Àâòîðèçàöèÿ
Ïîèñê ïî óêàçàòåëÿì
Wester M.J. — Computer Algebra Systems: A Practical Guide
Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå Íàøëè îïå÷àòêó?
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 |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Matrix operations, performance of various CASs 50—52 Matrix operations, synonyms 32 392—393 Maxima 337 355 see MEGA symposiums 370 Mellin transform, performance of various CASs 57 Memo functions 266—267 Menabrea, Luigi F. 325 Menabrea, translation by Ada Lovelace 325 329 Mixed-mode expressions, CAS-generated Fortran code for 242—243 Mixed-mode expressions, evaluation in Fortran 242—243 Mock-Mma 341 Modulo, synonyms 391 MPP/MPP3D quasi-CAS software 311 Multiple-valued complex functions 73—76 Multiplication of matrices, synonyms for 392 Multiplication, noncommutative multiplication, synonyms 391 MuMATH. 333 358—359 360 MuPAD, architecture 2 11 MuPAD, capabilities 11 341 MuPAD, case-sensitivity 241 MuPAD, code generation facilities 235 237 MuPAD, development of 11 MuPAD, general characteristics 341 358—359 MuPAD, integrability tests in 229 232 MuPAD, language syntax 11 31 MuPAD, latest version (1.4.0) introduced 26 MuPAD, manuals 363 MuPAD, newsletter 365 MuPAD, operating systems 341 355 MuPAD, origin of name 360 MuPAD, parallel functionality in 333 341 MuPAD, performance 10 12 13 41—60 MuPAD, performance, algebra 44—45 MuPAD, performance, Boolean logic 41 MuPAD, performance, Chebyshev polynomials 46 82—85 87—91 93 95—97 MuPAD, performance, code generation 42 238 MuPAD, performance, combinatorial theory 43 MuPAD, performance, complex analysis 34 46—47 MuPAD, performance, differentiation 13 54 MuPAD, performance, equations 13 48—49 103—110 112—120 MuPAD, performance, factoring of polynomials 13 MuPAD, performance, graphing 13 MuPAD, performance, inequalities 49—50 119 MuPAD, performance, integration 13 14 54—56 MuPAD, performance, limits computation 13 53—54 157 158 165 167 169 MuPAD, performance, matrix theory 50—52 MuPAD, performance, nonlinear equations 13 MuPAD, performance, number theory 43—44 MuPAD, performance, numbers 41—42 MuPAD, performance, numerical analysis/calculations 13 42 MuPAD, performance, operators 58—59 MuPAD, performance, ordinary differential equations 13 57—58 194 197 198 201 203 207 209 MuPAD, performance, partial differential equations 58 MuPAD, performance, pattern matching 60 MuPAD, performance, polynomial systems solution 103 126 129 131n[5] 133 135 140 142 147—148 MuPAD, performance, products 53 MuPAD, performance, programming operations 59 MuPAD, performance, recursion relations 13 MuPAD, performance, series 13 15 56—57 MuPAD, performance, set theory 41 MuPAD, performance, simplifications 13 28 29 33 43 44 MuPAD, performance, special functions 46 MuPAD, performance, statistics 43 MuPAD, performance, sums 13 52—53 MuPAD, performance, tensor analysis 52 MuPAD, performance, transforms 57 MuPAD, performance, trigonometries 45—46 115 117 MuPAD, performance, vector analysis 50 MuPAD, performance, zero equivalence determination 47—48 MuPAD, price/cost (nil!) 11 12 18 MuPAD, synonyms for, code generation 253 382 MuPAD, synonyms for, graphics operations 394 MuPAD, synonyms for, mathematical operations 150—151 388—394 MuPAD, synonyms for, programming operations 381—388 MuPAD, user interface 11 MuPAD, workshops 380 NAG Ltd see also "Numerical Algorithms Group" NAG Ltd, packages offered by 17 334 Nested radicals 62 Nested radicals, causes 63—64 Nested radicals, measure of degree of nesting 69—70 Nested radicals, simplifying of 64—71 Nested radicals, simplifying of, control of recursive simplification 70—71 Nested radicals, simplifying of, implementation of algorithms 68—69 Nested radicals, simplifying of, mathematical basis of algorithms 65—67 New Mexico Initiative for Math Reform, Best of Both Worlds forum 289 New Mexico Initiative for Math Reform, survey of technology usage 312—313 New Mexico, University of 312 New Zealand, conferences covering CA 376 Newsletters and journals [covering CAS] 364—365 Newspeak programming language 280n[7] Noncommutative multiplication, synonyms 391 Nonlinear equations, integrability tests 211—232 Nonlinear equations, numerical solutions, performance of various CASs 13 Nonlinear equations, numerical solutions, test problem 15—16 Nonlinear ordinary differential equations, solution of 200—202 Nonlinear ordinary differential equations, solution of, by Bernoulli equations 201—202 Nonlinear ordinary differential equations, solution of, by contact transformation 201 Nonlinear ordinary differential equations, solution of, by dependent-variable-missing method 202 Nonlinear ordinary differential equations, solution of, by integrating factors 200—201 Normal distribution, performance of various CASs 43 Not equal, synonyms for 384 Not, synonyms for 384 notations 37—38 Noun operator 264 NSF (National Science Foundation) funded projects 289 293 310 311 NTL library 352 355 Number theory, performance of various CASs 43—44 Number theory, programs 343—347 Numbers program 346 355 Numbers, performance of various CASs 41—42 Numerical Algorithms Group see also "Axiom" Numerical Algorithms Group, address 17 334 Numerical Algorithms Group, mathematics library 235 334 Numerical analysis/calculations of limits 163—164 Numerical analysis/calculations, CASs compared with compiled programming languages 233 Numerical analysis/calculations, performance of various CASs 13 42 233n[1] Numerical analysis/calculations, synonyms 390 Numerical analysis/calculations, test problems 12—13 Numerical packages 303 Object-oriented approach to evaluation 262 Object-Oriented Programming 2 3 Online documentation 31 OpenGL, support for 333 338 340 OpenMath project 34 OpenMath project, workshops 371 Operating systems 355 Operators, performance of various CASs 58—59 Or, synonyms for 384 Ordinary differential equations see also "Linear ordinary differential equations" "Non-linear Ordinary differential equations, solution of, input-driven methods 191 195—196 Ordinary differential equations, solution of, internal errors 205—206 Ordinary differential equations, solution of, out-of-time/memory errors 206—208 Ordinary differential equations, solution of, output-driven methods 191 198—200 Ordinary differential equations, solution of, performance of various CASs 13 57—58 192—209 Ordinary differential equations, solution of, synonyms for 394 Ordinary differential equations, solution of, test problems 16 Ordinary differential equations, solution of, transformation methods 196—198 Ordinary differential equations, solution of, unable to solve/not implemented failure 205 Ordinary differential equations, systems, higher-order systems 204 Ordinary differential equations, systems, inhomogeneous systems 204—205 Ordinary differential equations, systems, linear ODEs with constant coefficients 202—203 Ordinary differential equations, systems, solution by integrable combinations 203 Ordinary differential equations, systems, triangular systems 203—204 Ordinary differential equations, wrong solutions 208 Origins of CA 323—332 Origins of names of CASs 360 Orthogonal polynomials see also "Chebyshev polynomials" Orthogonal polynomials, computation of 79 Output operations, synonyms 382 Pade approximation, notation 38 Pade approximation, performance of various CASs 13 56 Pade approximation, test problems 15 56 Paderbom, University of see also "MuPAD" Paderbom, University of, address 18 Painleve test 212 Pancake, Cherri M. 35 PARI/GP package 346 355 Partial differential equations, solution of, performance of various CASs 58 PASCO conferences 371 Pattern containing keywords, finding 381 Pattern matching, notation 38 Pattern matching, performance of various CASs 60 Pattern matching, synonyms 386 Performance of various CASs 8 13 24 Piecewise function, synonyms 389 Pletsch, Bill, article 285—322 Pletsch, biography 411 Plotting, synonyms 394 Polynomial conserved densities algorithm for 216 Polynomial conserved densities algorithm for, implementation in Mathematica 217—218 Polynomials see also "Chebyshev polynomials" "Legendre Polynomials with infinitely many solutions 124—125 Polynomials with infinitely many solutions, performance of various CASs in solving 138—142 Polynomials, Fortran code 241—242 Polynomials, manipulation of roots of, synonyms for 391 Polynomials, solution of 61—62 102—103 123—126 174 Polynomials, solution of, performance of various CASs 103 126—148 Polynomials, solution of, synonyms for 149—151 Polynomials, student homework assignment 295—296 Polynomials, zero-dimensional systems 124 Polynomials, zero-dimensional systems with parameters 124—125 Polynomials, zero-dimensional systems with parameters, performance of various CASs in solving 136—138 Polynomials, zero-dimensional systems, performance of various CASs in solving 127—136 144 148 Postel, biography 412 Postel, Frank, article 191—209 Power series in computation of limits 157—159 Power series, Fortran code 242 Power series, notation 38 Power series, performance of various CASs 56 Prentice, biography 412 Prentice, John K., article 233—254 Prepend an element to a list, synonyms 383 Previous expression, synonyms 382 Print graph, performance of various CASs 13 Print text and result, synonyms for 387 Product of terms, performance of various CASs 53 Product of terms, synonyms 393 Programming operations, performance of various CASs 59 Programming operations, synonyms for 381—388 Psi function, notation 38 Psi function, performance of various CASs 46 Psi function, synonyms 389 PSODE program 209 Puiseux series 38 164 Purdue Calculus Reform Project 294 311 QEPCAD (Quantifier Elimination by Partial Cylindrical Algebraic Decomposition) algorithm 172 178 180 Quasi-CAS packages 302—304 311 Quit, synonyms 382 Quote operators 264 270 Radicals, equations containing 63—64 110 Radicals, meaning of term 61—62 Radicals, nested 62 Radicals, nested, causes of 63—64 Radicals, nested, measure of degree of 69—70 Radicals, nested, reasons for denesting 62—63 Radicals, nested, simplifying of 64—71 Raksanyi's example [polynomial systems] 137 Range arithmetic 275 Real part, synonyms for 392 Recurrence equations, Chebyshev polynomials, computation by 88—90 Recursion operators for systems 225—226 Recursion operators, algorithm for polynomial recursion operators 222—225 Recursion operators, definition 220—221 Recursion operators, examples 221 Recursion relations, solution of, performance of various CASs 13 Recursion relations, test problems 16 Recursive procedures, translation into C 239—240 Recursive simplification, of nested radicals 70—71 Recussion, meaning of term 69n[8] RedTen package 350 REDUCE, case-insensitivity 241 n[9] REDUCE, code generation facilities 234 235 236 237 237 239 240 REDUCE, evaluation in 278 279 REDUCE, general characteristics 341 358—359 REDUCE, historical origins 357 REDUCE, integrability tests in 228 229 231 232 REDUCE, latest version (3.6) introduced 26 REDUCE, manuals 363 REDUCE, operating systems 341 355 REDUCE, origin of name 360 REDUCE, performance 41—60 REDUCE, performance, algebra 44—45 REDUCE, performance, Boolean logic 41 REDUCE, performance, Chebyshev polynomials 46 82—85 87—91 93 95—97 REDUCE, performance, code generation 42 238 REDUCE, performance, combinatorial theory 43 REDUCE, performance, complex analysis 34 46—47 REDUCE, performance, differentiation 54 REDUCE, performance, equations 21 48—49 103—110 112—120 REDUCE, performance, inequalities 49—50 119 REDUCE, performance, integration 54—56 REDUCE, performance, limits computation 53—54 155 165 167 169 REDUCE, performance, matrix theory 50—52 REDUCE, performance, number theory 43—44 REDUCE, performance, numbers 41—42 REDUCE, performance, numerical analysis 42 REDUCE, performance, operators 58—59 REDUCE, performance, ordinary differential equations 57—58 194 195 200 202 209 REDUCE, performance, partial differential equations 58 REDUCE, performance, pattern matching 60 REDUCE, performance, polynomial systems solution 103 127 129 130—131 133 134 135 136 137 138 141 142 REDUCE, performance, products 53 REDUCE, performance, programming operations 59 REDUCE, performance, series 56—57 REDUCE, performance, simplifications 28 29 43 44 REDUCE, performance, special functions 46 REDUCE, performance, statistics 43 REDUCE, performance, sums 52—53 REDUCE, performance, tensor analysis 52 REDUCE, performance, transforms 57 REDUCE, performance, trigonometries 45—46 115 117 REDUCE, performance, vector analysis 50 REDUCE, performance, zero equivalence determination 47—48 REDUCE, synonyms for, code generation 253—254 382 REDUCE, synonyms for, graphics operations 394 REDUCE, synonyms for, mathematical operations 151 388—394 REDUCE, synonyms for, programming operations 381—388 REDUCE, workshops 380 References listed 395—406 Regression analysis, performance of various CASs 43 Return unevaluated symbol, synonyms 385 Review of CASs 13 41—60 313—319 334—342 Rewrite rules, notation 38 Rhine workshops [on CAS] 374 Ricci package 350 Rich, Albert D., article 61—72 Rich, biography 412—413 Riemann sum 13 Riemann sum, student calculations using CA 291—292 Riemann zeta function 38 46 RIKEN symposiums 378 RIMS meetings 377 Risa/Asir 342 355 Ritt — Wu characteristic set method [for polynomial systems] 146 Rodrigues formula, computation of Chebyshev polynomials by 86—87 ROMIN 3R-robot 137 RootOf symbol 128 129—130 131 201 Rosser matrix, performance of various CASs 51 RTA meetings 372
Ðåêëàìà
|
|
Î ïðîåêòå