Computer algebra and symbolic computation : elementary algorithms

Computer Algebra and Symbolic Computation: Elementary Algorithms provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and construct expressions, we can implement many elementary operations from algebra, trigonometry, calculus, and differential equations. With a minimum of prerequisites, this book is accessible and useful to students of mathematics, computer science, and other technical fields. The book contains a CD with the full, searchable text and implementations of all algorithms in Maple, Mathematica, and MuPad programming languages.

This book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and construct expressions, we can implement many elementary operations from algebra, trigonometry, calculus, and differential equations. With a minimum of prerequisites this book is accessible to and useful for students of mathematics, computer science, and other technical fields. The book contains a CD with the full, searchable text and implementations of all algorithms in the Maple, Mathematica, and MuPad programming languages.

Booknews

This textbook explains the formulation of algorithms that solve symbolic mathematical problems, and the implementation of these algorithms in computer algebra programming languages. The mathematical pseudo-language (MPL) is used throughout the book to illustrate the structure of recursive procedures, polynomials, rational expressions, and exponential and trigonometric functions. The CD- ROM contains algorithms and an electronic version of the text. Annotation c. Book News, Inc., Portland, OR

Elementary Algorithms 1 Contents 9 Preface 11 1. Introduction to Computer Algebra 21 1.1 Computer Algebra and Computer Algebra Systems 21 1.2 Applications of Computer Algebra 30 2. Elementary Concepts of Computer Algebra 49 2.1 Mathematical Pseudo-language (MPL) 49 2.2 Expression Evaluation 69 2.3 Mathematical Programs 78 2.4 Sets and Lists 88 3. Recursive Structure of Mathematical Expressions 97 3.1 Recursive Definitions and Algorithms 97 3.2 Expression Structure and Trees 104 3.3 Structure-Based Operators 128 4. Elementary Mathematical Algorithms 139 4.1 Mathematical Algorithms 139 4.2 MPL's Algorithmic Language 152 4.3 Case Study: First Order Ordinary Differential Equations 176 5. Recursive Algorithms 191 5.1 A Computational View of Recursion 191 5.2 Recursive Procedures 196 5.3 Case Study: Elementary Integration Operator 219 6. Structure of Polynomials and Rational Expressions 233 6.1 Single Variable Polynomials 234 6.2 General Polynomial Expressions 243 6.3 Relationships Between Generalized Variables 262 6.4 Manipulation of General Polynomial Expressions 267 6.5 General Rational Expressions 279 7. Exponential and Trigonometric Transformations 295 7.1 Exponential and Trigonometric Expansion 295 7.2 Exponential and Trigonometric Contraction 309 Bibliography 327 Index 336 "This text: is well-suited for self-study and can be used as the basis for an advanced undergraduate or beginning graduate course; maintains the style set by Elementary Algorithms; introduces advanced methods to treat complex operations; presents implementations in such programs as Mathematica, Maple, and MuPAD; and includes a CD with the complete text, hyperlinks, and algorithms as well as additional reference files.". "For the student, Mathematical Methods is an essential companion to Elementary Algorithms, illustrating applications of basic ideas. For the professional, Mathematical Methods is a look at new applications of familiar concepts."--BOOK JACKET. CD-ROM contains: Electronic version of text -- Links to references -- Complete algorithms