Computer Algebra in Scientific Computing
13th International Workshop, CASC 2011, Kassel, Germany, September 5-9, 2011. Proceedings
Published on 1. September 2011
XI, 359 pages
978-3-642-23568-9 (ISBN)
Description
This book constitutes the refereed proceedings of the 13th International Workshop on Computer Algebra in Scientific Computing, CASC 2011, held in Kassel, Germany, in September 2011. The 26 full papers included in the book were carefully reviewed and selected from numerous submissions. The articles are organized in topical sections on the development of object oriented computer algebra software for the modeling of algebraic structures as typed objects; matrix algorithms; the investigation with the aid of computer algebra; the development of symbolic-numerical algorithms; and the application of symbolic computations in applied problems of physics, mechanics, social science, and engineering.
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Vladimir P. Gerdt | Wolfram Koepf | Ernst W. Mayr
Computer Algebra in Scientific Computing
13th International Workshop, CASC 2011, Kassel, Germany, September 5-9, 2011. Proceedings
Book
08/2011
Springer
€53.49
Shipment within 7-9 days
Content
- Title
- Preface
- Organization
- Table of Contents
- A Recurrent Method for Constructing Irreducible Polynomials over Finite Fields
- Introduction
- Preliminaries
- Irreducibility of the Polynomial Composition
- Recurrent Method
- References
- Higher-Order Linear Differential Systems with Truncated Coefficients
- Introduction
- The Case of Scalar Equations
- The System Case
- Undecidability in the General Case
- Some Particular Decidable Cases
- Implementation
- Conclusion
- References
- Topology of Families of Implicit Algebraic Surfaces Depending on a Parameter
- Introduction
- Statement of the Main Result
- Special Cases
- Proof of the Main Result
- Open Questions
- References
- A Modular Approach for Beam Lines Design
- Introduction
- Matrix Presentation for LEGO Objects
- The Basic Concepts - The Ordinary Differential Equations
- The Basic Concepts - The Hamiltonian Formalism
- Particle Beam Presentation
- The Time Evolution of LEGO Objects
- Auxiliary LEGO Objects
- Computational Experiments - Mass-to-Charge Ratio Separator Design Problem
- References
- Computations on Simple Games Using RelView
- Introduction
- Relational Preliminaries
- The Computer Algebra System RelView
- Relational Models of Simple Games
- Three Applications Concerning Power of Players
- Conclusions
- References
- On the Regularity Property of Differential Polynomials Modulo Regular Differential Chains
- Introduction
- Basics of Differential Algebra
- The Normal Form of a Rational Differential Fraction
- On the Regularity Property of Polynomials
- On the Regularity Property of Differential Polynomials
- References
- Chemical Reaction Systems, Computer Algebra and Systems Biology
- Introduction
- Deterministic Modeling
- Approximating Models
- Reducing and Reparametrizing Models
- Stochastic Modeling
- Analysis of Statistical Moments
- Conclusion
- References
- On the Stability of Equilibrium Positions in the Circular Restricted Four-Body Problem
- Introduction
- Equilibrium Solutions and Their Linear Stability
- Normalization of the Third-Order Term H$_3$
- Normalizing the Fourth-Order Term H$_4$
- Stability Analysis in the Case of f = 0
- Conclusion
- References
- Semi-algebraic Description of the Equilibria of Dynamical Systems
- Introduction
- On the Complex Roots of a Univariate Polynomial
- Hurwitz Determinants and Stability of Hyperbolic Equilibria of Dynamical System
- Hurwitz Determinants and Subresultant Sequences
- Hurwitz Determinants and Symmetric Roots
- Stability of Hyperbolic Equilibria in View of Bifurcation
- Comprehensive Triangular Decomposition of Parametric Semi-algebraic Systems
- Disjoint Squarefree Comprehensive Triangular Decomposition
- Comprehensive Triangular Decomposition of a Parametric Semi-1lgebraic System
- Conclusion
- References
- Normal Forms of Two p : -q Resonant Polynomial Vector Fields
- Introduction
- Preliminaries
- D-isochronicity of Two Systems
- Concluding Remarks
- References
- On Muldowney's Criteria for Polynomial Vector Fields with Constraints
- Introduction and Preliminaries
- The Bendixson-Dulac Criterion for 2-Dimensional Vector Fields
- Muldowney's Extensions of the Bendixson-Dulac Criterion to Higher Dimensions
- Case Studies
- The SIRS Epidemiological Model
- Computations on the 3D Model
- A Model of Viral Dynamics
- References
- Knowledge-Based Automatic Generation of Partitioned Matrix Expressions
- Introduction
- Input to the System
- Pattern Learning
- Partitioning and Inheritance
- Operands Partitioning and Direct Inheritance
- Theorem-Aware Inheritance
- Combining the Partitionings
- Automation
- Matrix Arithmetic and Pattern Matching
- Conclusions
- References
- Involutive Division Generated by an Antigraded Monomial Ordering
- Introduction
- Preliminaries
- Pair Divisions Generated by Total Monomial Orderings
- Heuristical Superiority of alex-division over Janet Division
- Conclusion and Future Work
- References
- Symbolic-Numerical Algorithms to Solve the Quantum Tunneling Problem for a Coupled Pair of Ions
- Introduction
- Problem Statement
- Formulation of BVP for a Set of the Kantorovich ODEs
- Benchmark Calculation of Penetration Coefficient
- Conclusion
- References
- Symbolic-Numeric Investigation of the Aerodynamic Forces Influence on Satellite Dynamics
- Introduction
- Equations of Motion
- Equilibrium Orientations of a Satellite
- Stability Analysis of Equilibria
- Conclusion
- References
- Practical Divide-and-Conquer Algorithms for Polynomial Arithmetic
- Polynomial Composition
- Horner's Method
- Divide and Conquer Algorithm
- Practical Timings
- Divide and Conquer Division
- Description of the Short Division Algorithm
- Mulders' vs Divide-conquer-div-short-improved
- Comparison with other Implementations
- Conclusions
- References
- Fast and Robust Symbolic Model Order Reduction with Analog Insydes
- Introduction
- Symbolic Model Order Reduction
- Transient Symbolic Model Order Reduction
- Numerical Advantages due to Sequential Equations
- Example
- Conclusion
- References
- On Invariant Manifolds of Lagrange Systems
- Introduction
- The Case of the Linear Routh System
- Investigation of Stability of the Invariant Manifolds
- On Lagrange Systems with n & 2 Positional Coordinates
- The Case of the Nonlinear Routh System
- Conclusion
- References
- Construction of Explicit Optimal Value Functions by a Symbolic-Numeric Cylindrical Algebraic Decomposition
- Introduction
- Parametric Optimization
- Symbolic Approach to Parametric Optimization
- Solution Approach Based on Cylindrical Algebraic Decomposition
- Cylindrical Algebraic Decomposition and Quantifier Elimination
- Parametric Optimization by a Specialized CAD
- Computational Examples
- Illustrative Examples
- Dynamic Programming
- Conclusion
- References
- Convection in a Porous Medium and Mimetic Scheme in Polar Coordinates
- Governing Equations and the Cosymmetry
- Finite-Difference Scheme
- Approximation of the Buoyancy Term
- Approximation of the Jacobian
- Computation of the Family of Steady States
- Numerical Results
- Cosymmetric Family of Steady States for Trapezoidal Enclosure
- Cosymmetric Family of Steady States for Semi-ring
- Preservation of Cosymmetry
- Summary
- References
- Computations in Finite Groups and Quantum Physics
- Introduction
- Dynamical Systems and Quantum Evolution
- Groups, Numbers and Representations
- Finite Quantum Systems
- Reducing Quantum Dynamics to Permutations
- Connection with Observation: The Born Rule
- Example: Group of Permutations of Three Things
- Finite Symmetry Groups in Particle Physics
- Conclusion
- References
- Regular and Singular Boundary Problems in Maple
- Introduction
- Integro-Differential Operators
- Regular Boundary Problems in Maple
- Singular Boundary Problems
- Outlook
- References
- Algebraic Structures as Typed Objects
- Introduction
- Related Work
- Outline
- Algebraic Structures as Typed Objects
- Ring Elements and Ring Factories
- Algorithms and Factories
- Algebraic and Transcendental Field Extensions
- Real Algebraic Numbers and Complex Algebraic Numbers
- Algebraic Structures in Interactive Scripting Interpreters
- Problems
- Generic Types and Sub-classes
- Dependent Types
- Package Structure
- Conclusions
- References
- On Two-Generated Non-commutative Algebras Subject to the Affine Relation
- Preliminaries
- Main Theorem and Applications
- Operator Algebras and Model Algebras
- Binomial Theorems
- Application in Computer Algebra Implementation
- Centers and Ring-Theoretic Properties of Model Algebras
- References
- Acceleration of the Inversion of Triangular Toeplitz Matrices and Polynomial Division
- Introduction
- Our Subjects
- Previous Work
- Our Progress
- Organization of Our Paper
- Preliminaries
- Definitions and Basic Facts
- Polynomial Reciprocal and Triangular Toeplitz Inversion
- Linking Toeplitz Matrix and Polynomial Computation
- Divide-and-Conquer for Triangular Toeplitz Inversion
- Our Speedup
- Triangular Toeplitz Speedup
- Further Speedup for Banded Triangular Toeplitz Matrices
- Some Potential Implementation Advantages
- References
- Computing a Basin of Attraction to a Target Region by Solving Bilinear Semi-Definite Problems
- Introduction
- Problem Formulation
- Computing a Basin of Attraction
- Framework of our Algorithm
- Implementation Using Bilinear Semi-definite Programming
- Examples
- Conclusion
- References
- Symbolic-Numeric Solution of Ill-Conditioned Polynomial Systems (Survey Talk Overview)
- References
- Symbolic-Manipulation Constructions of Hilbert-Space Metrics in Quantum Mechanics
- Introduction
- Gegenbauerian Quantum N-site Lattices
- The Dieudonné's Equation
- An Interactive Algebraic-solution Technique
- The Case of General N
- The Formulation of Quantum Theory Using an Ad Hoc Triplet of Hilbert Spaces
- The Positive Definiteness of the Metric
- The Gegenbauerian Illustrative Example
- Summary
- References
- Author Index
