Computer Algebra in Scientific Computing: 12th International Workshop, CASC 2010, Tsakhadzor, Armenia, September 6-12, 2010, Proceedings / Edition 1

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The CASC Workshops are traditionally held in turn in the Commonwealth of IndependentStates(CIS)andoutsideCIS(Germanyinparticular,but,attimes, also other countries with lively CA communities). The previous CASC Wo- shop was held in Japan, and the 12th workshop was held for the—rst time in Armenia, which is one of the CIS republics. It should be noted that more than 35 institutes and scientific centers function within the National Academy of S- ences of Armenia (further details concerning the structure of the academy can be foundhttp://www. sci. am). These institutions are concerned, in particular, with problems in such branches of natural science as mathematics, informatics, physics, astronomy, biochemistry, etc. It follows from the talks presented at the previous CASC workshops that the methods and systems of computer algebra may be applied successfully in all the above-listed branches of natural sciences. Therefore, the organizers of the 12th CASC Workshop hope that the present workshop will help the Armenian scientists to become even more familiar with the capabilities of advanced computer algebra methods and systems and to get in touch with specialists in computer algebra from other countries. The 11 earlier CASC conferences, CASC 1998, CASC 1999, CASC 2000, CASC 2001, CASC 2002, CASC 2003, CASC 2004, CASC 2005, CASC 2006, CASC 2007, and CASC 2009 were held, respectively, in St. Petersburg (R- sia), Munich (Germany), Samarkand (Uzbekistan), Konstanz (Germany), Yalta (Ukraine), Passau (Germany), St.

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Table of Contents

Construction of Irreducible Polynomials over Finite Fields Sergey Abrahamyan 1

Factorization of Polynomials and GCD Computations for Finding Universal Denominators Sergei A. Abramov Amel Gheffar Denis E. Khmelnov 4

A Role of Symbolic Computations in Beam Physics Serge N. Andrianov 19

Thomas Decomposition of Algebraic and Differential Systems Thomas Bächler Vladimir Gerdt Markus Lange-Hegermann Daniel Robertz 31

On Multivariate Homogeneous Polynomial Decomposition Paula Bustillo Jaime Gutierrez 55

Computing Matrix Representations of Filiform Lie Algebras Manuel Ceballos Juan Núñez Ángel F. Tenorio 61

Type Specialization in Aldor Laurentiu Dragan Stephen M. Watt 73

An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models Ambedkar Dukkipati Joel George Manathara 85

On Sufficient Conditions for Integrability of a Planar System of ODEs Near a Degenerate Stationary Point Victor Edneral Valery G. Romanovski 97

Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models Alexander A. Gusev Ochbadrakh Chuluunbaatar Vladimir P. Gerdt Vitaly A. Rostovtsev Sergue I. Vinitsky Vladimir L. Derbov Vladislav V. Serov 106

On Reduction of Lagrange Systems Valentin Irtegov Tatyana Titorenko 123

Series Transformations to Improve and Extend Convergence German A. Kalugin David J. Jeffrey 134

Differential Resultant, Computer Algebra and Completely Integrable Dynamical Systems Zoia Kostova Nikolay Kostov Vladimir Gerdjikov 148

Generic, Type-Safe and Object Oriented Computer Algebra Software Heinz Kredel Raphael Jolly 162

Implementing Data Parallel Rational Multiple-Residue Arithmetic in Eden Oleg Lobachev Rita Loogen 178

Fast Generalized Bruhat Decomposition Gennadi Malaschonok 194

Computational Science in Armenia (Invited Talk) H. Marandjian Yu. Shoukourian 203

From Petri Nets to Polynomials: Modeling, Algorithms, and Complexity (Abstract) (Invited Talk) Ernst W. Mayr 204

Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests Winfried Neun Thomas Sturm Stefan Vigerske 205

Term Cancellations in Computing Floating-Point Gröbner Bases Tateaki Sasaki Fujio Kako 220

One Class of Third-Order Linear ODE's S. Yu. Slavyanov 232

GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials Akira Terui 238

Derivation of Explicit Difference Schemes for Ordinary Differential Equations with the Aid of Lagrange-Burmann Expansions Evgenii V. Vorozhtsov 250

Parametric Qualitative Analysis of Ordinary Differential Equations: Computer Algebra Methods for Excluding Oscillations (Extended Abstract) (Invited Talk) Andreas Weber Thomas Sturm Werner M. Seiler Essam O. Abdel-Rahman 267

An Analytical Model for the Probability Characteristics of a Crack Hitting an Encapsulated Self-healing Agent in Concrete Serguey V. Zemskov Henk M. Jonkers Fred J. Vermolen 280

Extending Clause Learning of SAT Solvers with Boolean Gröbner Bases Christoph Zengler Wolfgang Küchlin 293

Author Index 303

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