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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 Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients
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    Chapter 2 Janet Bases and Resolutions in CoCoALib
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    Chapter 3 Regular Chains under Linear Changes of Coordinates and Applications
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    Chapter 4 A Standard Basis Free Algorithm for Computing the Tangent Cones of a Space Curve
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    Chapter 5 Research on the Stability of Relative Equilibria of Oblate Axisymmetric Gyrostat by Means of Symbolic-Numerical Modelling
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    Chapter 6 A New Approach for Computing Regular Solutions of Linear Difference Systems
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    Chapter 7 Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation
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    Chapter 8 Finding First Integrals Using Normal Forms Modulo Differential Regular Chains
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    Chapter 9 Simplification of Cylindrical Algebraic Formulas
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    Chapter 10 Quasi-Steady State – Intuition, Perturbation Theory and Algorithmic Algebra
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    Chapter 11 Polynomial Complexity Recognizing a Tropical Linear Variety
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    Chapter 12 Computing Highest-Order Divisors for a Class of Quasi-Linear Partial Differential Equations
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    Chapter 13 Symbolic Algorithm for Generating Irreducible Bases of Point Groups in the Space of SO(3) Group
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    Chapter 14 Symbolic-Numeric Solution of Boundary-Value Problems for the Schrödinger Equation Using the Finite Element Method: Scattering Problem and Resonance States
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    Chapter 15 Application of Computer Algebra Methods to Investigation of Influence of Constant Torque on Stationary Motions of Satellite
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    Chapter 16 Bounds for the Condition Number of Polynomials Systems with Integer Coefficients
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    Chapter 17 On Invariant Manifolds and Their Stability in the Problem of Motion of a Rigid Body under the Influence of Two Force Fields
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    Chapter 18 Homotopy Analysis Method for Stochastic Differential Equations with Maxima
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    Chapter 19 On the Topology and Visualization of Plane Algebraic Curves
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    Chapter 20 Piecewise-Quadratics and Reparameterizations for Interpolating Reduced Data
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    Chapter 21 Parametric Solvable Polynomial Rings and Applications
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    Chapter 22 Triangular Decomposition of Matrices in a Domain
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    Chapter 23 Automated Reasoning in Reduction Rings Using the Theorema System
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    Chapter 24 On the Partial Analytical Solution of the Kirchhoff Equation
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    Chapter 25 Efficient Computation of Algebraic Local Cohomology Classes and Change of Ordering for Zero-Dimensional Standard Bases
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    Chapter 26 Polynomial Real Root Isolation by Means of Root Radii Approximation
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    Chapter 27 Randomized Circulant and Gaussian Pre-processing
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    Chapter 28 Symbolic Computation and Finite Element Methods
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    Chapter 29 Approximate Quantum Fourier Transform and Quantum Algorithm for Phase Estimation
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    Chapter 30 Two-Point Boundary Problems with One Mild Singularity and an Application to Graded Kirchhoff Plates
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    Chapter 31 Analysis of Reaction Network Systems Using Tropical Geometry
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    Chapter 32 Safety Verification of Hybrid Systems Using Certified Multiple Lyapunov-Like Functions
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    Chapter 33 A New Polynomial Bound and Its Efficiency
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    Chapter 34 Distance Evaluation Between an Ellipse and an Ellipsoid
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    Chapter 35 Algebraic General Solutions of First Order Algebraic ODEs
Attention for Chapter 19: On the Topology and Visualization of Plane Algebraic Curves
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Chapter title
On the Topology and Visualization of Plane Algebraic Curves
Chapter number 19
Book title
Computer Algebra in Scientific Computing
Published by
Springer, Cham, September 2015
DOI 10.1007/978-3-319-24021-3_19
Book ISBNs
978-3-31-924020-6, 978-3-31-924021-3
Authors

Kai Jin, Jin-San Cheng, Xiao-Shan Gao