Computer Algebra in Scientific Computing

1. Front Matter

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2. Comparison Maps for Relatively Free Resolutions

   • V. Álvarez, J. A. Armario, M. D. Frau, P. Real

   Pages 1-22

3. A Symbolic-Numeric Approach for Solving the Eigenvalue Problem for the One-Dimensional Schrödinger Equation

   • I. N. Belyaeva, N. A. Chekanov, A. A. Gusev, V. A. Rostovtsev, S. I. Vinitsky

   Pages 23-32

4. Reducing Computational Costs in the Basic Perturbation Lemma

   • Ainhoa Berciano, María José Jiménez, Pedro Real

   Pages 33-48

5. Solving Algorithmic Problems on Orders and Lattices by Relation Algebra and RelView

   • Rudolf Berghammer

   Pages 49-63

6. Intervals, Syzygies, Numerical Gröbner Bases: A Mixed Study

   • Marco Bodrato, Alberto Zanoni

   Pages 64-76

7. Application of Computer Algebra for Construction of Quasi-periodic Solutions for Restricted Circular Planar Three Body Problem

   • V. P. Borunov, Yu. A. Ryabov, O. V. Surkov

   Pages 77-88

8. Efficient Preprocessing Methods for Quantifier Elimination

   • Christopher W. Brown, Christian Gross

   Pages 89-100

9. Symbolic and Numerical Calculation of Transport Integrals for Some Organic Crystals

   • A. Casian, R. Dusciac, V. Dusciac, V. Patsiuk

   Pages 101-108

10. On the Provably Tight Approximation of Optimal Meshing for Non-convex Regions

    • Dmytro Chibisov, Victor Ganzha, Ernst W. Mayr, Evgenii V. Vorozhtsov

    Pages 109-128

11. Providing Modern Software Environments to Computer Algebra Systems

    • Svetlana Cojocaru, Ludmila Malahova, Alexander Colesnicov

    Pages 129-140

12. The Instability of the Rhombus-Like Central Configurations in Newton 9-Body Problem

    • D. Diarova, N. I. Zemtsova

    Pages 141-148

13. Algorithmic Invariants for Alexander Modules

    • Jesús Gago-Vargas, Isabel Hartillo-Hermoso, José María Ucha-Enríquez

    Pages 149-154

14. Sudokus and Gröbner Bases: Not Only a Divertimento

    • Jesús Gago-Vargas, Isabel Hartillo-Hermoso, Jorge Martín-Morales, José María Ucha-Enríquez

    Pages 155-165

15. Simplicial Perturbation Techniques and Effective Homology

    • Rocio Gonzalez-Díaz, Belén Medrano, Javier Sánchez-Peláez, Pedro Real

    Pages 166-177

16. Numerical Study of Stability Domains of Hamiltonian Equation Solutions

    • E. A. Grebenicov, D. Kozak-Skoworodkin, D. M. Diarova

    Pages 178-191

17. Numeric-Symbolic Computations in the Study of Central Configurations in the Planar Newtonian Four-Body Problem

    • Evgenii A. Grebenikov, Ersain V. Ikhsanov, Alexander N. Prokopenya

    Pages 192-204

18. A Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for a Hydrogen Atom in Magnetic Field

    • Alexander Gusev, Vladimir Gerdt, Michail Kaschiev, Vitaly Rostovtsev, Valentin Samoylov, Tatyana Tupikova et al.

    Pages 205-218

19. On Decomposition of Tame Polynomials and Rational Functions

    • Jaime Gutierrez, David Sevilla

    Pages 219-226

20. Newton Polyhedra and an Oscillation Index of Oscillatory Integrals with Convex Phases

    • Isroil A. Ikromov, Akhmadjon Soleev

    Pages 227-239

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.

• Gröbner bases
• Homological algebra
• algebra
• algebraic computation
• cellular automata
• computational geometry
• computer algebra
• computer algebra systems
• computer graphics
• computeralgebra
• geometric algebra
• nanosciences
• nanotechnology
• newton polyhedra
• quant
• algorithm analysis and problem complexity

• Institute of Informatics, Technische Universität München, Garching, Germany

  Victor G. Ganzha, Ernst W. Mayr

• Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

  Evgenii V. Vorozhtsov

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