SymbolicC++:An Introduction to Computer Algebra using Object-Oriented Programming

INTRODUCTION: What is Computer Algebra? Properties of Computer Algebra Systems. Pitfalls in Computer Algebra Systems. Design of a Computer Algebra Systems.- MATHEMATICS FOR COMPUTER ALGEBRA: Rings and Fields. Integers. Rational Numbers. Real Numbers. Complex Numbers. Vectors and Matrices. Quaternion. Polynomials. Differentiation. Integration. Commutativity and Noncommutativity. Tensor and Kronecker Product. Exterior Product.- COMPUTER ALGEBRA SYSTEMS: Introduction. REDUCE. Maple. Axiom. Mathematica. MuPAD.- OBJECT-ORIENTED PROGRAMMING: Objects, Classes and Abstract Data Types. Message Passing. Inheritance. Polymorphism. Object Oriented Languages. Summary.- BASIC TOOLS IN C++: Pointers and References. Classes. Constructors and Destructor. Copy Constructor and Assignment Operator. Type Conversion. Operators Overloading. Class Templates. Function Templates. Friendship. Inheritance. Virtual Functions. Wrapper Class. Standard Template Library. Recursion. Summary.- CLASSES FOR COMPUTER ALGEBRA: The Verylong Integer Class. The Rational Number Class. The Complex Number Class. The Quaternion Class. The Derive Class. The Vector Class. The Matrix Class. Array Classes. The String Class. Bit Vectors. The Linked List Class. The Polynomial Class. The Set Class. Summary.- THE SYMBOLIC CLASS: Object-Oriented Design. Data Fields and Types of Symbol. Constructors. Operators. Functions. Simplification. Commutativity. Symbolic and Numeric Interface. Summary.- APPLICATIONS: Bit Vector Class. Verylong Class. Verylong and Rational Class. Verylong, Rational and Derive Class. Verylong, Rational and Complex Class. Symbolic Class. Symbolic Class and Symbolic Differentiation. Matrix Class. Array Class and Symbolic Class. Polynomial and Symbolic Class. Lie Series Techniques. Spectra of Small Spin Clusters. Nonlinear Maps and Chaotic Behaviour. Numerical-Symbolic Application. Summary.- LISP AND COMPUTER ALGEBRA: Introduction. Basic Functions of LISP. Examples from Symbolic Computation. LISP System based on C++.- PROGRAM LISTING: Very long Class. Rational Class. Complex Class. Quaternion Class. Derive Class. Vector Class. Matrix Class. Array Class. String Class. Bit Vector Class. Linked List Class. Polynomial Class. Set Class. Symbolic Class.- PVM AND ABSTRACT DATA TYPES.- ERROR HANDLING TECHNIQUES: Error State. Exception Handling.- GNUPLOT AND POSTSCRIPT.- BIBLIOGRAPHY.- INDEX.