Computer Algebra in Scientific Computing

1. Front Matter

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2. On Polynomial Solutions of Linear Partial Differential and (q-)Difference Equations

   • S. A. Abramov, M. Petkovšek

   Pages 1-11

3. An Algebraic Characterization of Rainbow Connectivity

   • Prabhanjan Ananth, Ambedkar Dukkipati

   Pages 12-21

4. Application of the Method of Asymptotic Solution to One Multi-Parameter Problem

   • Alexander Batkhin

   Pages 22-33

5. A New Algorithm for Long Integer Cube Computation with Some Insight into Higher Powers

   • Marco Bodrato, Alberto Zanoni

   Pages 34-46

6. Lightweight Abstraction for Mathematical Computation in Java

   • Pavel Bourdykine, Stephen M. Watt

   Pages 47-59

7. Calculation of Normal Forms of the Euler–Poisson Equations

   • Alexander D. Bruno, Victor F. Edneral

   Pages 60-71

8. Stability of Equilibrium Positions in the Spatial Circular Restricted Four-Body Problem

   • Dzmitry A. Budzko, Alexander N. Prokopenya

   Pages 72-83

9. Computing Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates

   • Hassan Errami, Werner M. Seiler, Markus Eiswirth, Andreas Weber

   Pages 84-97

10. Comprehensive Involutive Systems

    • Vladimir Gerdt, Amir Hashemi

    Pages 98-116

11. A Polynomial-Time Algorithm for the Jacobson Form of a Matrix of Ore Polynomials

    • Mark Giesbrecht, Albert Heinle

    Pages 117-128

12. The Resonant Center Problem for a 2:-3 Resonant Cubic Lotka–Volterra System

    • Jaume Giné, Colin Christopher, Mateja Prešern, Valery G. Romanovski, Natalie L. Shcheglova

    Pages 129-142

13. Complexity of Solving Systems with Few Independent Monomials and Applications to Mass-Action Kinetics

    • Dima Grigoriev, Andreas Weber

    Pages 143-154

14. Symbolic-Numerical Calculations of High-|m| Rydberg States and Decay Rates in Strong Magnetic Fields

    • Alexander Gusev, Sergue Vinitsky, Ochbadrakh Chuluunbaatar, Vladimir Gerdt, Luong Le Hai, Vitaly Rostovtsev

    Pages 155-171

15. Quasi-stability versus Genericity

    • Amir Hashemi, Michael Schweinfurter, Werner M. Seiler

    Pages 172-184

16. Invariant Theory: Applications and Computations

    • Gregor Kemper

    Pages 185-185

17. Local Generic Position for Root Isolation of Zero-Dimensional Triangular Polynomial Systems

    • Jia Li, Jin-San Cheng, Elias P. Tsigaridas

    Pages 186-197

18. On Fulton’s Algorithm for Computing Intersection Multiplicities

    • Steffen Marcus, Marc Moreno Maza, Paul Vrbik

    Pages 198-211

19. A Note on the Space Complexity of Fast D-Finite Function Evaluation

    • Marc Mezzarobba

    Pages 212-223

20. Inversion Modulo Zero-Dimensional Regular Chains

    • Marc Moreno Maza, Éric Schost, Paul Vrbik

    Pages 224-235

This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2012, held in Maribor, Slovenia, in September 2012. The 28 full papers presented were carefully reviewed and selected for inclusion in this book. One of the main themes of the CASC workshop series, namely polynomial algebra, is represented by contributions devoted to new algorithms for computing comprehensive Gröbner and involutive systems, parallelization of the Gröbner bases computation, the study of quasi-stable polynomial ideals, new algorithms to compute the Jacobson form of a matrix of Ore polynomials, a recursive Leverrier algorithm for inversion of dense matrices whose entries are monic polynomials, root isolation of zero-dimensional triangular polynomial systems, optimal computation of the third power of a long integer, investigation of the complexity of solving systems with few independent monomials, the study of ill-conditioned polynomial systems, a method for polynomial root-finding via eigen-solving and randomization, an algorithm for fast dense polynomial multiplication with Java using the new opaque typed method, and sparse polynomial powering using heaps.

• complexity
• holonomic functions
• long integers
• parallel algorithms
• polynomial factorization
• algorithm analysis and problem complexity

• Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), Dubna, Russia

  Vladimir P. Gerdt

• Institut für Mathematik, Universität Kassel, Kassel, Germany

  Wolfram Koepf

• Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Garching, Germany

  Ernst W. Mayr

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

  Evgenii V. Vorozhtsov

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