Computer Algebra Handbook, w. CD-ROM

Matrix Groups
2.7.6 Black Box Groups
2.7.7 Abelian Groups
2.7.8 Polycyclic Groups
2.7.9 Finitely Presented Groups
2.7.10 Group-Theoretic Software
2.7.11 Another Perspective
2.8 Algorithms of Representation Theory
2.8.1 Ordinary Representation Theory
2.8.2 Modular Representation Theory
2.8.3 Generic Character Tables
2.8.4 Summary of Systems
2.9 Algebraic Methods for Constructing Discrete Structures
2.10 Summation and Integration
2.10.1 Definite Summation and Hypergeometric Identities
2.10.2 Symbolic Integration
2.11 Symbohc Methods for DiflFerential Equations
2.11.1 Introduction
2.11.2 Differential Galois Theory
2.11.3 Lie Symmetries
2.11.4 Painlevé Theory
2.11.5 Completion
2.11.6 Differential Ideal Theory
2.11.7 Dynamical Systems
2.11.8 Numerical Analysis
2.12 Symbolic/Numeric Methods
2.12.1 Computer Analysis
2.12.2 Algorithms for Computing Validated Results
2.12.3 Hybrid Methods
2.13 Algebraic Complexity Theory
2.14 Coding Theory and Cryptography
2.14.1 Coding Theory
2.14.2 QuantumCoding Theory
2.14.3 Cryptography
2.15 Algorithmic Methods inUniversal Algebra and Logic
2.15.1 Term Rewriting Systems
2.15.2 Decision Procedures and Quantifier Ehmination Methods for AlgebraicTheories
2.16 Knowledge Representation and Abstract Data Types
2.16.1 Mathematical Knowledge Representation and Expert Systems
2.16.2 Abstract Data Types
2.17 On the Design of Computer Algebra Systems
2.17.1 Memory Management
2.17.2 Program Verification and Abstract Data Types
2.17.3 The Concept of Types
2.17.4 Genericity
2.17.5 Modularization
2.17.6 Parallel Implementation
2.17.7 Continuing Developmentof Computer Algebra Systems
2.18 Parahel Computer Algebra Systems
2.18.1 Parallel Architectures and Operating Systems Supports
2.18.2 Parallel Execution: Mapping and Scheduling
2.18.3 Parallelism Expression and Languages
2.19 Interfaces and Standardization
2.19.1 Interfaces to Word Processors
2.19.2 Graphics
2.19.3 Interfaces to Numerical Software
2.19.4 User Interfaces
2.19.5 General Problem-Solving Environments
2.19.6 Standardisation
2.19.7 MathML
2.20 Hardware Implementation of Computer Algebra Algorithms

3 Applications of Computer Algebra
3.1 Physics
3.1.1 Elementary Particle Physics
3.1.2 Gravity
3.1.3 Central Configurations'in the Newtonian N-Body Problem of Celestial Mechanics
3.1.4 CA-Systems for Differential Geometry and Applications
3.1.5 Differential Equations in Physics
3.2 Mathematics
3.2.1 Computer Algebra in Group Theory
3.2.2 The Tangent Cone Algorithm and Applications in the Theory of Singularities
3.2.3 Automatic Theorem Proving in Geometry
3.2.4 Homological Algebra
3.2.5 Study of Differential Structures on Quantum Groups
3.2.6 Orthogonal Polynomials and Computer Algebra
3.2.7 Computer Algebra in Symmetric Bifurcation Theory
3.2.8 SymboUc-Numeric Treatment of Equivariant Systems of Equations
3.3 Computer Science
3.3.1 Computer Algebra in Computer Science
3.3.2 Decomposable Structures, Generating Functions and Average-Case of Algorithms
3.3.3 Telecommunication Management Networks
3.4 Engineering
3.4.1 Computer Algebra, a Modern Research Tool for Engineering
3.4.2 Critical Load Computations forJet Engines
3.4.3 Audio Signal Processing
3.4.4 Robotics
3.4.5 Computer Aided Design and Modelling
3.5 Chemistry
3.5.1 Computer Algebra in Chemistry and Crystallography
3.5.2 Chemical Reaction Systems
3.6 Computer Algebra in Education
3.6.1 New Hand-Held ComputerSymbolic Algebra Tools in Mathematics Education
3.6.2 The Dutch Perspective
3.6.3 Computer Algebra in Teaching and Learning Mathematics: Experiences at the University of Plymouth, England
3.6.4 The Educational Use of Computer Algebra Systems at the University of Illinois
3.6.5 Mathematics Education from a MATHEMATICA Perspective
3.6.6 Visualization: Courseware for Mathematics Education

4 Computer Algebra Systems
4.1 General Purpose Systems
4.1.1 Axiom
4.1.2 Aldor
4.1.3 Derive and the TI-92
4.1.4 Macsyma
4.1.5 Magma
4.1.6 Maple
4.1.7 Mathematica
4.1.8 MuPAD
4.1.9 Reduce
4.2 Special Purpose Systems
4.2.1 Algebraic Combinatorics Environment (ACE)
4.2.2 Building Nonassociative Algebras With Albert
4.2.3 Algeb
4.2.4 Amore
4.2.5 Bergman
4.2.6 Cannes/Parcan
4.2.7 Carat
4.2.8 Casa
4.2.9 Chevie
4.2.10 C-Meataxe
4.2.11 CoCoA
4.2.12 Crep
4.2.13 The Desir Project and Its Continuation
4.2.14 Discreta: A Tool for Constructing i-Designs
4.2.15 Felix
4.2.16 Fermat
4.2.17 FoxBox and Other Blackbox Systems
4.2.18 Gap
4.2.19 GiNaC
4.2.20 Kan/sml
4.2.21 Kant V4
4.2.22 Lidia
4.2.23 Lie
4.2.24 Lie
4.2.25 A Brief Introduction to Macaulay 2
4.2.26 Mas
4.2.27 Masyca
4.2.28 Moc
4.2.29 NTL: A Library for Doing Number Theory
4.2.30 Pari
4.2.31 Parsac
4.2.32 Quotpic
4.2.33 Redux
4.2.34 Reptiles A Program for Interactively Generating Periodic Tihngs
4.2.35 SAC-1, Aldes/SAC-2, Saclib
4.2.36 SciNapse: Software that Writes PDE Software
4.2.37 Senac
4.2.38 Simath - Algorithms in Number Theory
4.2.39 SINGULAR - A Computer Algebra System for Polynomial Computations
4.2.40 SymbMath
4.2.41 Symmetrica
4.2.42 Theorema: Computation and Deduction in Natural Style
4.2.43 Theorist-a User Interface for Symbolic Algebra
4.3 Packages
4.3.1 ANU Polycyclic Quotient Programs
4.3.2 Arep
4.3.3 Cali
4.3.4 Cln
4.3.5 Crack, Liepde, Applysym and Conlaw
4.3.6 Dimsym
4.3.7 EinS
4.3.8 FeynArts and FormCalc
4.3.9 FeynCalc - Tools and Tables for Elementary Particle Physics
4.3.10 Grape
4.3.11 Recognising Matrix Groups over Finite Fields
4.3.12 Molgen
4.3.13 Orme
4.3.14 Ratappr
4.3.15 TTC: Tools of Tensor Calculus

5 Meetings and Publications
5.1 Conferences and Proceedings
5.2 Books on Computer Algebra
- Cited References
- Index for Authors' Contributions