Ebook: Computer Algebra in Scientific Computing: 15th International Workshop, CASC 2013, Berlin, Germany, September 9-13, 2013. Proceedings

This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book.

The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.

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Content:
Front Matter....Pages -
On the Dimension of Solution Spaces of Full Rank Linear Differential Systems....Pages 1-9
Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem....Pages 10-29
Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One....Pages 30-45
On Consistency of Finite Difference Approximations to the Navier-Stokes Equations....Pages 46-60
Faster Sparse Interpolation of Straight-Line Programs....Pages 61-74
On Possibility of Additional Solutions of the Degenerate System Near Double Degeneration at the Special Value of the Parameter....Pages 75-87
Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates....Pages 88-99
Highly Scalable Multiplication for Distributed Sparse Multivariate Polynomials on Many-Core Systems....Pages 100-115
From the Product Example to PDE Adjoints, Algorithmic Differentiation and Its Application (Invited Talk)....Pages 116-129
Polynomial Complexity of Solving Systems of Few Algebraic Equations with Small Degrees....Pages 130-135
Computing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations....Pages 136-139
Complexity in Tropical Algebra (Invited Talk)....Pages 140-147
Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Identical Particles with Pair Oscillator Interactions....Pages 148-154
Symbolic-Numerical Investigation of Gyrostat Satellite Dynamics....Pages 155-168
On Stationary Sets of Euler’s Equations on so(3,1) and Their Stability....Pages 169-178
An Effective Implementation of a Special Quantifier Elimination for a Sign Definite Condition by Logical Formula Simplification....Pages 179-193
Categories as Type Classes in the Scala Algebra System....Pages 194-208
Generalized Bruhat Decomposition in Commutative Domains....Pages 209-218
Automatic Parallel Library Generation for General-Size Modular FFT Algorithms....Pages 219-230
Extended QRGCD Algorithm....Pages 231-242
Polynomial Evaluation and Interpolation and Transformations of Matrix Structures....Pages 243-256
A Note on the Need for Radical Membership Checking in Mechanical Theorem Proving in Geometry....Pages 257-272
A Symbolic Approach to Boundary Problems for Linear Partial Differential Equations....Pages 273-287
Towards Industrial Application of Approximate Computer Algebra....Pages 288-300
A Note on Sekigawa’s Zero Separation Bound....Pages 301-314
Applications of Symbolic Calculations and Polynomial Invariants to the Classification of Singularities of Differential Systems....Pages 315-330
Singularities of Implicit Differential Equations and Static Bifurcations....Pages 331-339
A Quantum Measurements Model of Hydrogen-Like Atoms in Maple....Pages 340-354
CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of 3D Navier–Stokes Equations....Pages 355-368
Construction of Classes of Irreducible Bivariate Polynomials....Pages 369-380
Algebraic Attacks Using IP-Solvers....Pages 381-392
Stationary Points for the Family of Fermat–Torricelli–Coulomb-Like Potential Functions....Pages 393-400
Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Tunneling of Clusters through Repulsive Barriers....Pages 401-411
Back Matter....Pages 412-426
....Pages 427-442