Elementary Algorithms
Contents
Preface
1. Introduction to Computer Algebra
1.1 Computer Algebra and Computer Algebra Systems
1.2 Applications of Computer Algebra
2. Elementary Concepts of Computer Algebra
2.1 Mathematical Pseudo-language (MPL)
2.2 Expression Evaluation
2.3 Mathematical Programs
2.4 Sets and Lists
3. Recursive Structure of Mathematical Expressions
3.1 Recursive Definitions and Algorithms
3.2 Expression Structure and Trees
3.3 Structure-Based Operators
4. Elementary Mathematical Algorithms
4.1 Mathematical Algorithms
4.2 MPL's Algorithmic Language
4.3 Case Study: First Order Ordinary Differential Equations
5. Recursive Algorithms
5.1 A Computational View of Recursion
5.2 Recursive Procedures
5.3 Case Study: Elementary Integration Operator
6. Structure of Polynomials and Rational Expressions
6.1 Single Variable Polynomials
6.2 General Polynomial Expressions
6.3 Relationships Between Generalized Variables
6.4 Manipulation of General Polynomial Expressions
6.5 General Rational Expressions
7. Exponential and Trigonometric Transformations
7.1 Exponential and Trigonometric Expansion
7.2 Exponential and Trigonometric Contraction
Bibliography
Index