Wester M.J. — Computer Algebra Systems: A Practical Guide
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Íàçâàíèå: Computer Algebra Systems: A Practical Guide
Àâòîð: Wester M.J.
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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.
Derive, programming capabilities300322 Derive, synonyms for graphics operations394 Derive, synonyms for mathematical operations388—394 Derive, synonyms for programming operations381—388 Derive, user interface4—5 Derive, word processing capabilities322 Derived types and structures247 Developer-user communication35—36 Differential equations, solution of, Chebyshev polynomials computation by90—91 Differential equations, solution of, performance of various CASs1357—58 Differential equations, solution of, synonyms for394 Differential equations, solution of, test problems16 Differential operator, defining and applying, synonyms for394 Differentiation, performance of various CASs1354 Differentiation, synonyms393 Differentiation, test problem14 Dilation invariance211212—214 Dirac delta notation37 Dirac delta synonyms389 DISCO symposiums369 Display output, synonyms382 Distance learning304see Distance learning, Distributed Maple338355 DMV equation214 Documentation [for various CASs]30—31362—363 EACA conferences375 ECCAD meetings373 Educational use of CA285—322see Ehime workshops377 Eigenvalues/eigenvectors of matrix, performance of various CASs1351 Elliptic integrals, synonyms389 Equal, synonyms for384 Equation notation, synonyms383 Equations, solution of, performance of various CASs2748—49103—120 Equations, solution of, synonyms for391 error messages31 Euler equations196 Euler operator216 Euler — Maclaurin formula13 Euler's constant, notation3738 Euler's constant, synonyms388 Euler's totient function, performance of various CASs43 Euler's transformation163 Europe, conferences covering CA374—375 Evaluation in Axiom267—269274279 Evaluation in Macsyma264266267269—271274279 Evaluation in Maple264266267271—275279 Evaluation in Mathematics266267274275—278279 Evaluation in Reduce278279 Evaluation, approaches by rules260—261 Evaluation, approaches, eval procedure259 Evaluation, approaches, multiphase model259—260 Evaluation, approaches, object-oriented evaluation262 Evaluation, context258 Evaluation, failures/limitations/problems262—265 Evaluation, failures/limitations/problems, arrays confused with matrices265 Evaluation, failures/limitations/problems, failure of top-down model262—263 Evaluation, failures/limitations/problems, inert functions/operators263—265 Evaluation, meaning of term255 Evaluation, user-programmed changes279 Exact rational arithmetic22 Expand into separate fractions, synonyms390 Exponentials, equations involving104—109 Export two space-separated columns of integers to file, synonyms387 Expressionist1031see Factorial, synonyms388 Factoring of polynomials, performance of various CASs13 Factoring of polynomials, test problem15 Factorization, performance of various CASs4445 Factorization, synonyms392 False, synonyms for384 FAMOUS system154 Fateman, biography408 Fateman, Richard J., article255—284 FEFIX333344355 Fermat program344355 FeynCalc package349 Fibonacci number3859389 Fibonacci number recursion262 Finite-precision arithmetic249 First operand, synonyms387 Fixed-point evaluation266 Flexibility of CASs300 Floating point calculations, performance of various CASs42 Floating point operations notation38 FORM335 FORM, code for computation of symmetries229232 FORM, operating systems355 Formulae1333 Fortran, case-insensitivity241 Fortran, generation as/translation to233—254 Fortran, generation as/translation to, data types237 Fortran, generation as/translation to, performance of various CASs4259238 Fortran, generation as/translation to, synonyms/instructions251—254387 Fortran, line breaks243—244 Fortran, new features [in Fortran 90/95]244—248 Fortran, new features [in Fortran 90/95], array expressions and intrinsics246—247 Fortran, new features [in Fortran 90/95], derived types and structures247 Fortran, new features [in Fortran 90/95], free-format source244—245 Fortran, new features [in Fortran 90/95], kind parameters245—246 Fourier series, notation38 Fourier series, performance of various CASs56—57 Fourier transform, notation38 Fourier transform, performance of various CASs57 Fractions over common denominator, synonyms391 Fractions, expansion into separate fractions, synonyms391 Frechet derivative215218 Frechet derivative, implementation in Mathematica220 FS (formal symmetries) program228231 Function definition with a local variable, synonyms385 Function definition, synonyms385 Function of an indefinite number of arguments, synonyms385 Gamma function, synonyms389 GANITH toolkit348355 GAP system342355 Gateway test [in education]289—290 GENCRAY code generation utility234 General purpose CASssee also "Axiom""Derive""Macsyma""Maple""Mathematica""MuPAD""REDUCE" General purpose CASs, general characteristics358—359 General purpose CASs, historical origins357 General purpose CASs, manuals362—363 General purpose CASs, origins of names360 General purpose CASs, reviews1341—60313—319334—342 General purpose CASs, synonyms, graphics operations394 General purpose CASs, synonyms, mathematical operations149—151388—394 General purpose CASs, synonyms, programming operations381—388 Generalized symmetries218—220 Generalized symmetries, algorithm for polynomial generalized symmetries219—220 Generalized symmetries, algorithm for polynomial generalized symmetries, implementation in Mathematica220 Generalized symmetries, definition218 Generalized symmetries, examples218—219 Generalized symmetries, software for228—229231—232 Generate * synonyms387 Generate a list, synonyms384 Generate a matrix, performance of various CASs13 Generate a matrix, synonyms for382 Generate a matrix, test problem16 Generate FORTRAN, synonyms387 GENTRAN utility234236239240248 Geometric modeling, areas172—179 Geometric modeling, volumes179 glimit package [in Maple program]165 glimit package [in Maple program], performance167169 GNU MP library351355 GNU-calc335 Goektas*, Uenal, article211—232 Goektas*, Uenal, biography409 Gonnet — Gruntz algorithm [for computation of limits]160161 Gonnet's example [polynomial systems]139147 Graebe, biography409
Graebe, Hans-Gert article121—151 Graphics capabilities [of various packages]6819—20 Graphics operations, performance of various CASs13 Graphics operations, synonyms for394 Graphics operations, test problems16 Graphing/symbolic calculators303319—320 Gravitational potential problem14 GRB program345355 GRG CAS349 Groebner basis calculations127129136142174181 Groebner basis calculations, programs343345347 Groebner basis calculations, synonyms392 Groebner factorizer method [for polynomials]122126136142 Groebner factorizer method [for polynomials], call/command/synonym127140 Group theory programs342—343 GRTensor package349 Gruntz, biography409 Gruntz, Dominik, article153—170 Hardware, educational use300 Hardy, G.H., on mathematics331 Hash-arrays266 Heaviside (unit step) function, notation38 Heaviside (unit step) function, synonyms389 Hereman, biography410 Hereman, Willy, article211—232 Hessian, performance of various CASs5152 Hewlett — Packard 48G calculator320—321 Homework assignments289295 Horner's rule, performance of various CASs42 HOW option307 Hypergeometric functions, notation38 Hypergeometric functions, performance of various CASs46 Hypergeometric functions, synonyms389 Hypergeometric functions, use by Mathematica9 IBM CASs3358see"Scratchpad" Idempotence266 If then else statements, synonyms384 IMACS-ACA conferences370 Import two space-separated columns of integers from file, synonyms387 Indefinite integrals, performance of various CASs1354—55 Indefinite integrals, test problem14 Indefinite integrals, traditional hand calculations286—287 Independent sets125 Inequalities117—119 Inequalities, performance of various CASs49—50119 Infinite evaluation266 Infix operators, defining and using, synonyms for386 Initialization synonyms381 Institutions, attitude to CA in education301—302 Institutions, survey of CAS use310—312 instructionssee "Synonyms" integer arithmetic242 Integrability tests for nonlinear equations211—232 Integrability tests for nonlinear equations, conservation laws214—218 Integrability tests for nonlinear equations, dilation/scaling invariance concept used211212—214 Integrability tests for nonlinear equations, generalized symmetries218—220 Integrability tests for nonlinear equations, recursion operators for scalar equations220—225 Integrability tests for nonlinear equations, recursion operators for systems225—226 Integrated curriculum301—302 Integrating factors [of ODEs]200—201 Integration, performance of various CASs1354—56 Integration, synonyms393 Integration, test problems14 Integration, traditional approach to solution287 Interface blocks247 Internet instruction304 internet resources361—362 Interval analysis, classroom example297 Interval analysis, performance of various CASs42 InvariantsSymmetries.m package212217219226—228231 Inverse Laplace transform, performance of various CASs57 Inverse Laplace transform, synonyms393 Inversion of matrices, performance of various CASs13 Inversion of matrices, test problem12 ISSAC conferences367 Iterative series computation of Chebyshev polynomials93 JACAL336355 Jacobian, performance of various CASs51 Jacquard cards325 Japan, conferences covering CA377—378 Java code248 Jeffrey, biography410 Jeffrey, David J., article61—72 Jenks, Richard3358 Jonquiere's polylogarithm function, notation38 Jordan matrix, performance of various CASs51 Journals and newsletters [covering CAS]364—366 JSSAC meetings378 Kan system345355 KANT (Computational Algebraic Number Theory) package352355 KASH shell352 Katsura examples [polynomial systems]133136 KdV (Kortweg — de Vries) equation212 KdV (Kortweg — de Vries) equation, building block of recursion operators for223 Keyword description synonyms381 Kind parameters [in Fortran]245—246 Koepf, biography410—411 Koepf, Wolfram, article79—99 Krider's example [polynomial systems]138139141147 Kronecker delta, notation37 l'Hopital's rule154155156 Lambert W function38110—111118 Language syntax3891131256—257314 Laplace transform, notation38 Laplace transform, performance of various CASs57 Laplace transform, synonyms393 Larcombe, biography411 Larcombe, Peter J., article323—332 Latin America, conferences covering CA374 Laurent series, notation38 Laurent series, synonyms393 Lax equation218 Learning curve [for new software]299 Least squares derivation, performance of various CASs52 Legendre function, notation38 Legendre polynomial, notation38 Legendre polynomial, performance of various CASs in computation59 Legendre polynomial, synonyms389 Length of list, synonyms383 Levi-Civita symbol52 Levin's u-transform163 lexical scoping258272 LiDIA library352355 Lie algebraic techniques228229 LiE package342355 Lie point symmetries212219 Lie point symmetries, software for computations228342343 Limits computation, heuristic approach153—157 Limits computation, infinite-cancellation problem159 Limits computation, infinite-cancellation problem, detecting and resolving160—161 Limits computation, limitations162—163 Limits computation, numerical determination of limits163—164 Limits computation, parameter-containing limits161—162 Limits computation, performance of various CASs1353—54164—165167169 Limits computation, power series approach157—159 Limits computation, synonyms393 Limits computation, test problems15166168 Line breaks [in C or Fortran]243—244 Line continuation, synonyms382 Linear equations, solution of101—102 Linear ordinary differential equations with constant coefficients195 Linear ordinary differential equations, adjoint equations196 Linear ordinary differential equations, Euler-type196 Linear ordinary differential equations, exact equations197—198 Linear ordinary differential equations, exponential solutions199 Linear ordinary differential equations, general form195 Linear ordinary differential equations, Liouvillian solutions200207 Linear ordinary differential equations, polynomial solutions198—199 Linear ordinary differential equations, rational solutions199 Linear ordinary differential equations, reduction of order197
* synonyms 
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