Computer Algebra in Scientific Computing [[electronic resource] ] : 17th International Workshop, CASC 2015, Aachen, Germany, September 14-18, 2015, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov

• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
• Edizione: 1st ed. 2015.
• Descrizione fisica: 1 online resource (XIII, 494 p. 75 illus. in color.)
• Disciplina: 005.1
• Soggetto topico: Algorithms; Computer science—Mathematics; Discrete mathematics; Computer arithmetic and logic units; Discrete Mathematics in Computer Science; Symbolic and Algebraic Manipulation; Arithmetic and Logic Structures
• Persona (resp. second.): GerdtVladimir P; KoepfWolfram; SeilerWerner M; VorozhtsovEvgenii V
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: Intro -- Preface -- Organization -- Contents -- Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients -- 1 Introduction -- 2 The Problem -- 3 The Reasoning Behind the Algorithm -- 3.1 The Resolving Equation and Matrix -- 3.2 The Minimal Subspace Containing All Solutions with yi=0 -- 3.3 The Use of RNF -- 3.4 The Space of Solutions with yi=0 -- 3.5 When k=m -- 3.6 Selection of yi -- 4 The Algorithm -- 5 On the Resolving Procedure -- 6 Implementation and Experiments -- 6.1 Implementation -- 6.2 Some Experiments -- 6.3 Comparison with the Cyclic Vector Approach -- Janet Bases and Resolutions in CoCoALib -- 1 Introduction -- 2 Involutive Bases and Free Resolutions -- 3 Free Resolutions with Janet Bases -- 4 Benchmarks -- Regular Chains under Linear Changesof Coordinates and Applications -- 1 Introduction -- 2 Preliminaries -- 3 Algorithm for Linear Change of Coordinates -- 4 Noether Normalization and Regular Chains -- 5 Applications of Random Linear Changes of Coordinates -- 6 On the Computation of lim(W(T)) and sat(T) -- 7 Conclusion -- A Standard Basis Free Algorithm for Computing the Tangent Cones of a Space Curve -- 1 Introduction -- 2 Preliminaries -- 2.1 Tangent Cone of a Space Curve -- 2.2 Regular Chains -- 3 Computing Intersection Multiplicities in Higher Dimension -- 4 Computing Tangent Lines as Limits of Secants -- 4.1 An Algorithmic Principle -- 4.2 Algorithm -- 4.3 Equations of Tangent Cones -- 4.4 Examples -- 5 Conclusion -- Research on the Stability of Relative Equilibria of Oblate Axisymmetric Gyrostat by Meansof Symbolic-Numerical Modelling -- 1 Introduction -- 2 Relative Equilibria -- 3 Construction of Symbolical Model and Parametrization of a Problem -- 4 Stability of the Third Class Equilibria -- 4.1 Necessary Conditions of Stability -- 4.2 Stable and Unstable Equilibria. ; 4.3 Gyroscopic Stabilization: Symbolic-Numerical Modelling -- 5 Parametrical Analysis of the Conditions of Gyroscopic Stabilization for Second Class Equilibria -- 6 Conclusion -- A New Approach for Computing Regular Solutions of Linear Difference Systems -- 1 Factorial Series -- 1.1 Definition -- 1.2 Ring Structure -- 1.3 Translation z z + -- 2 The Functions n -- 2.1 Definition -- 2.2 Properties -- 3 Regular Solutions of Linear Difference Systems -- 4 Appendix -- 4.1 Proof of Proposition 1 -- 4.2 Proof of Theorem 1 -- Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation -- 1 Introduction -- 2 Related Work and Alternative Approaches -- 3 Design and Implementation -- 4 Solving by Polynomial Homotopy Continuation -- 4.1 Running a Blackbox Solver -- 4.2 The Scripting Interface phcpy -- 5 Pattern Matching with a Database -- 5.1 The Classification Problem -- 5.2 The Graph Isomorphism Problem -- 5.3 Computing Canonical Graph Labelings With Nauty -- 5.4 Benchmarking the Canonization -- 5.5 Storing Labelings in a Database -- 6 Conclusions -- Finding First Integrals Using Normal Forms Modulo Differential Regular Chains -- 1 Introduction -- 2 Basis of Linear Dependences of Rational Functions -- 2.1 Preliminary Results -- 2.2 Algorithm findKernelBasis -- 2.3 A Variant of findKernelBasis -- 3 Incremental Computation of Linear Dependences -- 3.1 Algorithm incrementalFindDependence -- 3.2 Improvement Using a LU-decomposition -- 3.3 Finding the First Linear Dependence -- 3.4 Complexity of the Linear Algebra -- 4 Application to Finding First Integrals -- 4.1 Basic Differential Algebra -- 4.2 Normal Form Modulo a Differential Regular Chain -- 4.3 Normal Form Modulo a Decomposition -- 4.4 First Integrals in Differential Algebra -- 4.5 Algorithm findAllFirstIntegrals -- 4.6 Complexity -- Simplification of Cylindrical Algebraic Formulas. ; 1 Introduction -- 2 Preliminary -- 3 Motivating Examples -- 4 Algorithm -- 5 Experimentation -- 6 Conclusions -- Quasi-Steady State - Intuition, Perturbation Theory and Algorithmic Algebra -- 1 Introduction -- 2 Transferring Scientific to Mathematical Notions -- 3 Preliminaries and Notation -- 3.1 Lie Derivatives and Invariance Criteria -- 3.2 Singular Perturbations -- 4 The Ad Hoc Approach -- 5 Reduction in the SPT Setting -- 5.1 Conditions -- 5.2 Reduction of Rational Systems -- 5.3 Algorithmic Aspects -- 6 Identifying ``Small Parameters -- 6.1 Definition and Basic Properties -- 6.2 Structure of the TFPV Set -- 6.3 Algorithmic Aspects -- 7 The Ad Hoc Approach Revisited -- 7.1 Basics and Approximation Properties -- 7.2 Polynomial Systems and Algorithmic Aspects -- 8 Conclusion -- Polynomial Complexity Recognizing a Tropical Linear Variety -- Computing Highest-Order Divisors for a Classof Quasi-Linear Partial Differential Equations -- 1 Bound on a Degree of a Divisor -- 2 Algorithm to Find the Algebraic Variety of All the Divisors -- Symbolic Algorithm for Generating Irreducible Bases of Point Groups in the Space of SO(3) Group -- 1 Introduction -- 2 Rotations -- 2.1 Geometric Rotation -- 2.2 Rotation in Functional Spaces -- 3 Intrinsic Group -- 4 Generalized Projection Operators -- 5 Example of Using the Algorithm for the Octahedral Group -- 5.1 Construction of Elements of the Octahedral Group from Its Generators -- 5.2 Construction of Irreducible Representations of the Octahedral Group O in the Cartesian Bases -- 5.3 GPOs Implementation for Standard and Intrinsic Point Groups -- 6 Conclusion -- Symbolic-Numeric Solution of Boundary-Value Problems for the Schrödinger Equation Usingthe Finite Element Method: Scattering Problem and Resonance States -- 1 Introduction -- 2 Formulation of Boundary-Value Problems. ; 2.1 Scattering Problem: The Physical Asymptotic Solutions in Longitudinal Coordinates and the Scattering Matrix -- 3 Generation of Algebraic Problems -- 3.1 The Calculation Scheme for the Solution Matrix h=h -- 3.2 The Calculation Scheme for the Solution Matrix h=h -- 3.3 Algorithm for Calculating the Complex Eigenvalues and Eigenfunctions of Metastable States -- 4 Benchmark Calculations -- 5 Conclusion -- Application of Computer Algebra Methodsto Investigation of Influence of Constant Torque on Stationary Motions of Satellite -- 1 Introduction -- 2 Equations of Motion -- 3 Equilibrium Orientations -- 4 Conclusion -- Bounds for the Condition Number of Polynomials Systems with Integer Coefficients -- 1 Introduction -- 1.1 Our Results -- 1.2 Notation -- 2 Condition Number for Univariate Polynomials -- 3 Condition Number for Polynomial Systems -- 3.1 Multivariate Aggregate Condition Number -- On Invariant Manifolds and Their Stabilityin the Problem of Motion of a Rigid Bodyunder the Influence of Two Force Fields -- 1 Introduction -- 2 Formulation of the Problem -- 3 Finding Invariant Manifolds -- 3.1 Finding the Invariant Manifolds Embedded in One Another -- 3.2 Finding the Enveloping Invariant Manifolds -- 3.3 On Invariant Manifolds under Restrictions on the Constantsof the Problem Integrals -- 4 On the Stability of Stationary Invariant Manifolds -- 5 Conclusion -- Homotopy Analysis Method for StochasticDifferential Equations with Maxima -- 1 Introduction -- 2 The Model -- 3 Homotopy Analysis Method -- 4 Homotopy Analysis Method and Stochastic Differential Equation with Third-Order Nonlinearity -- 5 Concluding Remarks -- On the Topology and Visualization of Plane Algebraic Curves -- 1 Introduction -- 2 Topology Computation for Plane Algebraic Curves -- 2.1 Solving the System {f=fy=0} -- 2.2 Computing the Fibers. ; 2.3 Branch Number Computation and Connection -- 3 Isotopic Meshing for a Plane Curve -- 3.1 Tracing Regular Curve Segments -- 3.2 Error Control for the Meshing of a Plane Curve -- 4 Experiments -- 5 Conclusions -- Piecewise-Quadratics and Reparameterizations for Interpolating Reduced Data -- 1 Introduction -- 2 Problem Formulation and Motivation -- 3 Main Result -- 4 Experiments -- 5 Conclusions -- Parametric Solvable Polynomial Rings and Applications -- 1 Introduction -- 1.1 Related Work -- 1.2 Outline -- 2 Solvable Polynomial Rings -- 2.1 Parametric Solvable Polynomial Rings -- 2.2 Solvable Polynomial Coefficient Rings -- 2.3 Recursive Solvable Polynomial Rings -- 2.4 Solvable Quotient and Residue Rings -- 2.5 Solvable Quotient Rings as Coefficient Rings -- 3 Implementation of Solvable Polynomial Rings -- 3.1 Polynomial Rings -- 3.2 Solvable Polynomial Rings -- 3.3 Recursive Solvable Polynomial Rings -- 3.4 Solvable Quotient and Residue Rings -- 3.5 Solvable Polynomial Rings with Non-commutative Coefficients -- 4 Applications -- 4.1 Comprehensive Gröbner Bases -- 4.2 Gröbner Bases and Applications -- 4.3 Examples -- 4.4 Extension to Free Non-commutative Coefficients -- 5 Conclusions -- Triangular Decomposition of Matrices in a Domain -- 1 Introduction -- 2 Preliminary. Triangular Decomposition in Domain -- 2.1 LDU Algorithm for the Matrix with Nonzero Diagonal Minors Up to the Rank -- 3 Triangular Matrix Decomposition -- 4 LDU Algorithm with Permutation Matrices -- 4.1 Left Upper Block A Is Not Zero Block -- 4.2 Matrix A Has Full Rank, Matrices C and (or) B Are Zero Matrices -- 4.3 Matrix A Has No Full Rank, Matrices C and (or) B Are Zero Matrices, A =0 -- 5 Matrix A is Zero Matrix -- 5.1 Matrix A Is Zero Matrix, C and (or) B Are Nonzero Matrices -- 5.2 All Cases When Half of the Matrix Is Equal to Zero. ; 6 Example of Triangular Decomposition on Z.
• Sommario/riassunto: This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.
• Titolo autorizzato: Computer Algebra in Scientific Computing
• ISBN: 3-319-24021-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466451203316
• Lo trovi qui: Univ. di Salerno
• Serie: Theoretical Computer Science and General Issues, . 2512-2029 ; ; 9301