Ebook: Computer Algebra in Scientific Computing: 9th International Workshop, CASC 2006, Chişinău, Moldova, September 11-15, 2006. Proceedings

This volume contains revised versions of the papers submitted to the workshop by the participants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers not only various expanding applications of computer algebra to scienti?c computing but also the computer algebra systems themselves and the CA algorithms. The eight earlier CASC conferences, CASC 1998, CASC 1999, CASC 2000, CASC 2001, CASC 2002, CASC 2003, CASC 2004, and CASC 2005 were held, - spectively, in St. Petersburg, Russia, in Munich, Germany, in Samarkand, Uzb- istan, in Konstanz, Germany, in Crimea, Ukraine, in Passau, Germany, in St. Petersburg, Russia, and in Kalamata, Greece, and they proved to be successful. It was E. A. Grebenikow (Computing Center of the Russian Academy of S- ences, Moscow) who drew our attention to the group of mathematicians and c- puter scientists at the Academy of Sciences of Moldova conducting research in the ?eld of computer algebra. We were impressed that this group not only is concerned with applications of CA methods to problems of scienti?c computing but also c- ries out research on the fundamental principles underlying the current computer algebra systems themselves, see also their papers in the present proceedings v- ume. It was therefore decided to organize the 9th workshop on Computer Algebra in Scienti?c Computing, CASC 2006, in Chi¸ sin? au, the capital of Moldova.

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This book constitutes the refereed proceedings of the 9th International Workshop on Computer Algebra in Scientific Computing, CASC 2006, held in Chisinau, Moldova, in September 2006.

The 25 revised full papers presented together with 2 invited papers were carefully reviewed and selected from numerous submissions. The papers cover not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms. Topics addressed are studies in Gr?bner bases, polynomial algebra, homological algebra, quantifier elimination, the applications of computer algebra systems in the field of the solution of differential equations, celestial mechanics, Newton polyhedra, mathematical physics, nuclear physics, and fluid dynamics. Novel themes also addressed are the application of computer algebra techniques in the field of nanosciences and nanotechnology as well as the application of CA methods to cellular automata with symmetrical local rules.

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This book constitutes the refereed proceedings of the 9th International Workshop on Computer Algebra in Scientific Computing, CASC 2006, held in Chisinau, Moldova, in September 2006.

The 25 revised full papers presented together with 2 invited papers were carefully reviewed and selected from numerous submissions. The papers cover not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms. Topics addressed are studies in Gr?bner bases, polynomial algebra, homological algebra, quantifier elimination, the applications of computer algebra systems in the field of the solution of differential equations, celestial mechanics, Newton polyhedra, mathematical physics, nuclear physics, and fluid dynamics. Novel themes also addressed are the application of computer algebra techniques in the field of nanosciences and nanotechnology as well as the application of CA methods to cellular automata with symmetrical local rules.

Content:
Front Matter....Pages -
Comparison Maps for Relatively Free Resolutions....Pages 1-22
A Symbolic-Numeric Approach for Solving the Eigenvalue Problem for the One-Dimensional Schr?dinger Equation....Pages 23-32
Reducing Computational Costs in the Basic Perturbation Lemma....Pages 33-48
Intervals, Syzygies, Numerical Gr?bner Bases: A Mixed Study....Pages 49-63
Application of Computer Algebra for Construction of Quasi-periodic Solutions for Restricted Circular Planar Three Body Problem....Pages 64-76
Efficient Preprocessing Methods for Quantifier Elimination....Pages 77-88
Symbolic and Numerical Calculation of Transport Integrals for Some Organic Crystals....Pages 89-100
On the Provably Tight Approximation of Optimal Meshing for Non-convex Regions....Pages 101-108
Providing Modern Software Environments to Computer Algebra Systems....Pages 109-128
The Instability of the Rhombus-Like Central Configurations in Newton 9-Body Problem....Pages 129-140
Algorithmic Invariants for Alexander Modules....Pages 141-148
Simplicial Perturbation Techniques and Effective Homology....Pages 149-154
Numerical Study of Stability Domains of Hamiltonian Equation Solutions....Pages 155-165
Numeric-Symbolic Computations in the Study of Central Configurations in the Planar Newtonian Four-Body Problem....Pages 166-177
A Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for a Hydrogen Atom in Magnetic Field....Pages 178-191
On Decomposition of Tame Polynomials and Rational Functions....Pages 192-204
Newton Polyhedra and an Oscillation Index of Oscillatory Integrals with Convex Phases....Pages 205-218
Cellular Automata with Symmetric Local Rules....Pages 219-226
Parallel Laplace Method with Assured Accuracy for Solutions of Differential Equations by Symbolic Computations....Pages 227-239
On Connection Between Constructive Involutive Divisions and Monomial Orderings....Pages 240-250
A Symbolic-Numeric Approach to Tube Modeling in CAD Systems....Pages 251-260
Inequalities on Upper Bounds for Real Polynomial Roots....Pages 261-278
New Domains for Applied Quantifier Elimination....Pages 279-283
Algorithms for Symbolic Polynomials....Pages 284-294
Testing Mersenne Primes with Elliptic Curves....Pages 295-301
Back Matter....Pages 302-302
....Pages 303-312