Special Sessions

EDUCATION SESSION

Directors

• Alkis Akritas, University of Thessaly

• Michel Beaudin, ETS

• Bill Pletsch, Central New Mexico Community College

• Elena Varbanova, Technical University of Sofia

• Michael Wester, University of New Mexico

Education has become one of the fastest growing application areas for computers in general and computer algebra in particular. Computer Algebra Systems (CAS) make for powerful teaching and learning tools within mathematics, physics, chemistry, biology, economics, etc. Among them are: (a) the commercial "heavy weights" such as Casio ClassPad 330, Derive, Magma, Maple, Mathematica, MuPAD, TI N-Spire CAS, and TI Voyage 200, and (b) the free software/open source systems such as Axiom, Euler, Fermat, wxMaxima, Reduce, and the rising stars such as GeoGebra, Sage, SymPy and Xcas (the swiss knife for mathematics).

The goal of this session is to exchange ideas, discuss classroom experiences, and to explore significant issues relating to CAS tools/use within education. Subjects of interest for this session will include new CAS-based teaching/learning strategies, curriculum changes, new support materials, and assessment practices from all scientific fields.

Papers presented in this session will be considered for publication in a special issue of The International Journal for Technology in Mathematics Education (IJTME). Information on timeline for article submission will be given at a later time.

Session website

COMPUTER ALGEBRA IN KNOWLEDGE BASED APPLICATION

Directors

• Jacques Calmet, Karlsruhe Institute of Technology

• Volker Sorge, University of Birmingham

Overview: Symbolic Computation techniques are playing a significant role outside its traditional application areas in Computer Algebra. Over recent decades they have been successfully employed in several areas of traditional artificial intelligent systems such as automated reasoning, constraint solving or interactive tutoring. Conversely intelligent and knowledge based techniques have made their way into main stream symbolic computation such as the integration of equational reasoning into Computer Algebra systems. In this session we will be interested in a variety of application of symbolic computation in knowledge based artificial intelligence systems and vice versa of incorporation of AI

techniques and mathematical knowledge into computer algebra. We will also be interested in representation issues arising from these combinations as well as in the role played by ontologies in linking symbolic computation and AI as illustrated by Wolfram|Alpha. The scope of the session therefore includes the following topics:

-- System combinations and integrations

-- Knowledge acquisition and representation

-- Application areas

Call for Contributions:

If you are interested in giving a presentation at this session, please email an abstract to one of the organizers. Presentations will be up to 30 min in length, including time for discussion. The tentative deadline for submissions is May 29th, 2010. Selected contributions will be considered for inclusion in a special issue of the Annals of Mathematics and Artificial Intelligence. For more information please visit

http://events.cs.bham.ac.uk/aca10/

INTERACTION BETWEEN COMPUTER ALGEBRA AND INTERVAL COMPUTATIONS

Directors

• Walter Kraemer, University of Wuppertal

• Markus Neher

• Evgenija Popova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

For many years there is a considerable interaction between symbolic-algebraic and result-verification methods. The usage of validated computations at critical points of some algebraic algorithms improves the stability of the complete solution. Several hybrid algorithms using floating-point and/or interval arithmetic in intermediate computations combine the speed of numerical computations with the exactness of symbolic methods providing still guaranteed correct results and a dramatic speed up of the corresponding algebraic algorithm. Embedding of interval data structures, hybrid and result-verification methods in computer algebra systems turn the latter into valuable tool for reliable scientific computing while by applying symbolic-algebraic methods interval computations expand the methodology tools and get an increased efficiency.

This special session continues the tradition established by previous conferences and special sessions on interval and computer-algebraic methods in science and engineering. The aim is to bring together participants from diverse areas of mathematics, computer science, various life & engineering/science disciplines that will demonstrate the progress in the interaction between symbolic-algebraic and result-verification methods. The meeting goal is to stimulate the communication, coordination, integration, and cross-fertilization of ideas capable to meet the emerging challenges.

COMPUTER ALGEBRA FOR DYNAMICAL SYSTEMS AND CELESTIAL MECHANICS

Directors

• Victor Edneral, Lomonosov Moscow State University

• Aleksandr Mylläri, University of Turku

• Jesus Palacian, Universidad Publica de Navarra

• Nikolay Vasiliev, Steklov Institute of Mathematics at St.Petersburg

Celestial Mechanics and Dynamical Systems are traditional fields for applications of computer algebra. This session is intended to discuss Computer Algebra methods and modern algorithms in the study of general continuous and discrete Dynamical Systems, Ordinary Differential Equations and Celestial Mechanics.

Topics:

• Stability and bifurcation analysis of dynamical systems

• Construction and analysis of the structure of integral manifolds

• Symplectic methods.

• Symbolic dynamics.

• Normal forms and programs for their computations.

• Deterministic chaos in dynamical systems.

• Families of periodic solutions.

• Perturbation theories.

• Exact solutions and partial integrals.

• Computation of asymptotes of solutions and its program implementation.

• Integrability and nonintegrability of ODEs.

• Computation of formal integrals.

• Computer algebra for celestial mechanics and stellar dynamics.

• Specialized computer algebra software for celestial mechanics.

• Topological structure of phase portraits and computer visualization.

COMPUTATIONAL GROUP THEORY

Directors

• Stefan Kohl, University of Vlora

• Dmitri Malinin, University of Vlora

The session topics include, but are not restricted to, the description and analysis of algorithms and methods for computation in

• - group theory,

• - representation theory,

• - Galois theory and

• - lattice theory,

as well as the presentation of results obtained by their use.

The session also discusses applications of such algorithms and methods to other parts of mathematics and sciences.

Examples of possible session topics in group theory are algorithms

and methods for

• - finitely- or recursively presented groups,

• - p-groups or polycyclically presented groups,

• - finite or infinite matrix groups (including crystallographic groups),

• - finite or infinite permutation groups,

• - simple groups,

• - group actions,

• - geometry of groups,

• - group cohomology and

• - group rings

as well as algorithms and methods for classifying groups (or objects closely related to groups) with certain properties, and the presentation of results obtained using such algorithms and methods.

ALGEBRAIC AND ALGORITHMIC ASPECTS OF DIFFERENTIAL AND INTEGRAL OPERATORS

Directors

• Georg Regensburger, Johann Radon Institute for Computational and Applied Mathematics (RICAM)

• Markus Rosenkranz, University of Kent at Canterbury

The algebraic/symbolic treatment of differential equations is a flourishing field, branching out in a variety of subfields committed to different approaches. In this session, we want to give special emphasis to the operator perspective of both the underlying differential operators and various associated integral operators (e.g. as Green's operators for initial/boundary value problems).

In particular, we invite contributions in line with the following topics:

• Symbolic Computation for Operator Algebras

• Factorization of Differential/Integral Operators

• Linear Boundary Problems and Green's Operators

• Initial Value Problems for Differential Equations

• Symbolic Integration and Differential Galois Theory

• Symbolic Operator Calculi

• Algorithmic D-Module Theory

• Rota-Baxter Algebra

• Differential Algebra

• Discrete Analogs of the above

• Software Aspects of the above

Please see the session homepage at:

http://www.ricam.oeaw.ac.at/conferences/aca10/aadios.html

An MSC Special Issue on these sessions is currently being compiled

COMPLEXITY OF SOLVING DIFFERENTIAL ALGEBRAIC SYSTEMS

Directors

• Marc Giusti, CNRS/Polytechnique

• François Ollivier, LIX CNRS Ecole polytechnique

Overview

Differential algebraic equations appear in many fields of science and industry. Most of the time, physical laws will produce explicit systems, or systems that may be easilly reduced to explicit systems. But we cannot escape the difficult case of system that deserves preliminary symbolic computation before being reduced to a form suitable for numerical integration, the computation of some invariants. Sometimes, one also wishes to eliminate some differential unkowns or try to express some of them as functions of the others. Such questions are already difficult for algebraic systems, so that complexity issues are decisive to make algorithms useful in practice.

The following topics, among others, will be considered, from the complexity standpoint, which means with a strong emphasis on theoretical complexity bounds and/or experimental study of actual implementation:

1. Change of orderings and elimination;

2. Local computations and power series solutions;

3. Computation of dimensional invariants, differential Hilbert functions;

4. Regular decomposition, Ritt problem (*);

5. Flat systems, computation of linearizing outputs (*);

6. New data structures and “Gröbner free” algorithms;

7. Jacobi's bound and complexity bounds;

8. Index computation, index reduction;

9. Regular and singular solutions;

10. Local index, local singularities;

11. Symbolic generation of numerical solvers... (*) It is of course understood that showing a problem is decidable is a first complexity result... Efficient heuristic methods, semi-algorithms or algorithms dedicated to particular cases of special interest are welcome too.

Call for contributions

If you are interested in giving a presentation at this session, please email an abstract to one of the organizers. Presentations will be up to 30 min in length, including time for discussion. The tentative deadline for submissions is May 29th, 2010. Selected contributions will be considered for inclusion in a special issue of the journal AAECC (Applicable Algebra in Engineering, Communication and Computing).

Session webpage

NONSTANDARD APPLICATIONS OF COMPUTER ALGEBRA

Directors

• Michael Wester, University of New Mexico

The session traditionally collects contributions that, while using Computer Algebra techniques and/or Computer Algebra Systems, can not be easily allocated in the ``standard'' sessions. Examples of topics treated in papers presented in previous editions of the conference are: Verification and Development of Expert Systems (using algebraic techniques), Railway Traffic Control, Artificial Intelligence, Thermodynamics, Molecular Dynamics, Statistics, Electrical Networks, Logic, Robotics, Sociology, Integration, Mechanics, Discrete Mathematics ...

Session website

COMPUTATIONAL ALGEBRAIC GEOMETRY, CODING THEORY, AND CRYPTOGRAPHY

Directors

• Artur Elezi, American University

• Tanush Shaska, Oakland University

Computational algebraic geometry is one of the fastest areas of computational algebra. Some of its branches go to the hart of computational algebra and symbolic computation such as computing dimension of varieties, Groebener basis, Buchberger's Algorithm etc. Other aspects include automorphism groups of curves, invariants of curves, arithmetic in the jacobians of curves, elmination theory, etc. The session is open to all aspects of computational algebraic geometry.

PARALLEL COMPUTING

Directors

• Gennadi Malaschonok, Tambov State University

• Stephen Watt, University of Western Ontario

The session topics include but not restricted to:

reinvention and adaptation of existing symbolic algorithms to a parallel setting

computer algebra systems specifically designed to exploit and operate in multiprocessor environment

parallel methods for solving systems of differential equations

parallel methods for Groebner basis computations

parallel algorithms for solving linear and polynomial systems

applications of parallel computer algebra

If you are interested in participation, please send your name, email and approximate title to one of session organizers as soon as you make your decision but not later than:

Submission of talk title - April 15, 2010

Submission of abstract - May 15, 2010.

COMPUTATION OF SPECIAL FUNCTIONS

Directors

• Diego Dominici, SUNY New Paltz, TU Berlin

• Veronika Pillwein, DK Computational Mathematics, JKU Linz

A possible way of defining the so-called "special functions" is to choose those mathematical functions which are widely used in scientific and technical applications, and of which many useful properties are known.

A familiar classification of special functions is by increasing complexity, starting with polynomials and algebraic functions and progressing through the "elementary" or "lower" transcendental functions (logarithms, exponentials, trigonometric, etc.) to the "higher" transcendental functions (Bessel, parabolic cylinder, etc.) Special functions are used in all fields of science. The most well-known application areas are physics, engineering, chemistry and computer science. Because of their importance, several books and a large collection of papers have been devoted to the numerical computation of these functions. But up to this date, even environments such as Maple, Mathematica, MATLAB and libraries such as IMSL, CERN and NAG offer no routines for the reliable evaluation of special functions. Here the notion of reliable indicates that, together with the function evaluation, a guaranteed upper bound on the total error or, equivalently, an enclosure for the exact result, is computed. At the same time, recently developed methods in symbolic computation are applied for the simplification and evaluation of quantities involving special functions.

Many years ago proving special function identities was a tedious and error prone task which required long training and structural insight. Nowadays, scientists may choose among a variety of algorithms that are up to fulfilling the task of finding closed form expressions or reducing complexity by delivering a compact description in terms of difference or differential relations. With these programs, dealing with special functions is straight-forward, efficient and reliable.

The goal of this session will be to understand the latest developments in the computation of special functions and the implementation of these procedures using computer algebra.

COMPUTER ALGEBRA IN ALGEBRAIC TOPOLOGY AND ITS APPLICATIONS

Directors

• Eduardo Saenz-de-Cabezon, Universidad de La Rioja

Algebraic Topology is an area of pure mathematics with deep algebraic and geometrical-topological roots that has had an intense development in the last two centuries. The recent years have made evident the enormous potential for applications of Algebraic Topology. The powerful tools, techniques and ideas of this area have been used in various contexts related to data analysis, combinatorics, computer science, robotics, physics, computer vision or dynamical systems, to name just a few. On the other hand, the advances of computer science, in particular symbolic computation and manipulation, have increased the computability of the objects of algebraic topology and have made them actually applicable to real life problems.

It is the aim of this session to gather researchers with an active interest in potential and actual applications of algebraic topology as well as the computational techniques and problems related to algorithmic algebraic topology.

Contributions are welcome on:

• All aspects of algebraic topology in particular when considered from the point of view of its potential applications.

• Actual applications of algebraic topology in mathematics and other sciences, engineering, industry, communications, business, computer science, physics and other areas.

• Submissions on the computational aspects of algebraic topology are particularly encouraged.

Fields of application include but are not restricted to:

• Code theory

• Combinatorics

• Commutative algebra

• Computer science, including algorithms and distributed computing

• Data analysis

• Differential systems

• Digital images

• Discrete and computational geometry

• Dynamic systems

• Electromagnetism

• Graph theory

• Medical sciences

• Physics

• Reliability theory

• Robotics

• Statistics

Session website

COMPUTER ALGEBRA IN CHEMISTRY AND PHYSICS

Directors

• Robert Lewis, Fordham University

• J Ogilvie, Universidad de Costa Rica

Motivation and Importance

Techniques for computer algebra and systems for symbolic computation have found increasing use for solving problems in chemistry and physics. Therefore this session will feature pertinent recent developments. Furthermore, the session is expected to foster the interaction between the fields of computer algebra, chemistry, and physics that might stimulate progress in all these areas.

Scope

The sessions will cover advances in techniques of computer algebra and software for computer algebra and symbolic computation applied to chemistry and physics. The session is open to all areas of such applications. Expected topics of presentations include:

• - design of software dedicated to model molecular structure, chemical reactions, electric circuits and optical systems.

• - solution of differential equations for prototypical systems in physical chemistry and in chemical, molecular, and optical physics

• - software for unit operations in chemical industry.

• - optimization of laboratory systems in chemistry and physics.

• - applications of computer algebra in optical and radio-frequency spectroscopy and in analysis of spectra in all frequency regions.

• - databases based on engines for symbolic computation applicable to systematics of reactions in inorganic, organic, and biochemistry.

• - extension of free software for computer algebra applied to chemistry and physics.

• - environments for inter-university collaboration in research in chemistry and physics.

• - pedagogical tools in undergraduate chemistry, chemical engineering, physics and related areas.

• - research tools for graduate education in these areas.

SOLVING PARAMETRIC ALGEBRAIC SYSTEMS AND THEIR APPLICATIONS

Directors:

• Hitoshi Yanami, Fujitsu Laboratories Ltd.

• Hirokazu Anai, Fujitsu Laboratories Ltd.

Polynomial equations, inequations, and inequalities have been studied for a very long time. Solving systems or constraints on them with the help of computers is one of the main topics in Computer Algebra. These days parametric system solving that includes comprehensive Groebner bases and quantifier elimination has attracted more attentions. Research on using methods of solving them as a tool for analyzing practical problems in engineering, biology, chemistry, etc. has been active.

In this session our interests lie in new techniques and approaches in solving such problems as well as their applications to practical problems. The scope of the session includes:

• system design in control, signal processing, etc.

• modeling of parametric problems

• parametric optimization and optimization over parameters

• resolution of polynomial systems with boolean parameters

• resolution of sparse parametric systems

• description of the real solutions of a parametric system

• description of the parameter space of a polynomial system

• application of above topics in science and engineering