Computer Algebra with LISP and REDUCE: An Introduction to Computer-aided Pure Mathematics

Front Cover
Springer Science & Business Media, Nov 30, 1991 - Computers - 264 pages
One service mathematics has rendered the tEL moi, .... si j'avait su comment en revenir. je n'y serais point alle'.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non­ sense', The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com­ puter science ...'; 'One service category theory has rendered mathematics ,..'. All arguably true. And all statements obtainable this way form part of the raison d'elre of this series.
 

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Contents

Chapter 1 INTRODUCTION
1
12 Requirements for a computer algebra system
4
13 Why REDUCE?
8
14 Classical highlevel programming languages vs REDUCE
10
Standard LISP AND RLISP
17
22 A model for LISP memory
19
23 Basic Standard LISP
21
24 An overview of Standard LISP functions
27
3101 Factorization of polynomials and rational functions
176
3102 The functions gcd 1cm and mcd
178
3103 resultant
180
3104 remainder
181
3106 interpol
182
3108 den and num
183
31010 mainvar
184
31012 Floatingpoint coefficients
185

242 Structural predicates
46
243 Equality
52
245 Functions related to identifiers
56
246 Function definition
62
247 Logical functions
67
248 Vectors
70
249 Program constructs
72
2410 Numerical functions
74
2411 Evaluation
81
2412 Mapping functions
83
2413 Association lists
85
2414 Nonlocal jumps and error handling
86
2415 Variable binding
88
2416 Other Standard LISP functions
91
25 RLISP and Standard LISP
97
26 Standard LISP vs Common LISP
102
REDUCE ALGEBRAIC MODE
105
312 Rational numbers
106
313 Algebraic numbers
108
314 Transcendental numbers
109
315 Complex numbers
110
316 Floatingpoint numbers
111
32 Variables
113
33 Lists
115
34 Arrays
119
35 Matrices
121
36 Operators
127
362 The builtin prefix operators
128
363 Userdefined operators
136
37 Expressions and statements
142
372 Statements
146
38 Commands
152
381 bye and quit
153
384 Substitution commands
154
39 Special prefix operators
161
392 Finding primitives
163
393 Solving equations
166
394 The mkid operator
171
395 The pf operator
172
396 The length operator
173
397 The coeff operator
174
310 Polynomials
175
31013 Complex coefficients
186
311 Structure
188
3112 pri
189
3115 korder
190
3116 factor
191
3118 div
192
31110 rat
193
31112 revpri
194
31113 nero
195
313 Files
197
Chapter 4 APPLICATIONS
201
42 An algebra of onedimensional projection operators
204
43 Grobner bases
208
432 Polynomial ideals
209
433 The ideal associated to a system of polynomial equations
210
435 Complete reduction of a polynomial
212
436 Grobner bases
213
437 Buchbergers algorithm
214
438 The radical ideal
215
439 Eulers ninepoint circle
217
A PACKAGE FOR THREEDIMENSIONAL EUCLIDEAN GEOMETRY
219
52 Clifford algebra
220
53 Groups in the Clifford algebra
225
54 The geometric meaning of elements of the Clifford group
229
55 Objects
233
552
235
553
237
56 Incidence and coincidence of objects
239
57 Union and intersection of objects
240
58 Orthogonality of objects
241
582
242
584
243
510 Parallelism of objects
244
5102
245
5121
246
5124
247
5126
248
5127
249
514 Applications
254
Bibliography
257
INDEX
259
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