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

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Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov
Springer, Aug 15, 2013 - Computers - 443 pages
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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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Contents

On the Dimension of Solution Spaces of Full Rank Linear Differential Systems
1
Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic nroots Problem
10
Computing the Limit Points of the Quasicomponent of a Regular Chain in Dimension One
30
On Consistency of Finite Difference Approximations to the NavierStokes Equations
46
Faster Sparse Interpolation of StraightLine Programs
61
On Possibility of Additional Solutions of the Degenerate System Near Double Degeneration at the Special Value of the Parameter
75
Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates
88
Highly Scalable Multiplication for Distributed Sparse Multivariate Polynomials on ManyCore Systems
100
Generalized Bruhat Decomposition in Commutative Domains
231
Automatic Parallel Library Generation for GeneralSize Modular FFT Algorithms
243
Extended QRGCD Algorithm
257
Polynomial Evaluation and Interpolation and Transformations of Matrix Structures
273
A Note on the Need for Radical Membership Checking in Mechanical Theorem Proving in Geometry
288
A Symbolic Approach to Boundary Problems for Linear Partial Differential Equations Applications to the Completely Reducible Case of the Cauchy ...
301
Towards Industrial Application of Approximate Computer Algebra
315
A Note on Sekigawas Zero Separation Bound
331

Simulation of Quantum Error Correction with Mathematica
116
From the Product Example to PDE Adjoints Algorithmic Differentiation and Its Application Invited Talk
130
Polynomial Complexity of Solving Systems of Few Algebraic Equations with Small Degrees
136
Computing Divisors and Common Multiples of Quasilinear Ordinary Differential Equations
140
Complexity in Tropical Algebra Invited Talk
148
Identical Particles with Pair Oscillator Interactions
155
SymbolicNumerical Investigation of Gyrostat Satellite Dynamics
169
On Stationary Sets of Eulers Equations on so3 1 and Their Stability
179
An Effective Implementation of a Special Quantifier Elimination for a Sign Definite Condition by Logical Formula Simplification
194
Categories as Type Classes in the Scala Algebra System
209
Enumeration of Schur Rings over the Group A5
219
Applications of Symbolic Calculations and Polynomial Invariants to the Classification of Singularities of Differential Systems
340
Singularities of Implicit Differential Equations and Static Bifurcations
355
A Quantum Measurements Model of HydrogenLike Atoms in Maple
369
CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of 3D NavierStokes Equations
381
Construction of Classes of Irreducible Bivariate Polynomials
393
Algebraic Attacks Using IPSolvers
401
Stationary Points for the Family of FermatTorricelliCoulombLike Potential Functions
412
Tunneling of Clusters through Repulsive Barriers
427
Author Index
443
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