## Computer Algebra in Scientific Computing: 15th International Workshop, CASC 2013, Berlin, Germany, September 9-13, 2013, ProceedingsVladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov 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

1 | |

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 |

443 | |