ACA 2009 Accepted Sessions

Session Title 1. Computer Algebra in Education
Organizers Kathleen Pineau, École de technologie supérieure, Canada (chair)
Michael Wester, University of New Mexico, USA (chair)
Alkis Akritas, University of Thessaly, Greece
France Caron, Université de Montréal, Canada
Daniel H. Jarvis, Nipissing University, Canada
Bernhard Kutzler, Austrian Center for Didactics of Computer Algebra (ACDCA), Austria
Bill Pletsch, Central New Mexico Community College (CNM), USA
Education has become one of the fastest growing application areas for computers in general and computer algebra in particular. Computer Algebra Systems (CAS) such as Axiom, Casio ClassPad 330, Derive, Maple, Mathematica, Maxima, MuPAD, Reduce, TI N-Spire CAS, and TI Voyage 200 make for powerful teaching and learning tools within mathematics, physics, chemistry, biology, economics, etc.

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.

See Session website for more details.

Session Title 2. Interaction Between Computer Algebra and Interval Computations
Organizers Walter Kraemer, Bergische Universitaet, Wuppertal
Markus Neher, University of Karlsruhe
Evgenija D. Popova, Inst. of Maths & 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 (including e.g. the conferences Interval-xx, ACA 2000, ACA 2003, ACA 2006, and ACA 2008 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 research challenges.

For this special session, we invite survey papers, presentations of some recent developments, application case studies and research challenges. The topics include but are not limited to:
  • Algebraic approach to interval mathematics; theoretical foundations for combining interval and symbolic-algebraic techniques; formalisms for presentation of interval knowledge in CA; usage of analytical transformations and other techniques from computer algebra in interval computations;
  • Exact methods, computer aided proofs, computational complexity analysis of symbolic computation problems with interval uncertainty;
  • Verified multiple-precision computation of special functions
  • Bugs in current CA systems
  • Development and implementation of symbolic-numeric methods for problems involving interval data;
  • (Interval) Taylor models
  • Embedding of interval data structures, hybrid and result-verification algorithms in CA systems and specialized software;
  • Applications of combined interval-analytical techniques in science, biology, engineering, control and other areas;
  • Interval mathematics on the Internet: the use of web and grid service infrastructures, and semantic web technologies for identifying and describing web-based interval resources;
  • Interval Software Interoperability: interoperability between computing systems (like Mathematica, Maple, Matlab, etc.) and languages for dynamic applications (Java, JavaScript, C, C++,...) that support interval computations aiming at an increased functionality and effectiveness;
  • CA in interval education and online interval knowledge (e-Learning).
If you are interested in participation, please send your name, email and approximate title to or or or fill in the form available at our session's website.

Submission of talk title - April 15, 2009
Submission of abstract - May 15, 2009.
Papers presented at the special session will be proposed for post-conference publication in "Serdica Journal of Computing" or another specialised journal.
Session Title 3. Applications and Libraries development in Derive
Organizers José Luis Galán García, University of Málaga, Spain
Pedro Rodríguez Cielos, University of Málaga, Spain
Gabriel Aguilera Venegas, University of Málaga, Spain
Josef Böhm, Editor of the Derive Newsletter, Austria
DERIVE™ 6 is a powerful system for doing symbolic and numeric mathematics. It processes algebraic variables, expressions, equations, functions, vectors, matrices and Boolean expressions in the same way as a scientific calculator processes numbers.

Problems in the fields of arithmetic, algebra, trigonometry, calculus, differential equations, linear algebra, complex analysis and propositional calculus can be solved with a click of the mouse. Plots of mathematical expressions in two and three dimensions using various coordinate systems can be easily performed. Furthermore, the use of the slide bar utility allows beautiful presentations of plot movement and makes it possible to study plots depending on different parameters.

The seamless integration of numeric, algebraic and graphic capabilities makes DERIVE 6 an excellent tool not only for learning or teaching but also for doing mathematics in many applications.

Although Derive is no longer being developed, and TI-NSPIRE CAS has been proclaimed as its successor, there are many professionals who are still using DERIVE.

The main purpose of this Special Session is to share the applications and libraries developed in DERIVE or TI-NSPIRE CAS. Thus, papers about the use of DERIVE in different disciplines, the development of specific libraries, experiences involving DERIVE are welcome. Lectures using TI-NSPIRE CAS are also welcome.

Papers presented in this session will be published in a special issue of The Derive Newsletter.

See Session website for more details.

Session Title 4. Elimination Theory and Applications
Organizers Manfred Minimair, Seton Hall University, USA
Robert H. Lewis, Fordham University, USA
The Elimination Theory session concerns eliminating unknowns from systems of multivariate polynomial equations, including differential polynomials, and decomposing systems of equations with the goal of simplifying equations and computing their solutions.

Motivation and Importance:
Elimination theory is a classical area of research. It has been pursued for hundreds of years. The combination of techniques from symbolic and numeric computation has greatly stimulated the field in recent years. This has led to numerous computer based applications in areas such as computational chemistry, electrical engineering, dynamics of multibody systems, geometric theorem proving, computational algebraic geometry, robotics, and computer aided graphic design. The session will highlight and survey some advances in the area.
Presentations are expected to show relevance for applications.

Some of the typical computational tools in this area are:
  • Groebner bases
  • resultants
  • characteristic sets
  • homotopy
Call for Contributions:
If you want to suggest a speaker or want to give a talk yourself, please send an email to:
Manfred Minimair or Robert H. Lewis.

See Session website for more details.

Session Title 5. Chemistry and Computer Algebra
Organizers Mihai Scarlete, Department of Chemistry, Bishop's University, Sherbrooke, Québec, Canada
Manfred Minimair, Seton Hall University, South Orange, New Jersey, USA
Robert H. Lewis, Department of Mathematics, Fordham University, New York, New York, USA
Motivation and Importance:
In recent years computer algebra techniques and symbolic computation systems have found increasing use for solving problems in chemistry and for chemistry education. Therefore this session will showcase recent developments. Furthermore, the session is expected foster the interaction between the fields of computer algebra and chemistry which may stimulate advances in both areas.

The session will cover advances in computer algebra techniques and computer algebra/symbolic computation software systems for applications in chemistry. The session is open to all areas of applications.
Expected topics of presentations include:
  • pedagogical tools in undergraduate chemistry and chemical engineering
  • research tools in graduate education
  • design of dedicated molecular modeling software
  • software for unitary operations in chemical industry
  • applications of computer algebra in chemical spectroscopy
  • databases based on symbolic computation engines
  • environments for inter-university collaboration in chemical research
Call for Contributions:
If you want to suggest a speaker or want to give a talk yourself, please send an email to organizers:
Mihai Scarlete, Manfred Minimair or Robert H. Lewis.

See Session website for more details.

Session Title 6. Applications of Math Software to Mathematical Research
Organizer Daniel Lichtblau, Wolfram Research, USA
The focus of this session is on the various ways in which symbolic programs, broadly speaking, are nowadays employed in the research side of mathematics.

Symbolic computation and related software technologies have become an increasing presence in mathematical research. Many practitioners have come to see these as indispensible tools. For well over a decade, Bruno Buchberger and others have investigated ways in which software can be brought to bear on deducing and proving theorems, algorithms, and more (he refers to this as "Symbolic Computation in Mathematical Theory Exploration").

Our session is in this vein. Beyond the basic description, I will go so far as to suggest an underlying theme: these tools allow many of us to be wildly more productive than our graduate school credentials gave us any right to expect.

We solicit talks that show novel usage of mathematical software in conjecture, assisted and automated proof, computational experimentation, algorithm analysis, communication of results, and other aspects of mathematical research.

See Session website for more details.

Session Title 7. Computer Algebra for Dynamical Systems and Celestial Mechanics
Organizers Victor Edneral, Moscow State University, Russia
Aleksandr Myllari, University of Turku, Finland
Nikolay Vassiliev, Steklov Institute of Mathematics at St.Petersburg, Russia
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.

The following topics, among others, will be considered:
  1. Stability and bifurcation analysis of dynamical systems
  2. Construction and analysis of the structure of integral manifolds
  3. Symplectic methods.
  4. Symbolic dynamics.
  5. Normal forms and programs for their computations.
  6. Deterministic chaos in dynamical systems.
  7. Families of periodic solutions.
  8. Perturbation theories.
  9. Exact solutions and partial integrals.
  10. Computation of asymptotes of solutions and its program implementation.
  11. Integrability and nonintegrability of ODEs.
  12. Computation of formal integrals.
  13. Computer algebra for celestial mechanics and stellar dynamics.
  14. Specialized computer algebra software for celestial mechanics.
  15. Topological structure of phase portraits and computer visualization.

Call for Contributions:
If you want to suggest a speaker or want to give a talk yourself, please send an email to organizers: Victor Edneral, Aleksandr Myllari or Nikolay Vassiliev. You can also visit the session's website.
Session Title 8. Analogy in Reasoning and Construction
Organizer Michael P. Barnett, City University of New York, USA


The study of analogy is vast. It permeates every field of scholarship and research.
Symbolic calculation software provides powerful tools for exploring the mechanized use of analogy in reasoning and construction.
This session addresses:

  1. symbolic calculations that have involved analogy,
  2. models on which future software can be based,
  3. the selection of further topics for mechanization, from the overwhelming field of possibilities,
  4. the development of strategies to study these.

Suggested Scope for Further Talks:

  1. Representation and classification of analogies of general application.
  2. Representation and classification of analogies in mathematics.
  3. Representation and classification of analogies in experimental and theoretical science.
  4. Representation and classification of analogies in humanities, e.g. textual analysis, visual arts, music.
  5. Using analogy in symbolic calculation of mathematical formulas.
  6. Using analogy in symbolic calculation of text and other non-mathematical material.
  7. Analogy in mathematics, language and other education, with (potential) computer support.
  8. Mechanical recognition of analogy.
  9. Other topics that relate to the recognition and use of analogy.

Call for Submissions:

If you are interested in presenting a talk in this session, please email or upload an abstract by May 15, 2009 at the following URL.

You can also visit the session's website.

Session Title 9. Symbolic and Numeric Computation
Organizers Alkis Akritas, Univ. Volos, Greece
Hiroshi Kai, Ehime Univ., Japan
Itnuit Janovitz-Freireich, CINVESTAV-IPN, Mexico
Doru Stefanescu, Univ. Bucharest, Romania
Hybrid Symbolic and Numeric Computation or Approximate Algebraic Computation, is one of the main streams of current computer algebra. Even so, only relatively few fundamental algebraic operations have been studied so far, and many applications have been left untouched. Researchers continue to study many more algebraic operations from the viewpoint of approximate computation, to take advantage of the fusion of symbolic and numeric computations, and to apply approximate algebraic algorithms to science and technology. Research contributions as well as expository papers are welcomed. For more information please contact the session organizers by email.

This session covers the following topics, but is not restricted to these:
Approximate GCD and approximate factorization.
Approximate computation of Groebner bases.
Algebraic computation using floating-point numbers and numeric algorithms.
Approximate computation by series expansion.
Error analysis and stabilization of algorithms.
Validation of approximate algebraic computation.
Computation of bounds for roots of polynomials.
Isolation of polynomial roots Software for solving hyperbolic polynomials.
Symbolic-numerical methods of finding roots of polynomial systems.
Improved software for solving polynomial systems.
Algorithms and software for Approximate Radicals.
New algorithms suited to approximate algebraic computation.
Model construction by approximate algebraic algorithms.
Applications to science and technology.
New or improved theory and algorithm inspired by particular applications.
Application of existing theory and algorithm to challenging problem.
See Session website for more details.
Session Title 10. Algebraic and Algorithmic Aspects of Differential and Integral Operators
Organizers Markus Rosenkranz, Austrian Academy of Sciences, RICAM, Linz, Austria
Georg Regensburger, Austrian Academy of Sciences, RICAM, Linz, Austria
The algebraic treatment of differential equations is a well-established field with close ties to the symbolic community (see also the ACA Session "Symbolic Symmetry Analysis and its Applications"). Algebraic methods often commence from an operator perspective on the underlying differential equations, e.g. in D-Module theory or in factoring linear differential operators (ODE/PDE, scalar/vector). On the other hand, integral operators have as yet received comparably little attention in an algebraic setting. In the context of linear differential equations, they arise naturally as Green's operators for initial/boundary value problems.

In this session, we would like to examine various relations between differential and integral operators. To this end, we want to bring together the following topics and communities:
  • Factorization of Differential/Integral Operators
  • Constructive Methods for D-Modules
  • Linear Initial/Boundary Value Problems and Green's Operators
  • Rota-Baxter Algebras
  • Symbolic Computation with Differential Polynomials
  • Initial/Boundary Value Problems for Nonlinear Differential Equations
Recent connections between these topics include algebraic structures combining derivations with integrals (e.g. differential Rota-Baxter algebras) and the correspondence between factorizations of differential and integral operators (e.g. by splitting their boundary value problems). We hope that we will have a stimulating discussion that may lead to further interrelations.

See Session website for more details.

Session Title 11. High-Performance Computer Algebra
Organizers Jeremy Johnson, Drexel University, USA
Marc Moreno Maza, Univ. of Western Ontario, Canada
Improved algorithms, better implementations, and faster computers have enabled many previously time-consuming computer algebra computations to be performed routinely and have extended the range of what is practically possible to compute. However, there remains many computations that still require excessive computing time, and while existing computer algebra systems have had some practical success in applications, their widespread use in computational science and engineering remains limited. Part of this is due to inherent difficulties of exact computation; nevertheless, there are many cases where the performance achieved by an implementation could be dramatically improved through optimized implementations and parallel computation and the use of special purpose hardware.

While the computer algebra community has begun to incorporate high performance computing techniques, tuning algorithms to perform well on modern computer architectures and adapting algorithms and systems to parallel computers can be a difficult and time consuming process; much work remains in these directions. Moreover, there are many challenges in achieving high-performance in computer algebra algorithm implementations due to their irregular structure and higher level data types. Also the complexity of computer algebra systems make the incorporation of parallel computation challenging.

This session is devoted to exploring the application of high-performance computing to computer algebra algorithms, applications and systems, and the research and implementation challenges this poses.

Potential Topics:
  1. Practical implementation and performance analysis of computer algebra algorithms
  2. Implementation and optimization techniques for computer algebra algorithms
  3. Parallel implementations of computer algebra algorithms and parallel computer algebra systems
  4. The application and extension of optimizing compiler techniques to the implementation of computer algebra algorithms.
  5. Adapting the implementation of computer algebra algorithms to improve performance by better utilizing the underlying hardware
  6. Techniques for automating the optimization and platform adaptation of computer algebra algorithms
  7. Cache complexity and cache-oblivious computer algebra algorithms
  8. Hardware accelaration technologies (multi-cores, GPUs, FPGAs)

Conference Proceedings:
Papers presented at the session will be considered for publication in a special issue of the Journal of Symbolic Computation dedicated to high-performance computer algebra.

See Session website for more details.

Session Title 12. Nonstandard Applications of Computer Algebra
Organizers Eugenio Roanes-Lozano, Universidad Complutense de Madrid, Spain
Michael Wester, University of New Mexico, USA
Stanly Steinberg, University of New Mexico, USA
In many of the ACA conferences from 1996 onwards, we have chaired a session devoted to ``Nonstandard Applications of Computer Algebra''. 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 ...

A special volume with selected papers from the 2008 and 2009 Nonstandard sessions will be published in Mathematics and Computers in Simulation.

See Session website for more details.

Session Title 13. Symbolic and numeric approaches to dynamical modeling and simulation
Organizers Jürgen Gerhard, "Maplesoft", Canada.     email: jgerhard(at)maplesoft(dot)com
Austin Roche, "Maplesoft", Canada.     email: aroche(at)maplesoft(dot)com
Elena Shmoylova, "Maplesoft", Canada.     email: eshmoylova(at)maplesoft(dot)com
There are a few software packages such as "Dymola" and "MapleSim" that support high-level physics-based modeling and simulation of large-scale continuous and hybrid discrete-continuous dynamical systems. Internally these models are represented by so-called lumped parameter models or differential-algebraic equations (DAEs), and significant parts of the software perform symbolic manipulations of the equations before sending them to a numerical integrator, in order to reduce simulation time or even to enable the numerical integrator to handle the problem.

In this session, we will consider such symbolic and symbolic-numeric techniques for purely continuous DAEs and hybrid discrete-continuous models, including the following topics:

  • index reduction and causalization
  • graph-theory based modeling and simplification
  • model order reduction
  • multi- and cross-domain modeling
  • finding consistent initial conditions for hybrid systems
  • solvers for higher index DAEs
  • nonlinear model reduction
  • reducing the number of static parameters
  • differential elimination
  • reducing the number of discrete modes for hybrid systems
  • model size reduction
  • straight-line program techniques
  • optimized code generation
  • singular perturbation methods
  • parallel algorithms for dynamical simulation
  • multi-body dynamics
Another question that could be considered is related to "real world models". Many of the symbolic methods prevalent in dynamical modeling were designed specifically for a certain class of "nice" models, such as, e.g., polynomials with integer coefficients. However, in practice many models contain components that are not easily accessible to purely symbolic manipulations, such as floating point coefficients and exponents, lookup tables, or piecewise defined functions. The challenge is to apply symbolic techniques to such models appropriately and effectively.
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, 2009.

See Session website for more details.

Session Title 14. Algorithms for Parametric Systems and their Applications
Organizers Guillaume Moroz, Maplesoft, Canada
Hirokazu Anai, Fujitsu Laboratories Ltd/ Kyushu University, Japan
Parametric polynomial system solving is a challenge coming from many applications, such as biology, control theory, robotics, etc. When a problem can be modelled by a parametric system, the main issue is not only to return its solutions, but also to describe them. The design of algorithms to solve parametric systems has recently become an active and expanding research field. Manipulating parametric systems is at the heart of computer algebra. It calls upon a wide range of methods, such as Triangular sets, Gröbner bases, Cylindrical Algebraic Decomposition, Quantifier Elimination, etc.

This session is focused on the art of parametric system solving, for general class of systems or dedicated to specific application problems.

The different topics will include :
  • modelisation of parametric problems
  • optimization of parametric systems
  • resolution of sparse parametric systems
  • low-level computation with multivariate polynomial coefficients
  • resolution of polynomial systems with boolean parameters
  • description of the real solutions of a parametric system
  • description of the parameter space of a polynomial system
  • extension of algorithms from non parametric to parametric systems

Any applications in science and engineering of above topics are also welcome.

Call for Contributions:
The call for submission is now opened. If you are interested in presenting a talk in this session, please send an email to the organizers with a title and an abstract, by Monday, June 1st:
Guillaume Moroz or Hirokazu Anai.

See Session website for more details.