S. A. Abramov, M. Petkovšek (auth.), Victor G. Ganzha, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)3540751866, 9783540751861
The 35 revised full papers presented were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers cover not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms. Topics addressed are studies in polynomial and matrix algebra, quantifier elimination, and Gröbner bases, as well as stability investigation of both differential equations and difference methods for them. Several papers are devoted to the application of computer algebra methods and algorithms to the derivation of new mathematical models in biology and in mathematical physics.
Table of contents :
Front Matter….Pages –
Analytic Solutions of Linear Difference Equations, Formal Series, and Bottom Summation….Pages 1-10
Computations in Modules over Commutative Domains….Pages 11-23
Advances on the Continued Fractions Method Using Better Estimations of Positive Root Bounds….Pages 24-30
An Efficient LLL Gram Using Buffered Transformations….Pages 31-44
On the Computation of A ∞ -Maps….Pages 45-57
Algebraic Visualization of Relations Using RelView ….Pages 58-72
Comprehensive Triangular Decomposition….Pages 73-101
Stability Investigation of a Difference Scheme for Incompressible Navier-Stokes Equations….Pages 102-117
A Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for a Hydrogen Atom in the Magnetic Field: Cylindrical Coordinates….Pages 118-133
An Algorithm for Construction of Normal Forms….Pages 134-142
Computer Algebra: A ‘Classical’ Path to Explore Decoherence and Entanglement Phenomena in Quantum Information Theory….Pages 143-144
Deducing the Constraints in the Light-Cone SU (3) Yang-Mills Mechanics Via Gröbner Bases….Pages 145-159
On the Weight Spectra of Conway Matrices Related to the Non-transitive Head-or-Tail Game….Pages 160-168
Properties of the Liapunov Stability Zones of the Lagrange Triangle….Pages 169-180
Studying the Stability of the Second Order Non-autonomous Hamiltonian System….Pages 181-194
On the Peculiar Properties of Families of Invariant Manifolds of Conservative Systems….Pages 195-210
A Unified Algorithm for Multivariate Analytic Factorization….Pages 211-223
On the Computation of the Defining Polynomial of the Algebraic Riccati Equation….Pages 224-235
Symmetries and Dynamics of Discrete Systems….Pages 236-251
Exact Solutions of Completely Integrable Systems and Linear ODE’s Having Elliptic Function Coefficients….Pages 252-264
Dynamics of Nonlinear Parabolic Equations with Cosymmetry….Pages 265-274
Weak Integer Quantifier Elimination Beyond the Linear Case….Pages 275-294
Polynomial Division Using Dynamic Arrays, Heaps, and Packed Exponent Vectors….Pages 295-315
Ruppert Matrix as Subresultant Mapping….Pages 316-327
Construction of Computer System for Microobjects Recognition Based on Neural Networks….Pages 328-338
Analytical Solution for Transient Flow of a Generalized Bingham Fluid with Memory in a Movable Tube Using Computer Algebra….Pages 339-349
Some Elimination Problems for Matrices….Pages 350-359
A Full System of Invariants for Third-Order Linear Partial Differential Operators in General Form….Pages 360-369
Automatic Stability Analysis for a Diffusion Equation with Memories Using Maple….Pages 370-376
Bounds for Real Roots and Applications to Orthogonal Polynomials….Pages 377-391
Distance Computation from an Ellipsoid to a Linear or a Quadric Surface in IR n ….Pages 392-401
Robust Stability for Parametric Linear ODEs….Pages 402-422
Symbolic and Algebraic Methods for Linear Partial Differential Operators….Pages 423-423
A New Scheme for Deniable/Repudiable Authentication….Pages 424-432
An Algebraic-Numeric Algorithm for the Model Selection in Kinetic Networks….Pages 433-447
On the Representation of the Differential Operator in Bases of Periodic Coiflets and It’s Application….Pages 448-457
Back Matter….Pages –
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