Computer Algebra in Scientific Computing [[electronic resource] ] : 19th International Workshop, CASC 2017, Beijing, China, September 18-22, 2017, Proceedings / / edited by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov

• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
• Edizione: 1st ed. 2017.
• Descrizione fisica: 1 online resource (XIII, 407 p. 75 illus.)
• Disciplina: 004.0151
• Soggetto topico: Algorithms; Computer science—Mathematics; Computers, Special purpose; Electronic data processing—Management; Software engineering; Computer science; Mathematics of Computing; Special Purpose and Application-Based Systems; IT Operations; Software Engineering; Computer Science Logic and Foundations of Programming
• Persona (resp. second.): GerdtVladimir P; KoepfWolfram; SeilerWerner M; VorozhtsovEvgenii V
• Nota di contenuto: Intro -- Preface -- Organization -- Contents -- Linear Differential Systems with Infinite Power Series Coefficients (Invited Talk) -- 1 Introduction -- 2 Algorithmic Representation -- 2.1 Computable Infinite Power Series in the Role of Coefficients of Linear Differential Systems -- 2.2 Procedures for Constructing Local Solutions -- 3 Approximate (Truncated) Representation -- 3.1 Strongly Non-singular Matrices -- 3.2 When only a Truncated System Is Known -- 4 The Width -- References -- On the Asymptotic Stability of a Satellite with a Gravitational Stabilizer -- 1 Introduction -- 2 Description and Construction of a Symbolical Model -- 3 Formulation of the Problem -- 4 Regions of System's Instability -- 5 Parametric Analysis of Asymptotic Stability Conditions -- 5.1 Stabilization in the ``Pitch'' Subsystem -- 5.2 Stabilization in the ``Yaw-and-Roll'' Subsystem -- 6 Conclusion -- References -- Sparse Interpolation, the FFT Algorithm and FIR Filters -- 1 Sparse Interpolation -- 2 Divide and Conquer Approach -- 3 The FFT Algorithm -- 4 An Analog Version of the Splitting Technique -- 5 Connection to FIR Filters -- 6 Conclusion -- References -- On New Integrals of the Algaba-Gamero-Garcia System -- 1 Introduction -- 2 Problem Statement -- 3 Necessary Conditions of Local Integrability -- 4 Sufficient Conditions of Integrability -- 5 Case b2=2/3, Subcase 3 a0 - 2 b0 = b(3 a1 - 2 b1) -- 6 Analytical Properties of the Integrals -- 7 Conclusions -- References -- Full Rank Representation of Real Algebraic Sets and Applications -- 1 Introduction -- 2 Full Rank Representation of Real Algebraic Sets -- 3 Compute Full Rank Representation -- 4 Applications on Plotting Singular Plane and Space Curves -- 5 Experimentation -- 6 Conclusion and Future Work -- References -- Certifying Simple Zeros of Over-Determined Polynomial Systems -- 1 Introduction. ; 2 Preliminaries -- 3 Transforming Over-Determined Polynomial Systems into Square Ones -- 4 Certifying Simple Zeros of Over-Determined Systems -- References -- Decomposing Polynomial Sets Simultaneously into Gröbner Bases and Normal Triangular Sets -- 1 Introduction -- 2 Preliminaries -- 2.1 Triangular Set and Triangular Decomposition -- 2.2 Gröbner Basis and W-Characteristic Set -- 2.3 (Strong) Characteristic Decomposition and Characterizable Gröbner Basis -- 3 Algorithm for (Strong) Characteristic Decomposition -- 3.1 Algorithm to Handle the Variable Ordering Condition -- 3.2 Algorithms for Characteristic Decomposition -- 3.3 Algorithm for Strong Characteristic Decomposition -- 3.4 An Illustrative Example -- 4 Implementation and Experimental Results -- References -- Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks -- 1 Introduction -- 2 The Systems for the Case Studies -- 2.1 Biomod-26 -- 2.2 Biomod-28 -- 3 Graph-Theoretical Symbolic Preprocessing -- 4 Determination of Multiple Steady States -- 4.1 Numerical Approach -- 4.2 Symbolic Approach -- 4.3 Comparison -- 4.4 Going Further -- 5 Conclusion and Future Work -- References -- The Polymake Interface in Singular and Its Applications -- 1 Introduction -- 2 An Interface to Polymake -- 3 User Defined Types in Singular: Polyhedral Divisors -- 4 Quasihomogeneous Isolated Hypersurface Singularities -- 4.1 Finding Quasihomogeneous Isolated Hypersurface Singularities -- 4.2 Reconstruction of QHIS from the Milnor Algebra -- References -- Computation of Some Integer Sequences in Maple -- 1 Introduction -- 1.1 Definitions of Numbers -- 2 Stirling Partition Numbers -- 2.1 Sequence Calculation -- 3 Stirling Cycle Numbers -- 3.1 Singleton Computation -- 3.2 A Finite Sum -- 3.3 Sequence Calculation -- 4 Associated Stirling Numbers. ; 4.1 Singleton Stirling 2-Partition and 2-Cycle -- 4.2 Sequence Calculation of 2-Partition and 2-Cycle Numbers -- 4.3 Singleton Stirling r-Partition and r-Cycle Numbers -- 4.4 Sequence Calculation of r-Partition and r-Cycle Numbers -- 4.5 Implementation in Maple -- 5 A Multiple Threads Approach to Sequence Calculations -- 6 Implementation of Eulerian Numbers -- 6.1 Timings for Eulerian Number Calculations -- References -- Symbolic-Numerical Algorithm for Generating Interpolation Multivariate Hermite Polynomials of High-Accuracy Finite Element Method -- 1 Introduction -- 2 Setting of the Problem -- 3 FEM Calculation Scheme -- 3.1 Lagrange Interpolation Polynomials -- 3.2 Algorithm for Calculating the Basis of Hermite Interpolating Polynomials -- 3.3 Example: HIP for d=2 -- 3.4 Piecewise Polynomial Functions -- 4 Results and Discussion -- 5 Conclusion -- References -- Symbolic-Numerical Algorithms for Solving the Parametric Self-adjoint 2D Elliptic Boundary-Value Problem Using High-Accuracy Finite Element Method -- 1 Introduction -- 2 FEM Algorithm for Solving the Parametric 2D BVP -- 3 Fully Symmetric High-Order Gaussian Quadratures -- 4 The Algorithm for Calculating the Parametric Derivatives of Eigenfunctions and Effective Potentials -- 5 Benchmark Calculations of Helium Atom Ground State -- 6 Conclusion -- References -- A Symbolic Study of the Satellite Dynamics Subject to Damping Torques -- 1 Introduction -- 2 Equations of Motion -- 3 Equilibrium Orientations of Satellite -- 4 Conditions for the Existence of Equilibrium Orientations of the Satellite -- 5 Necessary and Sufficient Conditions of Asymptotic Stability of the Equilibrium Orientations of Satellite -- 6 Conclusion -- References -- Characteristic Set Method for Laurent Differential Polynomial Systems -- 1 Introduction -- 2 Laurent Polynomial Systems -- 2.1 Laurent Regular Chain. ; 2.2 Characteristic Set Method -- 2.3 Laurent Gröbner Basis and Minimal Decomposition -- 3 Differential Polynomial Systems -- 3.1 Laurent Regular Differential Chains -- 3.2 Decision of Univariate Laurent Regular Differential Polynomial -- References -- Sparse Polynomial Interpolation with Finitely Many Values for the Coefficients -- 1 Introduction -- 2 Univariate Polynomial Interpolation -- 2.1 Sparse Interpolation with Finitely Many Coefficients -- 2.2 The Sparse Interpolation Algorithm -- 2.3 The Rational Number Coefficients Case -- 3 Multivariate Polynomial Sparse Interpolation with Modified Kronecker Substitution -- 3.1 Find a Good Prime -- 3.2 A Deterministic Algorithm -- 3.3 Probabilistic Algorithm -- 4 Experimental Results -- 5 Conclusion -- References -- On Stationary Motions of the Generalized Kowalewski Gyrostat and Their Stability -- 1 Introduction -- 2 Formulation of the Problem -- 3 Finding the Stationary Solutions -- 3.1 Permanent Rotations -- 3.2 Equilibria -- 4 On Invariant Manifolds of Codimension 2 -- 5 On Stability of the Stationary Solutions -- 5.1 On Stability of the Permanent Rotations -- 5.2 On Stability of the Equilibria -- 6 Conclusion -- 7 Appendix -- References -- Computing the Integer Points of a Polyhedron, I: Algorithm -- 1 Introduction -- 2 Polyhedral Sets -- 3 Integer Solutions of Linear Equation Systems -- 4 Integer Solutions of Linear Inequality Systems -- 4.1 Normalization of Linear Inequality Systems -- 4.2 Representing the Integer Points -- 4.3 The IntegerSolve Procedure: Specifications -- 4.4 The DarkShadow Procedure -- 4.5 The GreyShadow Procedure -- 4.6 The IntegerSolve Procedure: Algorithm -- References -- Computing the Integer Points of a Polyhedron, II: Complexity Estimates -- 1 Introduction -- 2 Properties of the Projection of Faces of a Polyhedron -- 3 Complexity Estimates for Fourier-Motzkin Elimination. ; 4 Proof of Theorem1 -- 5 Experimentation -- References -- Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data -- 1 Problem Formulation -- 2 Non-Linearity of JTF and Numerical Difficulties -- 3 Non-Convexity of JTF -- 4 Numerical Experiments for Fitting Sparse Reduced Data -- 5 Conclusions -- References -- The Convergence Conditions of Interval Newton's Method Based on Point Estimates -- 1 Introduction -- 2 Notation and Preliminaries -- 3 Main Results -- 4 Example -- References -- Normalization of Indexed Differentials Based on Function Distance Invariants -- 1 Introduction -- 2 Indexed Differential Polynomial Ring -- 3 Distances Between Indexed Functions -- 4 Normalization with Respect to Monoterm Symmetries -- 5 Normalization -- References -- Symbolic-Numeric Integration of the Dynamical Cosserat Equations -- 1 Introduction -- 2 Governing Cosserat Equations and the General Solution of Their Kinematic Part -- 3 Symbolic-Numeric Integration Method -- 3.1 Naive Approach: Explicit Numerical Solving -- 3.2 Advanced Approach Based on Exponential Integration -- 4 Numerical Comparison with the Generalized alpha-Method -- 5 Conclusison -- A Generalized alpha-Method -- References -- Algorithms for Zero-Dimensional Ideals Using Linear Recurrent Sequences -- 1 Introduction -- 2 Generalities on Sequences and Their Annihilators -- 3 Computing Annihilators of Sequences -- 3.1 A First Algorithm -- 3.2 An Algorithm Under Genericity Assumptions -- 4 Main Algorithm -- 4.1 Representing Primary Zero-Dimensional Ideals -- 4.2 The Algorithm -- References -- Symbolic-Numerical Analysis of the Relative Equilibria Stability in the Planar Circular Restricted Four-Body Problem -- 1 Introduction -- 2 Equilibrium Solutions -- 3 Stability Analysis in Linear Approximation -- 4 Normalization of the Hamiltonian -- 5 Conclusion -- References. ; The Method of Collocations and Least Residuals Combining the Integral Form of Collocation Equations and the Matching Differential Relations at the Solution of PDEs.
• Sommario/riassunto: This book constitutes the proceedings of the 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, held in Beijing, China, in September 2017. The 28 full papers presented in this volume were carefully reviewed and selected from 33 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.
• Titolo autorizzato: Computer Algebra in Scientific Computing
• ISBN: 3-319-66320-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910483297903321
• Lo trovi qui: Univ. Federico II
• Serie: Theoretical Computer Science and General Issues, . 2512-2029 ; ; 10490