E-Book Overview
This book still remains the best introduction to computer algebra, catering to both the interested beginner and the experienced pure mathematician and computer scientist. This updated Second Edition provides a comprehensive review, and contains excellent references to fundamental papers and worked examples. In addition to being a general text on the subject, the book includes an appendix describing the use of one particular algebra system-REDUCE.
E-Book Content
Preface
An example
The example which follows is a work session on the computer, using the software MACSYMA. The user's commands are entered in the lines beginning with (ci). Here we are dealing with a limited (or Taylor series) expansion, calculating an integral and checking that the derivative in the result is indeed the initial function. (c2) taylor( sinh(sin(x))-sin(sinh(x)) ,x ,0 , 15); 7 11 15 x x 5699 x (d2)/T/ -- - ---- - ---------- + . . . 45 1575 1277025750 (c3) primitive:integrate( 1/(x**2 + 1) ** 4 ,x); 5 3 5 atan(x) 15 x + 40 x + 33 x (d3) --------- + ---------------------------16 6 4 2 48 x + 144 x + 144 x + 48 (c4) derivative:diff(primitive, x); 4 2 75 x + 120 x + 33 (d4) ---------------------------6 4 2 48 x + 144 x + 144 x + 48 5 3 5 3 (15 x + 40 x + 33 x) (288 x + 576 x + 288 x) 5 - ----------------------------------------------- + ----------6 4 2 2 2 (48 x + 144 x + 144 x + 48) 16 (x + 1)
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vi Preface (c5) factor(ratsimp(derivative)); (d5)
1 --------2 4 (x + 1)
All these calculations can, in theory, be done by a rst year student, but they are quite laborious and it is diÆcult to do them with pencil and paper without making a mistake. It is not suÆciently well-known that this type of calculation is as much within the range of computers as is numerical calculation. The purpose of this book is to demonstrate the existing possibilities, to show how t