Joel S. Cohen9781568811581, 1568811586
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.
Table of contents :
Elementary Algorithms……Page 1
Contents……Page 9
Preface……Page 11
1.1 Computer Algebra and Computer Algebra Systems……Page 21
1.2 Applications of Computer Algebra……Page 30
2.1 Mathematical Pseudo-language (MPL)……Page 49
2.2 Expression Evaluation……Page 69
2.3 Mathematical Programs……Page 78
2.4 Sets and Lists……Page 88
3.1 Recursive Definitions and Algorithms……Page 97
3.2 Expression Structure and Trees……Page 104
3.3 Structure-Based Operators……Page 128
4.1 Mathematical Algorithms……Page 139
4.2 MPL’s Algorithmic Language……Page 152
4.3 Case Study: First Order Ordinary Differential Equations……Page 176
5.1 A Computational View of Recursion……Page 191
5.2 Recursive Procedures……Page 196
5.3 Case Study: Elementary Integration Operator……Page 219
6. Structure of Polynomials and Rational Expressions……Page 233
6.1 Single Variable Polynomials……Page 234
6.2 General Polynomial Expressions……Page 243
6.3 Relationships Between Generalized Variables……Page 262
6.4 Manipulation of General Polynomial Expressions……Page 267
6.5 General Rational Expressions……Page 279
7.1 Exponential and Trigonometric Expansion……Page 295
7.2 Exponential and Trigonometric Contraction……Page 309
Bibliography……Page 327
Index……Page 336
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