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Computer algebra in scientific computing : 15th International Workshop, CASC 2013, Berlin, Germany, September 9-13, 2013 : proceedings / Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.).

By: (15th : CASC (Workshop : 2001- ) (15th : 2013 : Berlin, Germany)Contributor(s): Gerdt, V. P [editor.] | Koepf, Wolfram [editor.] | Mayr, Ernst [editor.] | Vorozhtsov, E. V. (Evgenii Vasilʹevich), 1946- [editor.]Material type: TextTextSeries: Serienbezeichnung | Lecture notes in computer science ; 8136.Publisher: Cham : Springer, [2013]Copyright date: ©2013Description: 1 online resource (xvi, 443 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783319022970; 3319022970; 3319022962; 9783319022963Subject(s): Computer science -- Mathematics -- Congresses | Science -- Data processing -- Congresses | Mathematics | Science | Electronic Data Processing | Computer science -- Mathematics | Science -- Data processingGenre/Form: Electronic books. | Congress. | Electronic books. | Ebook. | Conference papers and proceedings. Additional physical formats: Printed edition:: No titleDDC classification: 004.01/51 LOC classification: QA76.9.M35 | I58 2013NLM classification: QA 76.9.M35Online resources: Click here to access online
Contents:
On the Dimension of Solution Spaces of Full Rank Linear Differential Systems / S.A. Abramov, M.A. Barkatou -- Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem / Danko Adrovic, Jan Verschelde -- Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One / Parisa Alvandi, Changbo Chen, Marc Moreno Maza -- On Consistency of Finite Difference Approximations to the Navier-Stokes Equations / Pierluigi Amodio, Yuri Blinkov, Vladimir Gerdt -- Faster Sparse Interpolation of Straight-Line Programs / Andrew Arnold, Mark Giesbrecht, Daniel S. Roche -- On Possibility of Additional Solutions of the Degenerate System Near Double Degeneration at the Special Value of the Parameter / Alexander D. Bruno, Victor F. Edneral -- Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates / Hassan Errami, Markus Eiswirth, Dima Grigoriev.
Highly Scalable Multiplication for Distributed Sparse Multivariate Polynomials on Many-Core Systems / Mickaël Gastineau, Jacques Laskar -- Simulation of Quantum Error Correction with Mathematica / Vladimir P. Gerdt, Alexander N. Prokopenya -- From the Product Example to PDE Adjoints, Algorithmic Differentiation and Its Application (Invited Talk) / Andreas Griewank -- Polynomial Complexity of Solving Systems of Few Algebraic Equations with Small Degrees / Dima Grigoriev -- Computing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations / Dima Grigoriev, Fritz Schwarz -- Complexity in Tropical Algebra (Invited Talk) / Dima Grigoriev -- Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Identical Particles with Pair Oscillator Interactions / Alexander Gusev, Sergue Vinitsky -- Symbolic-Numerical Investigation of Gyrostat Satellite Dynamics / Sergey A. Gutnik, Vasily A. Sarychev -- On Stationary Sets of Euler's Equations on so(3,1) and Their Stability / Valentin Irtegov, Tatyana Titorenko.
An Effective Implementation of a Special Quantifier Elimination for a Sign Definite Condition by Logical Formula Simplification / Hidenao Iwane, Hiroyuki Higuchi, Hirokazu Anai -- Categories as Type Classes in the Scala Algebra System / Raphaël Jolly -- Enumeration of Schur Rings over the Group A 5 / Mikhail Klin, Matan Ziv-Av -- Generalized Bruhat Decomposition in Commutative Domains / Gennadi Malaschonok -- Automatic Parallel Library Generation for General-Size Modular FFT Algorithms / Lingchuan Meng, Jeremy Johnson -- Extended QRGCD Algorithm / Kosaku Nagasaka, Takaaki Masui -- Polynomial Evaluation and Interpolation and Transformations of Matrix Structures / Victor Y. Pan -- A Note on the Need for Radical Membership Checking in Mechanical Theorem Proving in Geometry / Eugenio Roanes-Lozano, Eugenio Roanes-Macías -- A Symbolic Approach to Boundary Problems for Linear Partial Differential Equations / Markus Rosenkranz, Nalina Phisanbut -- Towards Industrial Application of Approximate Computer Algebra / Tateaki Sasaki, Daiju Inaba, Fujio Kako.
A Note on Sekigawa's Zero Separation Bound / Stefan Schirra -- Applications of Symbolic Calculations and Polynomial Invariants to the Classification of Singularities of Differential Systems / Dana Schlomiuk, Nicolae Vulpe -- Singularities of Implicit Differential Equations and Static Bifurcations / Werner M. Seiler -- A Quantum Measurements Model of Hydrogen-Like Atoms in Maple / L. Sevastianov, A. Zorin, A. Gorbachev -- CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of 3D Navier-Stokes Equations / Vasily P. Shapeev, Evgenii V. Vorozhtsov -- Construction of Classes of Irreducible Bivariate Polynomials / Doru Ştefănescu -- Algebraic Attacks Using IP-Solvers / Ehsan Ullah -- Stationary Points for the Family of Fermat-Torricelli-Coulomb-Like Potential Functions / Alexei Yu. Uteshev, Marina V. Yashina -- Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Tunneling of Clusters through Repulsive Barriers / Sergue Vinitsky, Alexander Gusev.
Summary: 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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On the Dimension of Solution Spaces of Full Rank Linear Differential Systems / S.A. Abramov, M.A. Barkatou -- Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem / Danko Adrovic, Jan Verschelde -- Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One / Parisa Alvandi, Changbo Chen, Marc Moreno Maza -- On Consistency of Finite Difference Approximations to the Navier-Stokes Equations / Pierluigi Amodio, Yuri Blinkov, Vladimir Gerdt -- Faster Sparse Interpolation of Straight-Line Programs / Andrew Arnold, Mark Giesbrecht, Daniel S. Roche -- On Possibility of Additional Solutions of the Degenerate System Near Double Degeneration at the Special Value of the Parameter / Alexander D. Bruno, Victor F. Edneral -- Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates / Hassan Errami, Markus Eiswirth, Dima Grigoriev.

Highly Scalable Multiplication for Distributed Sparse Multivariate Polynomials on Many-Core Systems / Mickaël Gastineau, Jacques Laskar -- Simulation of Quantum Error Correction with Mathematica / Vladimir P. Gerdt, Alexander N. Prokopenya -- From the Product Example to PDE Adjoints, Algorithmic Differentiation and Its Application (Invited Talk) / Andreas Griewank -- Polynomial Complexity of Solving Systems of Few Algebraic Equations with Small Degrees / Dima Grigoriev -- Computing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations / Dima Grigoriev, Fritz Schwarz -- Complexity in Tropical Algebra (Invited Talk) / Dima Grigoriev -- Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Identical Particles with Pair Oscillator Interactions / Alexander Gusev, Sergue Vinitsky -- Symbolic-Numerical Investigation of Gyrostat Satellite Dynamics / Sergey A. Gutnik, Vasily A. Sarychev -- On Stationary Sets of Euler's Equations on so(3,1) and Their Stability / Valentin Irtegov, Tatyana Titorenko.

An Effective Implementation of a Special Quantifier Elimination for a Sign Definite Condition by Logical Formula Simplification / Hidenao Iwane, Hiroyuki Higuchi, Hirokazu Anai -- Categories as Type Classes in the Scala Algebra System / Raphaël Jolly -- Enumeration of Schur Rings over the Group A 5 / Mikhail Klin, Matan Ziv-Av -- Generalized Bruhat Decomposition in Commutative Domains / Gennadi Malaschonok -- Automatic Parallel Library Generation for General-Size Modular FFT Algorithms / Lingchuan Meng, Jeremy Johnson -- Extended QRGCD Algorithm / Kosaku Nagasaka, Takaaki Masui -- Polynomial Evaluation and Interpolation and Transformations of Matrix Structures / Victor Y. Pan -- A Note on the Need for Radical Membership Checking in Mechanical Theorem Proving in Geometry / Eugenio Roanes-Lozano, Eugenio Roanes-Macías -- A Symbolic Approach to Boundary Problems for Linear Partial Differential Equations / Markus Rosenkranz, Nalina Phisanbut -- Towards Industrial Application of Approximate Computer Algebra / Tateaki Sasaki, Daiju Inaba, Fujio Kako.

A Note on Sekigawa's Zero Separation Bound / Stefan Schirra -- Applications of Symbolic Calculations and Polynomial Invariants to the Classification of Singularities of Differential Systems / Dana Schlomiuk, Nicolae Vulpe -- Singularities of Implicit Differential Equations and Static Bifurcations / Werner M. Seiler -- A Quantum Measurements Model of Hydrogen-Like Atoms in Maple / L. Sevastianov, A. Zorin, A. Gorbachev -- CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of 3D Navier-Stokes Equations / Vasily P. Shapeev, Evgenii V. Vorozhtsov -- Construction of Classes of Irreducible Bivariate Polynomials / Doru Ştefănescu -- Algebraic Attacks Using IP-Solvers / Ehsan Ullah -- Stationary Points for the Family of Fermat-Torricelli-Coulomb-Like Potential Functions / Alexei Yu. Uteshev, Marina V. Yashina -- Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Tunneling of Clusters through Repulsive Barriers / Sergue Vinitsky, Alexander Gusev.

Includes bibliographical references and index.

Online resource; title from PDF title page (SpringerLink, viewed September 26, 2013).

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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