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Computer Algebra in Scientific Computing

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Cover of 'Computer Algebra in Scientific Computing'

Table of Contents

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    Book Overview
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    Chapter 1 Tropical Geometry of Biological Systems ( Invited Talk )
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    Chapter 2 Algebraic and Geometric Analysis of Singularities of Implicit Differential Equations ( Invited Talk )
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    Chapter 3 On the Complexity of Computing Integral Bases of Function Fields
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    Chapter 4 Truncated and Infinite Power Series in the Role of Coefficients of Linear Ordinary Differential Equations
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    Chapter 5 On Periodic Approximate Solutions of the Three-Body Problem Found by Conservative Difference Schemes
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    Chapter 6 Univariate Polynomials with Long Unbalanced Coefficients as Bivariate Balanced Ones: A Toom–Cook Multiplication Approach
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    Chapter 7 Power Series Arithmetic with the BPAS Library
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    Chapter 8 Enhancements to Lazard’s Method for Cylindrical Algebraic Decomposition
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    Chapter 9 The Complexity and Parallel Implementation of Two Sparse Multivariate Hensel Lifting Algorithms for Polynomial Factorization
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    Chapter 10 The GPGCD Algorithm with the Bézout Matrix
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    Chapter 11 On Parametric Linear System Solving
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    Chapter 12 Symbolic-Numeric Algorithm for Computing Orthonormal Basis of $$\text {O(5)}\times \text {SU(1,1)}$$ O(5) × SU(1,1) Group
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    Chapter 13 Symbolic-Numeric Study of Geometric Properties of Adiabatic Waveguide Modes
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    Chapter 14 Intrinsic Complexity for Constructing Zero-Dimensional Gröbner Bases
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    Chapter 15 On the Study of the Motion of a System of Two Connected Rigid Bodies by Computer Algebra Methods
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    Chapter 16 Complexity Estimates for Fourier-Motzkin Elimination
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    Chapter 17 Progress Report on the Scala Algebra System
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    Chapter 18 Routh – Hurwitz Stability of a Polynomial Matrix Family. Real Perturbations
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    Chapter 19 Hermite Rational Function Interpolation with Error Correction
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    Chapter 20 Good Pivots for Small Sparse Matrices
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    Chapter 21 Nullstellensatz-Proofs for Multiplier Verification
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    Chapter 22 “Mathemachines” via LEGO, GeoGebra and CindyJS
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    Chapter 23 Balanced NUCOMP
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    Chapter 24 Contact Linearizability of Scalar Ordinary Differential Equations of Arbitrary Order
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    Chapter 25 Faster Numerical Univariate Polynomial Root-Finding by Means of Subdivision Iterations
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    Chapter 26 Computing Parametric Standard Bases for Semi-weighted Homogeneous Isolated Hypersurface Singularities
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    Chapter 27 Acceleration of Subdivision Root-Finding for Sparse Polynomials
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    Chapter 28 Analytical Computations in Studying Translational-Rotational Motion of a Non-stationary Triaxial Body in the Central Gravitational Field
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    Chapter 29 A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks
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    Chapter 30 First-Order Tests for Toricity
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    Chapter 31 Looking for Compatible Routes in the Railway Interlocking System of an Overtaking Station Using a Computer Algebra System
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    Chapter 32 Computing Logarithmic Vector Fields Along an ICIS Germ via Matlis Duality
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    Chapter 33 Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers
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    Chapter 34 Symbolic-Numeric Computation of the Bernstein Coefficients of a Polynomial from Those of One of Its Partial Derivatives and of the Product of Two Polynomials
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    Chapter 35 Comparative Study of the Accuracy of Higher-Order Difference Schemes for Molecular Dynamics Problems Using the Computer Algebra Means
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    Chapter 36 Characterizing Triviality of the Exponent Lattice of a Polynomial Through Galois and Galois-Like Groups
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Title
Computer Algebra in Scientific Computing
Published by
Springer International Publishing, December 2020
DOI 10.1007/978-3-030-60026-6
ISBNs
978-3-03-060025-9, 978-3-03-060026-6
Editors

Boulier, François, England, Matthew, Sadykov, Timur M., Vorozhtsov, Evgenii V.

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