Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Geddes K., Czapor S., Labahn G. — Algorithms for computer algebra
Geddes K., Czapor S., Labahn G. — Algorithms for computer algebra

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Algorithms for computer algebra

Авторы: Geddes K., Czapor S., Labahn G.

Аннотация:

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 1992

Количество страниц: 585

Добавлена в каталог: 22.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$Applicable\,Algebra\,in\,Engineering,\,Communication\,and\,Computing$      10
$Journal\,of\,Symbolic\,Computation$      10
0-reduction      449
Addition, in finite fields      116
Addition, in quotient fields      61
Addition, of extended power series      69
Addition, of multiprecision integers      112
Addition, of polynomials      38
Addition, of power series      63 114
Addition, on residue classes      167
Adjoint, form      396 402
Adjoint, solution      403 423
Admissible ordering      431 459
ALDES      7
Algebra      153
Algebraic, algorithms      1
Algebraic, extension      12 15 406—407 458
Algebraic, function      141 421
Algebraic, function, differentiation of      522
Algebraic, function, integration of      561
Algebraic, manipulation      1
Algebraic, number field      378—9 383—4
Algebraic, over      514
Algebraically closed      414 463
Algol      5 7
Allocation, array      94
Allocation, dynamic array      94
Allocation, linked      94
ALPAK      6 279
ALTRAN      2 6 90 96—7 99
ANALITIK      8
Arctangent over      571
Associate classes      27
Associates      26
Associativity      23
Augmented matrix      390—1 400
Axiom      9
B      8
B$\acute{e}$zout, determinant      409—11 423
B$\acute{e}$zout, theorem      407 422
Back-solving      394 399 416 420 460—2
Bad-zero problem      260
Band matrix      424
Base      93 112 189
Basis, of degree $n$ polynomials      186
Berlekamp’s algorithm      337 347 351 353 358 360—361 366
Berlekamp’s algorithm, big prime version      364 366 371
Bessel functions      18
Bifurcation theory      452
Binary operation      154 359—60 364
Buchberger, B.      431
Buchberger’s Algorithm      431 445 447 450
Buchberger’s algorithm, complexity of      451 456 462
C      8—11 99
CAMAL      6
Cancellation law      24
Canonical, form      61 82
Canonical, form, expanded      85 89
Canonical, form, factored      86
Canonical, function      82 451
Canonical, simplifier      444 452
Cantor — Zassenhaus method      371
Cantor, D.      371
Cartesian product      46
Cauchy’s inequality      322 326
Cayley      9—10
Chain of ideals      445
Change of basis      462
Characteristic      344
Characteristic, field      74
Characteristic, nonzero      343
Characteristic, zero      338—43 474
Characterization theorem      164
Chebyshev polynomials      2 4 20
Chinese remainder, algorithm (CRA)      153 179 303—304 313 402 412
Chinese remainder, problem      174 206
Chinese remainder, theorem      120—121 175 348
Chinese remaindering      159
Coefficient, block      100—1
Coefficient, function      91
Cofactor      227 395 400
Cofactor, expansion      392
Common, divisor problem      317
Common, successor      438
Common, zeros      454
Commutative ring      24
Commutativity      23
Completion algorithm      447
Complex numbers ($\mathds{C}$)      24
Computer algebra      1
Congruence      402
Congruence, class      452
Congruence, notation      172
Congruence, problem      449
Congruence, relation      167
conjugate      378—380 501
Constant term      38 63 68
Content      53
Continuous Fourier transform (CFT)      129
Convergence      215
Convergence, quadratic      218
CRA      see "Chinese remainder algorithm"
Cramer’s Rule      152 287 391 400 405
Critical pair      447
Dedekind, R.      567
Degree      38 40 49
Degree, vector      47
Dense interpolation      311 313
Derivation      474
Derivative      50
DERIVE      9
Descriptor block      97 99
Determinant      16 389 392 394 398 400 407 423
Determinant, cofactor definition      400
Differential, algebra      474
Differential, extension field      476
Differential, field      474
Differential, homomorphism      476
Differential, operator      474
Differentiation, of exponential polynomial      520
Differentiation, of logarithmic polynomial      520
Diophantine equations      15
Discrete Fourier transform (DFT)      124
Distinct degree factorization      337 368 370—2
Distributivity      24
Divide-and-conquer      123
Divided-difference form      185
Divided-differences      186
Division, algorithm      411
Division, in finite fields      117
Division, of polynomials      40
Division, property      30
Divisor      26
Divisor, of algebraic function      567
Early ALTRAN      6
EEA      see "Extended Euclidean algorithm"
Elementary, extension      515
Elementary, function      18 474 511—512
Elementary, function, differentiation of      519
Elimination ideal      459
Embedding      155
Epimorphism      155
Equivalence relation      430
Error      209 214
Error, function      529
Euclid      34
Euclidean Domain      30
Euclid’s algorithm      14 33—34 42 158 279—280 305—306 315 393 411—412 447
Euclid’s algorithm, primitive form      282
Euler phi function      134
Evaluation, homomorphism      402 404 413
Evaluation, points      184
Exponent, block      100—101
Exponent, vector      46
Exponential, over      514
Exponential, polynomial, differentiation of      520
Extended Euclidean Algorithm (EEA)      35 42 117 173 186 280 483
Extended power series      68
Extended power series, constant      68
Extended power series, order      68
Extended power series, zero      68
Extension      156
Extension, field      75 452
Extraneous root      462
EZ — GCD algorithm      261 314—5 318—9 321 451
Factorization      12
Fast Fourier transform (FFT)      14 124 128
Fermat’s Little Theorem      368
FFT      see "Fast Fourier transform"
Fibonacci sequence      76
Field      24
Field, of characteristic zero      463
Field, of elementary functions      515
Field, of transcendental elementary functions      515
Finite, field      24
Finite, inclusion      415 457
floating-point numbers      11
FORM      10
FORMAC      6
Formal product block      102
FORTRAN      2 5 7 11
Fourier, points      124
Fourier, primes      134
Fraction field      437
Fundamental theorem, of integral calculus      511
Fundamental theorem, of PRS      296 299
Fundamental theorem, of resultants      414
Galois field      12 15 75 279 337 343—5 347
Gap      10
Garner, H.      176
Garner’s algorithm      176 178 191—2 206
Gaussian elimination      16 129 152 359 389—390 402 407 447
Gaussian elimination, division-free      392 393
Gaussian elimination, fraction-free      392 398
Gaussian elimination, ordinary      390—392 403
Gaussian elimination, single-step      397 423
Gaussian elimination, single-step, fraction-free      393 398 400—401 422
Gaussian elimination, two-step      397
Gaussian elimination, two-step, fraction-free      396 423
Gaussian integers      74
Gauss’ Lemma      54 331
GCD      see "Greatest common divisor"
GCDHEU algorithm      321 329
Geometry theorem      462
Gr$\ddot{o}$bner basis      390 407 421 429 431 439—440 443—445
Gr$\ddot{o}$bner basis, decomposition      460
Gr$\ddot{o}$bner basis, lexicographic      451 456 458—60
Gr$\ddot{o}$bner basis, monic      447
Gr$\ddot{o}$bner basis, reduced      447 450—1 460
Gr$\ddot{o}$bner basis, refinement      457—8 460
Gr$\ddot{o}$bner basis, total degree      451 456 458
Gr$\ddot{o}$bner, W.      431
greatest common divisor (GCD)      5 12—14 26 32 42 57 391 393 407 411 460 464
Greatest common divisor (GCD), of $n$ elements      53
Group      23
Group, abelian      23
Group, commutative      23
Group, cyclic      134
Group, multiplicative      133
Hadamard’s inequality      299 404 423
Hardy, G.      512
Head coefficient      433 437
Headterm      433
Hensel construction      230 243
Hensel construction, multivariate      258
Hensel lifting      233 250 272 337
Hensel’s Lemma      230 256 314 318 429
Hermite, C.      512
Hermite’s method      485 530
Hilbert, divisor chain condition      445
Hilbert, function      462
Hilbert, matrix      424
Hilbert, Nullstellensatz      454 463
Homomorphic image      155
Homomorphism      155
Homomorphism, composite      169
Homomorphism, evaluation      158
Homomorphism, modular      157
Homomorphism, multivariate evaluation      171
Horowitz, method      489 533
Horowitz, reduction      490
Ideal      160 567
Ideal, basis      162 429—31 439 445
Ideal, inclusion      445
Ideal, maximal      464
Ideal, membership problem      430—1
Ideal, polynomial      429 431 449
Ideal, power series      431
Ideal, principal      162
Ideal, proper      160
Ideal, universal      160
Ideal, zero      160
Ideal-adic representation      213
Idempotent      275
Identity      23—24
Indefinite, integral      511
Indefinite, integration      473
Integers ($\textit{Z}$)      24
Integers ($\textit{Z}$), fixed-length      11
Integers ($\textit{Z}$), Gaussian      74
Integers ($\textit{Z}$), indefinite-precision      96
Integers ($\textit{Z}$), modulo $m$      168
Integers ($\textit{Z}$), multiprecision      93 96 112 120 178
Integers ($\textit{Z}$), non-negative ($\textit{N}$)      30
Integers ($\textit{Z}$), single-precision      93 178
Integral, basis      563
Integral, closure      563
Integral, domain      24
Integral, indefinite      511
Integration by parts      473 482—483
Interpolation      159 402 404—5 412—413 429
Interpolation, points      184
Inverse      23—24
Inverse, discrete Fourier transform (IFDT)      130
Inverse, Fourier transform      130
Inverse, multiplicative      173
Inverse, of differential operator      478
Inverse, of extended power series      69
inversion      154
Inversion, of power series      139
Invertible      26
Irreducible      28
Irreducible, component      461
Irreducible, polynomial      434 452
Isomorphism      155
Karatsuba’s algorithm      118—119
Kernel      164 170
Knuth — Bendix algorithm      447
Kronecker, L.      337 378
Kummer, E.      567
Lagrange, interpolation      129
Lagrange, inversion formula      115
Lagrange, method      202
Lagrange, Theorem      133 135 344
Laplace, P.      527
Laurent series      18 494
Layout block      100—101
Lazard/Rioboo/Trager improvement      504—505
LCM      see "Least common multiple"
Leading, coefficient      38 47 460
1 2 3
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте