Computer Algebra with SymbolicC++

The following sections are included:

• Preface

• Contents

The following sections are included:

• What is Computer Algebra?

• Properties of Computer Algebra Systems

• Pitfalls in Computer Algebra Systems

• Design of a Computer Algebra System

The following sections are included:

• Sets

• Rings and Fields

• Integers

• Rational Numbers

• Real Numbers

• Complex Numbers

• Vectors and Matrices

• Determinants

• Quaternions

• Polynomials

• Gröbner Bases

• Differentiation

• Integration

• Risch Algorithm

• Commutativity and Non-Commutativity

• Tensor and Kronecker Product

• Exterior Product

The following sections are included:

• Introduction

• Reduce
  • Basic Operations
  • Example

• Maple
  • Basic Operations
  • Example

• Axiom
  • Basic Operations
  • Example

• Mathematica
  • Basic Operations
  • Example

• MuPAD
  • Basic Operations
  • Example

• Maxima
  • Basic Operations
  • Example

• GiNaC
  • Basic Operations
  • Example

The following sections are included:

• Pointers and References

• this Pointer

• Classes

• Constructors and Destructor

• Copy Constructor and Assignment Operator

• Type Conversion

• Operator Overloading

• Class Templates

• Function Templates

• Friendship

• Inheritance

• Virtual Functions

• Wrapper Class

• Recursion

• Error Handling Techniques

• Exception Handling

• Run-Time Type Identification

The following sections are included:

• Introduction

• A String Class

• C++ String Class

• Applications

The following sections are included:

• Introduction

• Namespace Concept

• Vector Class

• List Class

• Stack Class

• Queue Class

• Deque Class

• Bitset Class

• Set Class

• Pair Class

• Map Class

• Algorithm Class

• Complex Class

The following sections are included:

• Identity Elements

• Verylong Integer Class
  • Abstraction
  • Data Fields
  • Constructors
  • Operators
  • Type Conversion Operators
  • Private Member Functions
  • Other Functions
  • Streams
  • BigInteger Class in Java

• Rational Number Class
  • Abstraction
  • Template Class
  • Data Fields
  • Constructors
  • Operators
  • Type Conversion Operators
  • Private Member Functions
  • Other Functions
  • Streams
  • Rational Class for Java

• Quaternion Class
  • Abstraction
  • Template Class
  • Data Fields
  • Constructors
  • Operators
  • Other Functions
  • Streams

• Derive Class
  • Abstraction
  • Data Fields
  • Constructors
  • Operators
  • Member Functions
  • Possible Improvements

• Vector Class
  • Abstraction
  • Templates
  • Data Fields
  • Constructors
  • Operators
  • Member Functions and Norms
  • Streams

• Matrix Class
  • Abstraction
  • Data Fields
  • Constructors
  • Operators
  • Member Functions and Norms
  • Matrix Class for Java

• Array Class
  • Abstraction
  • Data Fields
  • Constructors
  • Operators
  • Member Functions

• Polynomial Class
  • Abstraction
  • Template Class
  • Data Fields
  • Constructors
  • Operators
  • Type Conversion Operators
  • Private Member Functions
  • Other Functions
  • Streams
  • Example

• Multinomial Class
  • Abstraction
  • Template Class
  • Data Fields
  • Constructors
  • Operators
  • Private Member Functions
  • Other Functions
  • Streams
  • Example

The following sections are included:

• Main Header File

• Memory Management

• Object-Oriented Design
  • The Expression Tree
  • Polymorphism of the Expression Tree

• Constructors

• Operators

• Functions and Member Functions
  • Functions

• Simplification
  • Canonical Forms
  • Simplification Rules and Member Functions

• Commutativity

• Symbolic and Numeric Interface

• Example Computation

The following sections are included:

• Bitset Class

• Verylong Class
  • Big Prime Numbers
  • Gödel Numbering
  • Inverse Map and Denumerable Set

• Verylong and Rational Classes
  • Logistic Map
  • Contracting Mapping Theorem
  • Ghost Solutions
  • Iterated Function Systems

• Verylong, Rational and Derive Classes
  • Logistic Map and Ljapunov Exponent

• Verylong, Rational and Complex Classes
  • Mandelbrot Set

• Symbolic Class
  • Polynomials
  • Cumulant Expansion
  • Exterior Product

• Symbolic Class and Symbolic Differentiation
  • First Integrals
  • Spherical Harmonics
  • Nambu Mechanics
  • Taylor Expansion of Differential Equations
  • Commutator of Two Vector Fields
  • Lie Derivative and Killing Vector Field

• Matrix Class
  • Hilbert-Schmidt Norm
  • Lax Pair and Hamilton System
  • Padé Approximant

• Array and Symbolic Classes
  • Pseudospherical Surfaces and Soliton Equations

• Polynomial and Symbolic Classes
  • Picard's Method

• Lie Series Techniques

• Spectra of Small Spin Clusters

• Nonlinear Maps and Chaotic Behavior

• Numerical-Symbolic Application

• Bose Systems

• Grassman Product and Lagrange Multipliers

• Interpreter for Symbolic Computation

The following sections are included:

• Introduction

• Basic Functions of LISP

• LISP Macros and Infix Notation

• Examples from Symbolic Computation
  • Polynomials
  • Simplifications
  • Differentiation

• LISP, Haskell and Computer Algebra
  • A simple computer algebra system in LISP
  • A simple computer algebra system in Haskell

The following sections are included:

• Lisp Operations in C++

• λ-Calculus and C++
  • λ-Calculus
  • C++ Implementation

The following sections are included:

• Introduction
  • Example

• Multi Expression Programming

The following sections are included:

• Identities

• Verylong Class

• Rational Class

• Quaternion Class

• Derive Class

• Vector Class
  • Vector Class
  • Vector Norms

• Matrix Class
  • Matrix Class
  • Matrix Norms

• Array Class

• Polynomial Class

• Multinomial Class

• Symbolic Class
  • Main Header File
  • Memory Management
  • Constants
  • Equations
  • Functions
  • Numbers
  • Products
  • Sums
  • Symbols
  • Symbolic Expressions
  • Symbolic Matrices
  • Errors

The following sections are included:

• Bibliography

• Index