ACA 2000 Sessions
6th International IMACS Conference on Applications of Computer Algebra

Algebraic Algorithms and Complexity

Approximate Algebraic Computation:
towards SymbolicNumeric Algorithms

Association Schemes and their Applications

Celestial Mechanics and General Relativity

Computational Commutative and Differential Algebra

Computational Number Theory and Group Theory

Computer Algebra Application to Involutivity and
Group Analysis of Differential Equations I

Computer Algebra Application to Involutivity and
Group Analysis of Differential Equations II

Computer Algebra for Dynamical Systems and Mechanics I

Computer Algebra for Dynamical Systems and Mechanics II

Computer Algebra Meets Education I

Computer Algebra Meets Education II

Computer Algebra Methods in Control Systems and Applications

Creative Mathematical and Logic Problem Solving Environment

Groebner Bases and Applications

High Energy and Nuclear Physics

Interval and ComputerAlgebraic Methods in Science and Engineering I

Interval and ComputerAlgebraic Methods in Science
and Engineering II

Nonstandard Applications

Problem Solving Environments for Differential Equations

Teaching of Efficient Mathematics

Computational Number Theory and Group Theory
Organizers:
Song Yan
&
Ilias Kotsireas
 How to create countable groups+
(Anatoly Vershik)
 To be announced+
(John McKay)
 Some weight distributions for binary codes
(Igor Gachkov)
 Unitary fractions
(Ilias Kotsireas)
 Representatives classes conjugation of nilpotet elements in a simple Lie
algebra. Low dimensions
(A. A. Suhanov)
 Fast computing with subgroup lattices in GAP
(V. I. Mysovskih)
 Finitely Presented Universal Groups and Computational Algebra
(Natasha Bozovic)

Teaching of Efficient Mathematics
Organizers:
Alkiviadis G. Akritas
&
Gennadi Malaschonok
 The facilities of Theorema for teaching Logic and Mathematics
(Bruno Buchberger & Tudor Jebelean)
 Teaching Linear Algebra with SVD Analysis
(Alkiviadis Akritas)
 Virtual Mathematical Experiments
(G. Albano, V. Martuscelli, S. Miranda & S. Salerno)
 Mathematics and Mathematica
(G. Albano, C. D'Apice & R. Manzo)
 The algorithms of discrete mathematics and graph theory with Mathematica and
TI83,89
(Igor Gachkov)

Celestial Mechanics and General Relativity
Organizer:
Sergei Klioner
 Symplectic integrators and Computer Algebra in Celestial Mechanics+
(J. Laskar)
 Applications of computer algebra in general relativity+
(R. d'Inverno)
 Poisson series processor for analytical manipulations in celestial mechanics
problems
(T. V. Ivanova)
 Simplification of tensor polynomials with indices
(X. Jaen & A. Balfagon)
 Application of computational group theory for tensor simplification
(R. Portugal)
 On the number of independent components of an indexed object
with symmetries
(S. A. Klioner & N. N. Vassiliev)
 Application of GB technique to the geometry of pairs of Keplerian ellipses
(K. V. Kholshevnikov & N. N. Vassiliev)

Computer Algebra Methods in Control Systems
and Applications
Organizers:
Gerard Jacob
&
Michael G. Dmitriev
 Formal validation of Algebraic Identification algorithm: example of Duffing
equation
(F. Benmakrouha, C. Hespel, G. Jacob & E. Monnier)
 The Construction of Adaptive Control Systems for Transport Means.
(Zoya Ilyichenkova & Nina Zaharova)
 Computer Methods in Analytic Synthesis of Nonlinear
ContinuousDecrete Control Systems
(!!! Yevgeny I. Somov)

Algebraic Algorithms and Complexity
Organizer:
Victor Pan
 Polynomial rootfinding and factorization+
(Victor Pan)
 How quickly can we split generic polynomials?
(D. J. Bernstein)
 Lower bounds for the bilinear complexity of matrix multiplication and of
associative algebras
(Markus Blaeser)
 Completeness and Reduction in Algebraic Complexity
(Peter Buergisser)
 Decomposing Matrix Algebras
(Wayne Eberly & Mark Giesbrecht)
 Fast computations of Integer Determinants
(Mark Giesbrecht, Gilles Villard & Wayne Eberly)
 Efficient exponentiation in finite fields
(Joachim von zur Gathen)
 Complexity lower bounds of Positivstellensatz proofs
(Dima Grigoriev)
 Accuracy and efficiency of parallel implementation of
matrix multiplication
(Igor Kaporin)
 Systems of polynomial equations: normal forms and effective algorithms
(Bernard Mourrain)
 Computations with structured matrices
(Victor Pan)
 Solving polynomial systems of equations by Newton's method
(Michael Shub)

Groebner Bases and Applications
Organizers:
QuocNam Tran
&
Alexander Levin
 Computer Algebra in Robust Stability Analysis
(NainnPing Ke)
 Groebner Bases and Involutive Bases
(A. V. Astrelin & E. V. Pankratev)
 Discrete Comprehensive Groebner Bases
(Yosuke Sato & Akira Suzuki)
 Generalized Characteristic Sets and Multivariable Differential Dimension
Polynomials
(Alexander Levin)
 An Application of Zerodimensional Ideals in Experimental
Design and Discrete Probability
(Eva Riccomagno)

Computer Algebra for Dynamical
Systems and Mechanics I
Organizers:
Victor Edneral,
Raya Khanin,
Ilias Kotsireas
&
Nikolay Vassiliev
 Asymptotics of solutions of Euler equations for a rigid body
(A. Aranson)
 Local simplification for systems of ordinary differential equations
(I.Bacha)
 Parametric analysis of the stability of complex systems by means of computer
algebra
(A. V. Banshchikov & L. A. Bourlakova)
 Formal validation of Algebraic Identification algorithm: example of Duffing
equation
(F. Benmakrouha, C. Hespel, G. Jacob & E. Monnier)
 Integrable dynamical systems: new classes
(L. Berkovich)
 Some applications of differential resultant systems
(G. Carra' Ferro)
 Modular dynamical systems and efficient computation of
their trajectories
(N. Glazunov)

Creative Mathematical and Logic Problem
Solving Environment
Organizer:
Nickolai K. Kossovski
 An algorithm for solvability testing of elementary linear
inequalities systems
(Daniele Beauquier & Elena Smirnova)
 A polynomial algorithm of cubic complexity for solving systems of linear
inequalities with bounded integer variables and at most two variables per
inequality
(Dmitri Davydok)
 Decidability and undecidability of fuzzy and universal theories of ring of
kary numbers
(Nikolai K. Kossovski)
 Program of solvability of linear equality and inequality systems with
parameters
(Evguenia Prokofieva)
 Applications of real/integer quantifier elimination to describe decidable
classes of realtime verification
(Anatol O. Slissenko)
 Coherence theorems and their use in computer algebra
(Sergei Soloviev)
 Combining LevelSaturation Strategies and MetaVariables for Predicate Logic
Proving in Theorema
(B. Konev & T. Jebelean)
 Proving theorems in Mathematical Information Environment+
(A. Letichevsky, J. Kapitonova & V. Volkov)
 The Natural Style Provers of Theorema: A Survey of Various Strategies for
Different Mathematical Domains
(B. Buchberger, C. Dupre', T. Jebelean, B. Konev, F. Kriftner,
T. Kutsia, K. Nakagawa, F. Piroi, D. Vuasaru & W. Windsteiger)

Computer Algebra Meets Education I
Organizers:
Vlasta KokolVoljc
&
Bernhard Kutzler
 On the Use of Derive and MathCad When Training Teachers of Mathematics
(Olga V. Lobanova)
 Developing Conceptual Understanding Through the Use of Computer Based
Mathematics
(Cynthia L. Glickman)

Computer Algebra Meets Education II
Organizers:
Vlasta KokolVoljc
&
Bernhard Kutzler
 Learning Calculus of Several
Variables with New Technologies
(Francisco Javier Gonzalez, Alfonsa Garcia*, Francisco Garcia, Alvaro
Franco, Pedro Franco, Agustin de la Villa, Sara Hoya &
Gerardo Rodriguez)
 Computer Algebra and Functional
Programming in Mathematics Education
(Nina A. Kalinina* & Lidija V. Gorodnjaja)
 The Solver HM: A New Software for
Studying and Applying Mathematics
(Andrei I. Kirilov)
 A Discrete Look at Elementary
Functions
(Bill Pletsch)
 MINOS SE  A New Symbolic
Computation Package with Intuitive ("Natural Syntax") Interface
(Kyril Tintarev)
 Experimenting with Mathematics by
Mathematica
(Giovanna Albano*, Ciro D'Apice & Rosanna Manzo*)
 Using Math Software Packages and
Mathematical Contest in Modeling (MCM) in China
(Ye Qixiao)
 Indispensable Manual Calculation
Skills in a CAS Math Teaching Environment+
(Bernhard Kutzler)
 Plotting and Function Graphs as
tools to face problem solving: A study with 1213 year olds using graphing
calculators
(Tenoch E. Cedillo A.)
 Some Unexpected Results Using
Computer Algebra Systems
(Alfonsa Garcia*, Francisco Garcia, Felix Alonso, Agustin de la Villa,
Sara Hoya & Gerardo Rodriguez)
 Preliminary Phases Of The
Conversion Step And Computer Algebra Systems
(Eno Tonisson)
 A Certain Educational Course in
Mechanics with Computer Algebra System
(M. V. Grosheva* & V. A. Samsonov)

Approximate Algebraic Computation:
towards SymbolicNumeric Algorithms
Organizers:
Robert Corless,
Tateaki Sasaki,
Bernard Mourrain
&
MatuTarow Noda
 Solving Inverse Problem for Discrete Schrodinger Equation
by Using CAS REDUCE
(Svetlana I. Serdyukova)
 On Factorization of Interval Polynomials, Rational Approximation of
Sufficiently Smooth Real Functions and Optimal Interval Evaluation
(Glazunov Nikolay Mihaylovich)
 Hensel Construction of $F(x,u_1,...,u_n), n >= 2$,
at a Singular point and Its Applications
(Tateaki Sasaki)
 Bivariate Rational Approximation and Multivariate Approximate GCD
(Hiroshi Kai & MatuTarow Noda)
 Wu's method for a system of floating point coefficient
polynomial equations
(MatuTarow Noda, Hiroshi Kai & Yoshio Notake)
 Symbolicnumeric methods for solving zero dimensional polynomial systems
(Bernard Mourrain)

Nonstandard Applications
Organizers:
Richard Liska,
Stanly Steinberg
&
Michael Wester
 Algebra is Not Analysis
(Jacques Carette, Rob Corless, David Jeffrey & Stephen Watt)
 A Computer AlgebraBased
Expert System for Diagnosis of Anorexia
(Cristina PerezCarretero, Luis M. Laita, Eugenio RoanesLozano,
Luis Lazaro & Jesus GonzalezCajal)
 The Regulation of Restoration
Algorithms
(Svetlana Ivanova & Robert Ashinyants)
 Operator factorization methods in the form of a hypergeometric calculator
based on the use of Internet clientserver technology
(V. A. Mitrofanov, O. S. Paramonova & A. W. Niukkanen)

Computational Commutative and Differential Algebra
Organizers:
Alkiviadis G. Akritas,
Gennadi Malaschonok
&
Eugeny Pankratiev
 Hensel lifting and solving systems of linear equations
(G. Malaschonok)
 Fast matrix computation of subresultant polynomial remainder sequences
(A. Akritas & G. Malaschonok)
 NO TITLE
(N. Vassiliev)
 Characteristic polynomials of finitely generated modules over
Weyl algebras
(A. B. Levin)
 Construction of primitive elements in differential modules
(M. V. Kondratieva, V. A. Mityunin & N. A. Makarevich)
 Classification using repetitiondependent transformation distance measure on
strings
(O. D. Golubitsky)
 Computation of the weight enumerators of the binary linear codes by linear
programming
(I. Gachkov)
 Generalized chain fractions
(D. A. Maslov)

Computer Algebra Application to Involutivity and Group Analysis of
Differential Equations I
Organizers:
Vladimir Gerdt
&
Fritz Schwarz
 Computation of Janet Bases. I. Monomial
Bases
(Vladimir Gerdt, Yuri Blinkov & Denis Yanovich)
 Computation of Janet Bases. II. Polynomial
Bases
(Vladimir Gerdt, Yuri Blinkov & Denis Yanovich)
 Solving Ordinary Differential Equations by
Equivalence Transformations
(Matthias Berth)

Computer Algebra for Dynamical
Systems and Mechanics II
Organizers:
Victor Edneral,
Raya Khanin,
Ilias Kotsireas
&
Nikolay Vassiliev
 Perturbed oscillators in resonance p:q:r
(A. Elipe & A. Riaguas)
 Structural invariant synthesis of the multiparametrical
nonlinear systems
(A. Flegontov)
 The Identification of Continued Linear Dynamical Systems
(Z. Ilyichenkova, S. Ivanova & N. Zaharova)
 On Using the Transformations of Coordinates in the Problems of Dynamics
(V. D. Irtegov & T. N. Titorenko)
 On choosing scalings for series expansion
in singular perturbation problems
(R. Khanin)
 Recent results on central configurations
(I. Kotsireas)
 Evolution of caustics in dynamical systems with 2 degrees of freedom
(A.Mioulliari)
 Computer Algebra and Random Regimes Analysis
(I. E. Poloskov)
 The application of Computer Algebra to Central configuration dynamics
(A. Rosaev)
 Solution of the principal resonance problem in the case of massless $\phi^4$
theory
(S. Vernov)

Problem Solving Environments for
Differential Equations
Organizers:
Robert van Engelen
&
Stanly Steinberg
 A Problem Solving Environment for
Numerical Partial Differential Equations
(Stanly Steinberg)
 An Approach from AI to the Design
of Routes in a Railway Interlocking
(E. RoanesLozano & L. M. Laita)
 SFTools  Knowledge Based and
Educational System on Special Functions
(A. B. Pirozhnikov)
 Application of Computer Algebra Systems to
Construct Formulae of the Collocation and Least Squares Method
(L. G. Semin & V. P. Shapeev)
 Operating Modeling Environment on
Multisyntax Language Base
(A. V. Kosteltsev)
 Application of Computer Algebra Systems
to Construct HighOrder Difference Schemes
(A. V. Shapeev)
 Code Generation Using Computer Algebra
Systems
(Michael Wester & John K. Prentice)
 Vector Finite Difference Method
(Nicholas M. Bessonov)
 Integrated Environment BARSIC as a Tool
for Development and RunTime Support of Research and Educational
Software
(!!! V. V. Monakhov, A. V. Kozhedub, S. B. Paramonov, E. Yu. Komarov &
L. A. Evstegneev)

Computer Algebra Application to Involutivity and Group Analysis of
Differential Equations II
Organizers:
Vladimir Gerdt
&
Fritz Schwarz
 Morphisms and Binomial Ideals in Polynomial
and Differential Polynomial Rings
(Giuseppa Carra' Ferro)
 Vector Representations of Involutive
Divisions and Some New Involutive Divisions
(YuFu Chen)
 Involutive Algebraic and Differential
Systems+
(Vladimir Gerdt)
 GeometricAlgebraic Completion of Linear
Differential Equations
(Marcus Hausdorf & Werner M. Seiler)
 Application of Computer Algebra to
Analysis of Differential Equations Systems Compatibility
(S. V. Meleshko & V. P. Shapeev)
 Implementation of the Differential
Involutive Algorithms in the CAS Maple VR5
(Vladimir A. Mityunin)

High Energy and Nuclear Physics
Organizers:
Vyacheslav Ilyin,
Michael Dubinin
&
Andrei Semenov
 LanHEP  a package for automatic generation of Feynman rules from the
Lagrangian
(Andrei V. Semenov)
 Heat Invariants of Differential Operators on Manifolds with Torsion
(Vladimir Kornyak)
 Algebraic calculations of multipole matrix elements
(S. Yu. Slavyanov)
 Application of the Lambert W function in
Perturbative Quantum Chromodynamics
(B. A. Magradze)
 Do we need highlevel languages in CA? The GiNaC approach
(Richard Kreckel)
 Calculation of Feynman diagrams in Computer Algebra
(Alexander Kryukov)

Interval and ComputerAlgebraic Methods
in Science and Engineering I
Organizers:
V. M. Nesterov
&
Vladik Kreinovich
 Applications of Interval Sensitivity Analysis
(Boris Dobronets)
 An Application of Interval Taylor Series for Solving
Inertial Navigation Systems
(D. A. Peregudov and V. S. Zyuzin)
 Analysis of Interval Models with Floating Bounds
(Vladimir Krischuk, Galina Shilo, Nikolay Gaponenko)
 Twin Hulls of Fixed Point of a Volterra Integral Operator
in Twin Spaces
(Oleg B. Ermakov)
 Twin Hulls for the Reachable Set of ODE Interval Systems
(Oleg B. Ermakov)
 The Preliminary Enclosing of the ODE Solutions on the Base
of CauchyDuhamel Identity
(Gregory G. Menshikov)
 Choice of an initial approximation for an iterative method of a
solution of an interval system of the linear algebraic equations
(L. Kupriyanova)
 Outer Estimation of Generalized Solution Sets
to Interval Equations Systems
(Sergey Shary)
 J  complex analysis and interval mathematic
(O. S. Peskova and V. S. Zyuzin)
 Solving geometric problems with interval parameters
by means of symbolic construction plans
(R. JoanArinyo and N. Mata)

Interval and ComputerAlgebraic Methods
in Science and Engineering II
Organizers:
V. M. Nesterov
&
Vladik Kreinovich
 Approximate Quantified Constraint Solving By Cylindrical Box
Decomposition
(Stefan Ratschan)
 Universal algorithms and Idempotent Interval Analysis
(Grigiry Litvinov)
 Universal Algorithms, Idempotent Mathematics and Interval
Solutions of Optimization Problems
(G. L. Litvinov, A. N. Sobolevskii)
 Analysis of Dynamic System with Interval Parametric Uncertainty:
Stability Margins in the Frequency Domain
(Farit M. Akhmedjanov and Victor G. Krymsky)
 The Use of IntervalSymbolical Methods for Estimation of Domains
of Attraction of ODE's
(Alexey Rogalev)
 Inner estimation of a range of values
(V. M. Nesterov)
 Discrete Optimization Problems with Interval Data: Connection
between Pareto Set of Alternatives and the Set of Weak Solutions
(Galina Kozina)
 Verification of Invertibility and Charting of Constraint
Manifolds in Differential Algebraic Equations
(Jens Hoefkens and Martin Berz)
 Differential Algebraic Structures and Verification
(Kyoko Makino)
 Best relative placement: a new ability for spatial processing
(Mohammad Reza Malek and Michael Hahn)
 Friction Models with Interval Parameters
(N. A. Khlebalin and A. I. Kostikov)
 Combined IntervalAnalytical Constraint Satisfaction in
Declarative Geometry
(Evgueni Roukoleev and Dmitry Ushakov)

Association Schemes and their Applications
Organizers:
I. Ponomarenko
&
S. Evdokimov
 Graphs, codes, and schemes from nonlinear functions
(D. FonderFlaass)
 The Role of Circulant Graphs in Computer Science and How to Recognize Them
Efficiently
(G. Tinhofer)
 Coding theory and uniform distributions
(M. Skriganov)
 Separability and Schurity of association schemes and the Graph Isomorphism
Problem
(I. Ponomarenko)
 Separability number and Schurity number of coherent configurations
(S. Evdokimov)
 Computer search for Moore graphs
(Sergei Duzhin)
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