group classification of differential equations
c. Canonical form transformation of equations with symmetries
d. Nonclassical and approximate symmetries
e. Symmetries and conservation laws
f. Involutivity of differential systems
g. Differential algebra methods
h. Involutive polynomial and differential bases
i. Formal theory of differential equations
j. Differential-algebraic equations
k. Applications of symmetry and involutivity methods in science and engineering

Computer Algebra for Dynamical Systems and Mechanics

Session Organizers:

This session is intended to discuss Computer Algebra methods and algorithms in the study of Dynamical Systems. The session will also focus on important applications of Computer Algebra to Dynamical Systems arising in many areas of science and engineering.

Since nonlinear Dynamical Systems cannot be exactly solved in general, the role of Computer Algebra in finding approximate solutions as well as in the pre-analysis for the numerical methods, is extremely important. From this point of view, the construction of exact or approximate solutions in symbolic form constitutes the most powerful approach to study the behavior of Dynamical Systems. Computer Algebra methods have also emerged as powerful tools in investigating stability and bifurcations.


  • Stability and bifurcation analysis of dynamical systems.
  • Investigation of limit cycles.
  • Symbolic integration of ODEs.
  • Construction and analysis of the structure of integral manifolds.
  • Construction of approximate solutions in symbolic form.
  • Construction of normal forms.
  • Construction and investigation of formal integrals of dynamical systems.
  • Non-Holonomic systems.
  • Construction of integral invariants and partial integrals.
  • Invariants of symplectic mapping.
  • Symplectic integration of hamiltonian systems.
  • Semi-numerical algorithms.
  • Symbolic dynamics.
  • Applications of computer algebra methods to celestial mechanics.
  • Computer algebra software and and special-purpose packages.
  • Applications to control theory and mechanical engineering.
  • Discrete simulation and automata theory

Computer Algebra Meets Education

Session organizers/chairpersons: Vlasta KOKOL-VOLJC & Bernhard KUTZLER

Short Description:

Education has become one of the fastest growing application areas for computers in general and computer algebra in particular. Computer algebra tools such as TI-92/89, DERIVE, MATHEMATICA, MAPLE, AXIOM, REDUCE, MACSYMA, or MUPAD make powerful teaching tools in mathematics, physics, chemistry, biology, economy.

The goal of this session is to exchange ideas and experiences, to hear about classroom experiments, and to discuss all issues related with the use of computer algebra tools in classroom (such as assessment, change of curricula, new support material, ...)

Interval and Computer-Algebraic Methods in Science and Engineering

Session Organizers:
  • V. M. Nesterov P. O. Box 52 St. Petersburg 256, 195256 Russia
  • Vladik Kreinovich Department of Computer Science University of Texas at El Paso, El Paso, TX 79968, USA


There is a need to combine methods of computer algebra and of interval computations.


  • Most applications of computer algebra and symbolic computations, (in particular, most applications to control, dynamical system analysis, computer graphics, etc.), deal with situations in which we know the exact all the coefficients of the corresponding analytical expressions.
  • In many real-life situations, however, these coefficients have to be determined from measurements and observations. Since a measurement is never 100% accurate, after measuring a value x, we can only conclude that the actual (unknown) value of the measured coefficient lies within the interval [x-D,x+D], where D is the upper bound on the measurement error (guaranteed by the manufacturer of the measuring instrument). We therefore need to take this interval uncertainty into consideration.


  • Most algorithms developed in computer algebra assume that all the coefficients are (exactly represented) real numbers.
  • In the computers, many real numbers can only be approximately represented. The resulting rounding errors lead to the inaccuracy of the coefficients in the final result. It is therefore desirable to estimate this inaccuracy. For this estimation, we can also use methods of interval computations.

In recognition of this need, in 1994, an International Conference on Interval and Computer-Algebraic Methods in Science and Engineering (Interval'94) was held in St. Petersburg, Russia. This first conference of this type was a huge success. At this conference, more than 100 researchers from 18 countries presented their practical and theoretical results.

Since 1994, there has been a tremendous progress both in computer algebra and in interval computations. This progress is largely due to the rapidly increasing computer processing speed, which makes previously theoretical algorithms of computer algebra practically feasible. In some cases, we can directly apply these algorithms; in most cases, however, there is a need for further fine-tuning, a need which leads to interesting challenging new theoretical problems whose solution, in its turn, results in new exciting applications.

We believe that time is ripe for a new major meeting devoted to the relation between computer algebra and interval computations. This meeting will hopefully not only highlight the results, but it will also give a new boost to a much-needed combination of numerical and symbolic techniques.


For this special session, we are soliciting papers in the following areas:
  • applications of combined interval-analytical techniques in science and engineering (and in other possible application areas);
  • special languages, software and hardware tools which either
  • combine interval techniques with techniques of computer algebra, or
  • enhance such a combination;
  • theoretical foundations for combining interval and symbolic algebra techniques, including (but not limited to):
  • the use of analytical transformations (and other techniques from computer algebra) in interval computations;
  • algebraic approach to interval mathematics (including interval-based formalisms of computer algebra);
  • computational complexity analysis of symbolic computation problems with interval uncertainty;
  • new semi-heuristic ideas on how interval and computer algebra methods can be combined (either in general, and with some specific application area in mind), and
  • new potential applications area for the combined interval-analytical techniques.

In this solicitation, we are targeting researchers and practitioners from both communities: interval computations and computer algebra. To achieve a greater success, we are making this appeal as broad as possible:

  • It is OK to have a result which is mainly devoted to interval computations, but has some relation to computer algebra.
  • It is also OK to have a result which is mainly devoted to computer algebra, but has some relation to interval computations.

Since this session is oriented towards two different communities, we encourage the authors to do their best to be understandable by researchers from both communities (even if this means adding extra phrases into the introduction which, e.g., for an interval computations community would not be necessary at all).

Problem Solving Environments for Differential Equations

Session Organizers:


This session will focus on problem solving environments (PSEs) that are designed to help users solve and understand the solutions of differential equations:

If you wish to present a talk at our session, please submit an abstract including title, author(s), and e-mail address(es) to one of the organizers. To be certain of inclusion in this special session, please submit this material as soon as possible.

You are responsible for your own expenses (travel, hotel, food). We are looking forward to see you at our special session of IMACS ACA'2000!

Approximate Algebraic Computation: towards Symbolic-Numeric Algorithms

Session Organizers:
Contact address
Matu-Tarow Noda
Department of Computer Science, Ehime University,
Matsuyama Japan

Creative Mathematical and Logic Problem Solving Environment

Session Organizer: Nickolai K. Kossovski

The session will be divided on two parts. The first one will be composed by programs which support creative thinking of students or investigators through mathematical and logic problems. The second one will be composed by new EXPTIME algorithms for decision of some mathematical and logic theories.

Teaching of Efficient Mathematics

Session Organizers:

The title of this session indicates that we are welcoming everybody who is doing constructive mathematics with the help of computer algebra systems. Among the topics covered by this session are:

  1. Reports on successful classroom experiences using mathematical software systems.

  2. Impact of mathematical software systems on mathematical thinking and problem solving.

  3. Impact of new technologies on mathematics teaching and learning.

  4. New algorithms, (network) software for organising new forms of math teaching and studying, computer-based math texts, lectures and teaching units.
Papers presented at this session of IMACS-ACA'99 were published in the journal Tambov University Reports V.4, No.4, 1999. To get this issue one must contact Gennadi Malaschonok.

Computational Commutative and Differential Algebra

Session Organizers:

The topics to be covered in this session are:

Association Schemes and their Applications

Session Organizers:

The purpose of the session is to discuss the problems of algebraic combinatorics (in sense of Bannai-Ito) and computer algebra techniques arising in this connection. Since to almost any problem in this field one can associate some computation, both theoretical and algorithmic contributions are welcomed. Explicit computations and relevant software are of special interest.


High Energy and Nuclear Physics

Session Organizers:

Many pioneer developments on Computer Algebra have been made by High Energy Physicists like M.Veltman (Schoonschip), A.C.Hearn (REDUCE), S.Wolfram (Mathematica) and J.A.M.Vermaseren (Form).

From an original narrow field of application these systems have become general purpose tools. It is therefore natural that a session of this conference deals with applications of Computer Algebra in High Energy or Particle Physics.


Please, send to us short abstracts of your potential contributions including your affiliation and addresses till April 1. We would be also very grateful to you for spreading of this information to your Colleagues.

Computational Number Theory and Group Theory

Computer Algebra Computations in Group Thery and Number Theory
Session Organizers:

Papers pertaining to all aspects of computational number theory and group theory, particularly the applications of computer algebra to computations in these fields are solicited. Papers may present theory, algorithms, packages, and practical experiences on any relevant topic including but not limited to:

Groebner Bases and Applications

Session Organizers:

This session is a continuation of the series of sessions on the theory of Groebner bases and its applications organized at previous IMACS-ACA conferences and and other workshops.

The Gr\"obner basis method has become one of the most important techniques in providing exact solutions of nonlinear problems in multivariate polynomial ideal theory, in computational commutative algebra, in elimination theory, in solving systems of algebraic equations, and in many other related areas. It is also being used fruitfully in a variety of seemingly unrelated research areas such as geometrical theorem proving, integer programming, solid modeling and engineering. The method is implemented in all major computer algebra systems.

Nevertheless, the field is still under active development both in the direction of improving the method by new theoretical insights and in finding new applications.

This time we will concentrated on basis conversion and the applications of the Gr\"obner basis methods in linear difference-differential equations, commutative/noncommutative algebra, and constructive geometry.

Computer Algebra Methods in Control Systems and Applications

Session Organizers:

The topics to be covered in this session are:

Theoretical questions of computer algebra applications in optimal control systems

New algorithms in control theory on the base of the Computer Algebra Systems and Asymptotics

Control systems in real time

Nonstandard Applications

Session Organizers:

This session should serve as a basis for talks which do not fit into any of the sessions already organized for the IMACS ACA'2000 conference and can include computer algebra applications from any area. Potential speakers should submit their talk to session organizers. The submission should include title, author(s) and abstract.

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