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Wester M.J. Ч Computer Algebra Systems: A Practical Guide
Wester M.J. Ч Computer Algebra Systems: A Practical Guide

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Ќазвание: Computer Algebra Systems: A Practical Guide

јвтор: Wester M.J.


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.

язык: en

–убрика: Computer science/

—татус предметного указател€: ”казатель в процессе заполнени€

ed2k: ed2k stats

√од издани€: 1999

 оличество страниц: 505

ƒобавлена в каталог: 11.02.2015

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
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      310Ч311
Algebra, performance of various CASs      44Ч45
Algebra, programs      343Ч347
Algebraic geometry packages      347Ч348
Algebraic number, equations involving      103Ч104
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      312Ч313
ANALITTK      333 357
Analytical Engine [Babbage's]      324
Analytical Engine [Babbage's] and modern computers      327
Analytical Engine [Babbage's], Ada Lovelace's article      325Ч326 329 330
Analytical Engine [Babbage's], Menabrea's description      325
Analytical Engine [Babbage's], symbolic aspects      324Ч331
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      21Ч22
Archimedes, Way of      288
Areas, computation of      172Ч179 181Ч188
Areas, creation of cells and cylinders      173Ч178
Areas, problems with parameters      178
Arizona, University of      303 311 see
Arnborg examples [polynomial systems]      126 135
Array expressions      31Ч32 246Ч247
Arrays, confusion with matrices      265
Arrays, meaning of term      265
ASCM conferences      376
Asia, conferences covering CA      376
Aslaksen, Helmer, article      73Ч78
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 236Ч237 237 240 241
Axiom, compiler in      333
Axiom, conferences      378
Axiom, development of      3
Axiom, evaluation in      267Ч269 274 279
Axiom, general characteristics      3Ч4 334 358Ч359
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 41Ч60
Axiom, performance, algebra      44Ч45
Axiom, performance, Boolean logic      41
Axiom, performance, Chebyshev polynomials      46 82Ч85 87Ч91 93 95Ч97
Axiom, performance, code generation      42 238
Axiom, performance, combinatorial theory      43
Axiom, performance, complex analysis      34 46Ч47
Axiom, performance, differentiation      13 54
Axiom, performance, equations      27 48Ч49 103Ч110 112Ч119
Axiom, performance, factoring of polynomials      13
Axiom, performance, graphing      13
Axiom, performance, inequalities      49Ч50 117
Axiom, performance, integration      13 54Ч56
Axiom, performance, limits computation      13 53Ч54 164 167 169 170
Axiom, performance, matrix theory      50Ч52
Axiom, performance, nonlinear equations      13 49
Axiom, performance, number theory      43Ч44
Axiom, performance, numbers      41Ч42
Axiom, performance, numerical analysis/calculations      13 13 42
Axiom, performance, operators      58Ч59
Axiom, performance, ordinary differential equations      13 57Ч58 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 140Ч141 141 142
Axiom, performance, products      53
Axiom, performance, programming operations      59
Axiom, performance, recursion relations      13
Axiom, performance, series      13 56Ч57
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 52Ч53
Axiom, performance, tensor analysis      52
Axiom, performance, transforms      57
Axiom, performance, trigonometries      45Ч46 115 117
Axiom, performance, vector analysis      50
Axiom, performance, zero equivalence determination      47Ч48
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 388Ч394
Axiom, synonyms for programming operations      381Ч388
Axiom, user interface      3 19
Babbage, Charles      324Ч332
Babbage, Charles, Analytical Engine      324
Babbage, Charles, Analytical Engine, symbolic aspects      324Ч331
Babbage, Charles, Difference Engine      324
Bergman program      343 355
Bernardin, Laurent, article      101Ч120
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      407Ч415
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      233Ч254
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      251Ч254
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      249Ч250
CAP meetings      371
Cartan package      348
CAS substrates      351Ч354
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      81Ч82
Chebyshev polynomials, computation of, by determinants      83Ч84
Chebyshev polynomials, computation of, by differential equations      90Ч91
Chebyshev polynomials, computation of, by matrix powers      87Ч88
Chebyshev polynomials, computation of, by recurrence equations      88Ч90
Chebyshev polynomials, computation of, by Rodrigues formula      86Ч87
Chebyshev polynomials, computation of, by series representations      91Ч94
Chebyshev polynomials, computation of, divide-and-conquer approach      94Ч98
Chebyshev polynomials, computation of, generating functions used      85Ч86
Chebyshev polynomials, computation of, performance of various CASs      46 82Ч85 87Ч93 95Ч97
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      233Ч254 see "Fortran"
Code generation facilities, capabilities of various CASs      235Ч241
Code generation facilities, caution in use of generated code      248Ч250
Code generation facilities, critique of code generated      241Ч248
Code generation facilities, data types handled by various CASs      237
Code generation facilities, optimized options      240Ч241
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 73Ч76
Complex analysis, performance of various CASs      34 46Ч47
Complex analysis, synonyms      392
Complex analysis, test problems      34 46Ч47 49 76Ч78
Complex expression, conversion to rectangular form, performance of various CASs      47
Complex expression, conversion to rectangular form, synonyms for      392
Complex functions, multiple-valued      73Ч76
Complex loop iterating on a list, synonyms      384
Computer classroom instruction      290Ч294
Computer classroom instruction, example      291Ч292
Computer classroom instruction, problems/limitations      297Ч298
Computer classroom instruction, progress to date      293Ч294
Computer classroom instruction, techniques      293Ч294
Computer classroom instruction, theory      292Ч293
Concatenated strings, synonyms      384
conditional expressions      283Ч284
Conferences      367Ч380
Conix3D Explorer      333 340
CONLAW 1/2/3      229 231
Conservation laws      214Ч218
Conservation laws, algorithm for polynomial conserved densities      216
Conservation laws, algorithm for polynomial conserved densities, implementation in Mathematica      217Ч218
Conservation laws, definition      214Ч215
Conservation laws, examples      215Ч216
Conservation laws, software for      228Ч229 231Ч232
Contact transformation [of ODEs]      201
Control considerations      299Ч300
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.      34Ч35
Cosine integral, synonyms      389
Counter-clockwise continuity      73
Crack program      209 229
Cramer's rule      249n[17]
Cubic equation, solution of      26Ч27
Curriculum considerations      298Ч299
Customizing of CAS      308 309
Cylinders, two-dimensional, projection onto x-axis      175Ч176
Cylinders, two-dimensional, projection onto y-axis      176Ч178
Cylindrical decomposition algorithm, projection phase      175 179
Cylindrical decomposition problems      172Ч179
D'Alembert's method/procedure      197 207
DALI program      154
de Morgan, Augustus      329
de Souza, biography      407Ч408
de Souza, Paulo Ney, article      333Ч355
Define a function from an expression, synonyms      385
Definite integrals, performance of various CASs      13 55Ч56
Definite integrals, test problem      14
DELIA package      228Ч229 231
DELIMITER program      154
Denesting of square roots      62
Denesting of square roots, algorithms for      64Ч71
Denesting of square roots, control of recursive denesting      69Ч71
Denesting of square roots, reasons for      62Ч63
Derive, capabilities      2 4Ч5 313Ч314 322 335
Derive, conferences      378Ч379
Derive, Converge package run in tandem      303
Derive, denesting problems      69n[7] 72
Derive, educational use      312 313Ч314
Derive, general characteristics      335 358Ч359
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      5Ч6 8 13 41Ч60
Derive, performance, algebra      44Ч45
Derive, performance, Boolean logic      41
Derive, performance, Chebyshev polynomials      46 84 93
Derive, performance, combinatorial theory      43
Derive, performance, complex analysis      34 46Ч47
Derive, performance, differentiation      13 54
Derive, performance, equations      27 48Ч49 103Ч110 112Ч119
Derive, performance, factoring of polynomials      13
Derive, performance, graphing      13
Derive, performance, inequalities      49Ч50 119
Derive, performance, integration      13 54Ч56
Derive, performance, limits computation      13 53Ч54 164 167 169
Derive, performance, matrix theory      50Ч52
Derive, performance, nonlinear equations      13 16 49
Derive, performance, number theory      43Ч44
Derive, performance, numbers      41Ч42
Derive, performance, numerical analysis/calculations      13 13 42 322
Derive, performance, operators      58Ч59
Derive, performance, ordinary differential equations      13 57Ч58
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 56Ч57
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 52Ч53
Derive, performance, tensor analysis      52
Derive, performance, transforms      57
Derive, performance, trigonometries      45Ч46 115 117
Derive, performance, vector analysis      50
Derive, performance, zero equivalence determination      47Ч48
Derive, price/cost      18
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