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Wester M.J. — Computer Algebra Systems: A Practical Guide
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Íàçâàíèå: Computer Algebra Systems: A Practical GuideÀâòîð: Wester M.J. Àííîòàöèÿ: This thorough overview of the major computer algebra (symbolic mathematical) systems compares and contrasts their strengths and weaknesses, and gives tutorial information for using these systems in various ways.
Compares different packages quantitatively using standard 'test suites' Ideal for assessing the most appropriate package for a particular user or application Examines the performance and future developments from a user's and developer's viewpoint Internationally recognized specialists overview both the general and special purpose systems and discuss issues such as denesting nested roots, complex number calculations, efficiently computing special polynomials, solving single equations and systems of polynomial equations, computing limits, multiple integration, solving ordinary differential and nonlinear evolution equations, code generation, evaluation and computer algebra in education. The historical origins, computer algebra resources and equivalents for many common operations in seven major packages are also covered.
By providing such a comprehensive survey, the experienced user is able to make an informed decision on which system(s) he or she might like to use. It also allows a user new to computer algebra to form an idea of where to begin.
Since each system looked at in this book uses a different language, many examples are included to aid the user in adapting to these language differences. These examples can be used as a guide to using the various systems once one understands the basic principles of one CAS. The book also includes contributions which look at the broad issues of the needs of various users and future developments, both from the user's and the developer's viewpoint.
The author is a leading figure in the development and analysis of mathematical software and is well known through the 'Wester test suite' of problems which provide a bench mark for measuring the performance of mathematical software systems. The book will help develop our range of titles for applied mathematcians.
The book will provide a unique, fully up-to-date and independent assessment of particular systems and will be of interest to users and purchasers of CAS's.
ßçûê: Ðóáðèêà: Computer science /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Óêàçàòåëü â ïðîöåññå çàïîëíåíèÿ ed2k: ed2k stats Ãîä èçäàíèÿ: 1999Êîëè÷åñòâî ñòðàíèö: 505Äîáàâëåíà â êàòàëîã: 11.02.2015Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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AAECC conferences 368 ACA conferences 370 see Ada" ACA conferences, Ada programming language 330n[5] Adaptability of CASs 300 Addition of matrices, synonyms for 392 ADG workshops 368 AISC forums 368 Albuquerque Technical Vocational Institute 310—311 Algebra, performance of various CASs 44—45 Algebra, programs 343—347 Algebraic geometry packages 347—348 Algebraic number, equations involving 103—104 Algebraic number, meaning of term 62 AMATYC (American Mathematical Association of Two Year Colleges), Crossroads document 287 288 AMATYC (American Mathematical Association of Two Year Colleges), survey of technology usage 312—313 ANALITTK 333 357 Analytical Engine [Babbage's] 324 Analytical Engine [Babbage's] and modern computers 327 Analytical Engine [Babbage's], Ada Lovelace's article 325—326 329 330 Analytical Engine [Babbage's], Menabrea's description 325 Analytical Engine [Babbage's], symbolic aspects 324—331 And, synonyms for 384 Andante programming language 280n[7] Antisymmetric function, performance of various CASs 46 Apfloat package 351 Append an element to a list, synonyms 383 Append two lists, synonyms 383 Apply "+" to sum a list, synonyms 385 Apply a function to a list of its arguments, synonyms 386 Arbitrary precision decimal arithmetic 21—22 Archimedes, Way of 288 Areas, computation of 172—179 181—188 Areas, creation of cells and cylinders 173—178 Areas, problems with parameters 178 Arizona, University of 303 311 see Arnborg examples [polynomial systems] 126 135 Array expressions 31—32 246—247 Arrays, confusion with matrices 265 Arrays, meaning of term 265 ASCM conferences 376 Asia, conferences covering CA 376 Aslaksen, Helmer, article 73—78 Aslaksen, Helmer, biography 407 Assignment, synonyms 385 Assumptions and performance of various CASs 13 49 Assumptions, synonyms 390 Assumptions, test problem 14 Asymptotes, failure of CAS 288 ATCM conferences 376 Australia, conferences covering CA 376 Austria, educational use of CA 312 Automated algebraic manipulation see also "Analytical Engine [Babbage's]" Automated algebraic manipulation, Babbage's ideas 328 Automated algebraic manipulation, progress since 1950s 331 Axiom, architecture 2 Axiom, capabilities 3 334 Axiom, case-sensitivity 241 Axiom, code generation facilities 235 236—237 237 240 241 Axiom, compiler in 333 Axiom, conferences 378 Axiom, development of 3 Axiom, evaluation in 267—269 274 279 Axiom, general characteristics 3—4 334 358—359 Axiom, language syntax 3 Axiom, latest version (2.1) introduced 26 Axiom, manuals 362 Axiom, operating systems 334 355 Axiom, origin of name 360 Axiom, performance 4 13 41—60 Axiom, performance, algebra 44—45 Axiom, performance, Boolean logic 41 Axiom, performance, Chebyshev polynomials 46 82—85 87—91 93 95—97 Axiom, performance, code generation 42 238 Axiom, performance, combinatorial theory 43 Axiom, performance, complex analysis 34 46—47 Axiom, performance, differentiation 13 54 Axiom, performance, equations 27 48—49 103—110 112—119 Axiom, performance, factoring of polynomials 13 Axiom, performance, graphing 13 Axiom, performance, inequalities 49—50 117 Axiom, performance, integration 13 54—56 Axiom, performance, limits computation 13 53—54 164 167 169 170 Axiom, performance, matrix theory 50—52 Axiom, performance, nonlinear equations 13 49 Axiom, performance, number theory 43—44 Axiom, performance, numbers 41—42 Axiom, performance, numerical analysis/calculations 13 13 42 Axiom, performance, operators 58—59 Axiom, performance, ordinary differential equations 13 57—58 192 195 196 200 203 205 207 209 Axiom, performance, partial differential equations 58 Axiom, performance, pattern matching 60 Axiom, performance, polynomial systems solution 103 128 131 132 134 135 136 137 138 140—141 141 142 Axiom, performance, products 53 Axiom, performance, programming operations 59 Axiom, performance, recursion relations 13 Axiom, performance, series 13 56—57 Axiom, performance, set theory 41 Axiom, performance, simplifications 13 28 29 33 43 44 Axiom, performance, special functions 46 Axiom, performance, statistics 43 Axiom, performance, sums 13 52—53 Axiom, performance, tensor analysis 52 Axiom, performance, transforms 57 Axiom, performance, trigonometries 45—46 115 117 Axiom, performance, vector analysis 50 Axiom, performance, zero equivalence determination 47—48 Axiom, price/cost 17 Axiom, routine-calling capability 235 Axiom, synonyms for code generation 251 382 Axiom, synonyms for graphics operations 394 Axiom, synonyms for mathematical operations 149 388—394 Axiom, synonyms for programming operations 381—388 Axiom, user interface 3 19 Babbage, Charles 324—332 Babbage, Charles, Analytical Engine 324 Babbage, Charles, Analytical Engine, symbolic aspects 324—331 Babbage, Charles, Difference Engine 324 Bergman program 343 355 Bernardin, Laurent, article 101—120 Bernardin, Laurent, biography 407 Bernoulli equations 201 Bernoulli number 15 46 Bessel functions, notation 38 Bessel functions, problems involving 14 Bessel functions, problems involving, performance of various CASs 13 46 Bessel functions, synonyms 389 BigNum package 351 355 Binomial distribution, performance of various CASs 43 Biographies of contributors 407—415 Black box approach of CA 300 Boolean logic, performance of various CASs 41 Bowden, B.V. 331 Buchberger's algorithm 344 C [programming language], case-sensitivity 241 C [programming language], line breaks 243 C [programming language], translation to 233—254 C [programming language], translation to, data types 237 C [programming language], translation to, performance of various CASs 42 238 C [programming language], translation to, synonyms for 251—254 C++ [programming language] 248 C++ [programming language], libraries 352 CADE workshops 369 Calculus see also "Differentiation" "Integration" Calculus, performance of various CASs 54 Calling of external routines 235 Calls see "Synonyms" Canada, conferences covering CA 374 Cancellation problems 249—250 CAP meetings 371 Cartan package 348 CAS substrates 351—354 CASA package 347 CASC workshops 369 case sensitivity 241 Case sensitivity, synonyms 382 Casio CFX-9970G calculator 320 Chebyshev polynomials 80 Chebyshev polynomials, computation of, by built-in polynomials 81—82 Chebyshev polynomials, computation of, by determinants 83—84 Chebyshev polynomials, computation of, by differential equations 90—91 Chebyshev polynomials, computation of, by matrix powers 87—88 Chebyshev polynomials, computation of, by recurrence equations 88—90 Chebyshev polynomials, computation of, by Rodrigues formula 86—87 Chebyshev polynomials, computation of, by series representations 91—94 Chebyshev polynomials, computation of, divide-and-conquer approach 94—98 Chebyshev polynomials, computation of, generating functions used 85—86 Chebyshev polynomials, computation of, performance of various CASs 46 82—85 87—93 95—97 Chebyshev polynomials, notation 38 Chebyshev polynomials, size 80 Chebyshev polynomials, synonyms 81 389 Chi square test, performance of various CASs 43 Christoffel symbol 38 46 Clausen's paradox 74 Clear variables and functions, synonyms 385 CLOS (Common Lisp's object system) 281 CoCoa 344 CoCoA, operating systems 344 355 CoCoA, symposiums 369 Code generation facilities 233—254 see "Fortran" Code generation facilities, capabilities of various CASs 235—241 Code generation facilities, caution in use of generated code 248—250 Code generation facilities, critique of code generated 241—248 Code generation facilities, data types handled by various CASs 237 Code generation facilities, optimized options 240—241 Code generation facilities, performance of various CASs 42 238 CODEGEN utilities 234 Cohen, Joel 307 Combinatorial theory, performance of various CASs 43 Commands see "Synonyms" Comment, synonyms 382 Common denominator, synonyms 391 Common Lisp 258 280 see Common Lisp, object system 281 Commutative algebra program 344 Complex analysis 34 73—76 Complex analysis, performance of various CASs 34 46—47 Complex analysis, synonyms 392 Complex analysis, test problems 34 46—47 49 76—78 Complex expression, conversion to rectangular form, performance of various CASs 47 Complex expression, conversion to rectangular form, synonyms for 392 Complex functions, multiple-valued 73—76 Complex loop iterating on a list, synonyms 384 Computer classroom instruction 290—294 Computer classroom instruction, example 291—292 Computer classroom instruction, problems/limitations 297—298 Computer classroom instruction, progress to date 293—294 Computer classroom instruction, techniques 293—294 Computer classroom instruction, theory 292—293 Concatenated strings, synonyms 384 conditional expressions 283—284 Conferences 367—380 Conix3D Explorer 333 340 CONLAW 1/2/3 229 231 Conservation laws 214—218 Conservation laws, algorithm for polynomial conserved densities 216 Conservation laws, algorithm for polynomial conserved densities, implementation in Mathematica 217—218 Conservation laws, definition 214—215 Conservation laws, examples 215—216 Conservation laws, software for 228—229 231—232 Contact transformation [of ODEs] 201 Control considerations 299—300 Converge package 303 Convert a column vector into a list, synonyms 383 Convert a list into a column vector, synonyms 383 CONVODE program 209 Corbato, Fernando J. 34—35 Cosine integral, synonyms 389 Counter-clockwise continuity 73 Crack program 209 229 Cramer's rule 249n[17] Cubic equation, solution of 26—27 Curriculum considerations 298—299 Customizing of CAS 308 309 Cylinders, two-dimensional, projection onto x-axis 175—176 Cylinders, two-dimensional, projection onto y-axis 176—178 Cylindrical decomposition algorithm, projection phase 175 179 Cylindrical decomposition problems 172—179 D'Alembert's method/procedure 197 207 DALI program 154 de Morgan, Augustus 329 de Souza, biography 407—408 de Souza, Paulo Ney, article 333—355 Define a function from an expression, synonyms 385 Definite integrals, performance of various CASs 13 55—56 Definite integrals, test problem 14 DELIA package 228—229 231 DELIMITER program 154 Denesting of square roots 62 Denesting of square roots, algorithms for 64—71 Denesting of square roots, control of recursive denesting 69—71 Denesting of square roots, reasons for 62—63 Derive, capabilities 2 4—5 313—314 322 335 Derive, conferences 378—379 Derive, Converge package run in tandem 303 Derive, denesting problems 69n[7] 72 Derive, educational use 312 313—314 Derive, general characteristics 335 358—359 Derive, graphical capabilities 5 19 314 322 Derive, language syntax 314 Derive, latest version (4.11) introduced 26 Derive, manuals 362 Derive, operating systems 335 355 Derive, origin of name 360 Derive, performance 5—6 8 13 41—60 Derive, performance, algebra 44—45 Derive, performance, Boolean logic 41 Derive, performance, Chebyshev polynomials 46 84 93 Derive, performance, combinatorial theory 43 Derive, performance, complex analysis 34 46—47 Derive, performance, differentiation 13 54 Derive, performance, equations 27 48—49 103—110 112—119 Derive, performance, factoring of polynomials 13 Derive, performance, graphing 13 Derive, performance, inequalities 49—50 119 Derive, performance, integration 13 54—56 Derive, performance, limits computation 13 53—54 164 167 169 Derive, performance, matrix theory 50—52 Derive, performance, nonlinear equations 13 16 49 Derive, performance, number theory 43—44 Derive, performance, numbers 41—42 Derive, performance, numerical analysis/calculations 13 13 42 322 Derive, performance, operators 58—59 Derive, performance, ordinary differential equations 13 57—58 Derive, performance, partial differential equations 58 Derive, performance, pattern matching 60 Derive, performance, products 53 Derive, performance, programming operations 59 Derive, performance, recursion relations 13 Derive, performance, series 13 56—57 Derive, performance, set theory 41 Derive, performance, simplifications 13 28 29 33 43 44 Derive, performance, special functions 46 Derive, performance, statistics 43 Derive, performance, sums 13 52—53 Derive, performance, tensor analysis 52 Derive, performance, transforms 57 Derive, performance, trigonometries 45—46 115 117 Derive, performance, vector analysis 50 Derive, performance, zero equivalence determination 47—48 Derive, price/cost 18
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