von zur Gathen J., Gerhard J. — Modern computer algebra :: Электронная библиотека попечительского совета мехмата МГУ

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von zur Gathen J., Gerhard J. — Modern computer algebra

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Название: Modern computer algebra

Авторы: von zur Gathen J., Gerhard J.

Аннотация:

Computer algebra systems are gaining more and more importance in all areas of science and engineering. This textbook gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems.
It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority make it also an essential reference for professionals in the area.
Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). Some of this material has never appeared before in book form. Finally, a great deal of historical information and illustration enlivens the text.

Язык:

Рубрика: Computer science/Компьютерная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 753

Добавлена в каталог: 25.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Cardinality, #      668
Carlyle, Thomas      690
Carmichael function, $\lambda$       510
Carmichael number      494 495—497 506 507 510 512 699
Carmichael, Robert Daniel      506 702
Caron, Thomas R.      506 541 702
Carroll, Lewis (Rev. Charles Lutwidge Dodgson)      26 689
Carry flag      28 29 39 40 210 248 266
Carry look-ahead addition      39
Castelnuovo, Guido, — Mumford regularity      592
Cataldi, Pietro Antonio      82 702
Cauchy interpolation      109 110 113 128 129 179 304 309
Cauchy sequence      277
Cauchy — Schwarz inequality      459 473 529
Cauchy, Augustin Louis      122 123 186 272 349 703 716
Cavalieri, Bonaventura      596
Caviness, Bob Forrester      606 703
Cayley — Hamilton theorem      319 680
Cayley, Arthur      186 703
Center of gravity      566 567 586 587 616
CERES      350
Chahal, Jasbir Singh      542 703
Chain rule      252 331
Chair conformation      see “Cyclohexane conformation”
Chandler, Raymond      693 698
Change of representation      91 92 219 339
Char, Bruce Walter      191 703
Characteristic of a ring or field, char      370 371 373 390 434 532 535 556 597 600 604 622 629 674 676
Characteristic polynomial of a matrix      315 324 395 680
Characteristic polynomial of a sequence      119 320—322 326 327 332
Characteristic set      593
Chebotarev theorem      415 416 417 440 442 714 720 724
Chebotarev, Nikolai Grigor’evich      415 416 440
Chebyshev, Pafhuti L’vovich’      472 507 703
Chen, Pehong      7
Chen, Zhi-Zhong      187 703
Chernac, Ladislaus      692
Chinese Remainder Algorithm (CRA)      3 17 92 93 92 96—129 160 161 178 179 231 233 272 279 310 554 671
Chinese Remainder Algorithm, fast      122 285 287 289 293 309 600
Chinese Remainder Problem      100 104 106 289 290
Chinese Remainder Problem, rational      129
Chinese remainder theorem (CRT)      15 69 97 96—129 218 230 279 285 293 360 399 492 528
Chistov, Aleksandr Leonidovich      441 593 703
Chor, Ben-Zion (Benny)      483 703
Chou, Chung-Chiang      330 703
Chromatic scale      80
Chudnovsky, David Vol’fovich      712
Church, Alonzo      712
Ch’ung-chih, Tsu      75 76
Cicero, Marcus Tullius      26 690
Circuit, boolean      30
Clancy, Tom      352 546 691 692
Clarke, Arthur A.      708
Clarkson, Roland      491
Class field theory      560
Classical algorithm      34
Classical Euclidean Algorithm      45 46 87 91
Classical polynomial multiplication      32
Clausen, Michael Hermann      81 210 272 316 330 472 702 703
Clebsch, Rudolf Friedrich Alfred      693
Clegg, Matthew      643 703
Clifford, William Kingdon      666 693
Closed form      61 609 637 639 661
Co- $\mathcal{NP}$       504 513 686 687
Co- $\mathcal{RP}$       504 686 687
Code      9 16 197—200 202 203
Code, cyclic      391
Code, dimension of a code      197 198 199
Code, erasure      16 203
Code, error correcting      16 197
Code, Huffman      291 341—344
Code, instantaneous      291
Code, length of a code      197 198—200
Code, linear      197
Code, minimal distance of a code      198 199—201 203
Coding theory      35 197 203 303 391
Coefficient growth      131 133
Coefficient matrix      679
Coefficient of a polynomial      30
Coefficient representation      92
Cohen, Henri Jose      18 508 704
Coincide up to      296 297 298 310
Collins, George Edwin      18 186—188 310 430 440 593 704 712 714 718
Combinatorial identity      645
Commutative group      320 327 668 669 677
Commutative ring      669 670 673 675 677
Commute      673
complete      277 686
Completion      261
Complexity class      685—687
Complexity theory      3 210 547 554 590 667 685
Complexity, asymptotic      6 316
Composite      491
Compositeness test      504
COMPOSITES      504
Computational algebraic geometry      4 565 569 593
Computational complexity      483 550
Computational complexity (journal)      19
Computational group theory      4
Computational number theory      3 4 491—545 560
Computer algebra system      1 2 4 9 17—19 186 209 210 263 265 354 468 507 592 597 605 606 609
Conditional probability      646 682
Conformation      see “Cyclohexane conformation”
Congruent modulo, mod      63 670
Conjugacy class      440
Conjugates      677
Construction of irreducible polynomials      353 382 386
Content, $cont(\cdot)$       137 138—142 152 181 187—189 407 659
Continuant polynomial      59 60 86
Continued expansion      73 74 75 78 80 82 542
Continued factoring method      515 542
Continued fraction      3 63 73—75 78 79 82 84 86 87 123 516
Convergent      87
Convex body      447
Convex hull      187
Convolution of polynomials      217 218 223 240
Convolution of signals      344
Convolution property      344
Convolution, cyclic      217 218
Convolution, fast      223 227 231 237 238 239 240 241
Convolution, negative wrapped      225 227
Convolution, Vandermonde      636
Conway, John Horton      508
Cook, Stephen Arthur      6 234 272 686 704
Cookie Monster      126
Cooley, James William      220 234 278 691 704
Cooperman, Gene D.      187 704
Coppersmith, Don      330 331 396 704 705 712 726
Coprime      44 54 671
Cori, Robert      717
Corless, Robert M.      712
Cormen, Thomas H.      39 344 704
Coset      668 679
Coset of an ideal      670
Cosine Theorem      10
Cot, Norbert      709 721
Courant, Richard      560
Cowie, James      516 543 704
Cox, David A.      542 588 591 592 704
Coxeter, Harold Scott Macdonald      508 700
CRA      see “Chinese Remainder Algorithm”
Cramer conjecture      509
Cramer rule      107 127 147 173 176 189 193 194 459 680
Cramer, Carl Harald      509 710
Cramer, Gabriel      187 688 704
Cray      315
Crichton, Michael      196 690
Critical line      507 508
Cromwell, Oliver      196 690
Crossley, John Newsome      691 704

Crossover point      209 210 229 239 264 265 267—269
CRT      see “Chinese Remainder Theorem”
Cryptanalysis      477 478 549
Cryptography      9 14 16 35 197 471 477 479 483 491 497 499 547—557
cryptography, public key      3 14 15 477 549 547—557
Cryptosystem      3 15 477 478 515 516 541 547—557
Cryptosystem, asymmetric      14 549
Cryptosystem, ElGamal      547 553 554
Cryptosystem, elliptic curve      547 554 555
Cryptosystem, key in a cryptosystem      14 16 479 483 547 547—557
Cryptosystem, knapsack      477 483
Cryptosystem, Rabin      547 553
Cryptosystem, short vector      547 554
Cryptosystem, subset sum      483
Cryptosystem, symmetric      14 549 552
Cucker, Felipe      708
Cunn, Samuel      689 690 719
Cunningham number      210 516
Cunningham Project      515 516 543
Cunningham, Lt.-Col. Allan Joseph Champneys      515 517 704
Curve, algebraic      9 161 163 164 660
Curve, Bezier      128
Curve, Gauss bell      348
Curve, nonsingular      532 542 545
Curve, plane      163 187 192 569 588
Curve, projective      541 542
Cycle structure of a permutation      440
Cyclic code      391
Cyclic convolution      217 218
Cyclic group      238 327 398 552 668 676 677
Cyclic module      326 327
Cycloheptane      658 662
Cyclohexane      9 10 12 13 468 593 649—663 689
Cyclohexane, conformation of      9 10 13 649 652 653 662 663
Cyclohexane, conformation of, boat      10 11 13 14 654 655 660
Cyclohexane, conformation of, chair      10 11 14 650 656 657
Cyclohexane, conformation of, flexible      10 13 14 660 662
Cyclohexane, conformation of, rigid      10 13 14 662
Cyclotomic polynomial, $\Phi_n$       154 190 199 240 387 388 389 391 397 415 416 442 542
Cyclotomic primality test      508
D, differential operator      598 633 637
D, division time      282
Damgard, Ivan Bjerre      507 704
Data compression      291 339—342
Data structure      89 467
Database integrity      35
Davies, Charles      406 692
Davis, Martin David, — Putnam procedure      642
DCT, discrete cosine transform      339 339—345
de Buffon, Georges Louis Leclerc, Comte      187
de Casteljau, Paul de Faget      128 702
de Cervantes Saavedra, Miguel      82 703
de Correa, Isabel      6
de Fermat, Clement-Samuel      488 689
de Groote, Hans Friedrich      330 710
de la Place, Pierre Simon, Marquis      see “Laplace”
de la Vallee Poussin, Charles Jean Gustave Nicolas      507 726
de la Vallee Poussin, Charles Jean Gustave Nicolas      507 726
de Lagrange (la Grange), Joseph Louis, Comte      82 84 122 123 394 564 692 714
de Lalande, Joseph-Jerome Lefrancais      692
de Laplace (la Place), Pierre Simon, Marquis      278 406 688 689 691 692 715
De Moivre, Abraham      330
de Montaigne, Michel Eysquem, Seigneur      663 693
de Morgan, Augustus      42 62 88 596 690 692
de Weger, Benjamin M.M.      471 726
de Weger, Benjamin M.M.      471 726
Dean, Basil      693
Debes, Pierre      471 704
Decimal representation      29 35 38 64 65 76 85 92 479
Decision problem      685 686
Decision problem, hard      686
Decision problem, instance of a decision problem      685
decryption      14 15 547—557
Dedekind, Julius Wilhelm Richard      349 394 705 709
Degeyter, Pierre-Chretien      691
Degree formula      674
Degree function      58 86
Degree of a field extension      360 605 674 675
Degree of a polynomial, deg      30 672 673
Degree of an algebraic element      674
Degree sequence      85 86 132 168—170 177 179 193 295 307
Degree sequence normal      86 183 296 299 301 302 304 311
Degree valuation      84 87 260
Degree, total      147 162 165 467 571 590 653 673
Delaunay, Charles Eugene      18
DeMillo, Richard Allan      81 187 704
Deng, Yuefan      330 703
Denning, Dorothy Elizabeth Robling      555 704
Dense representation      93 219 467 468
Derivation      186 598
Derivative      105 114 124 146 201 245 251 252 253 274—276 284 369 597 598 607 611 631
Derivative Hasse — Teichmueller      see “Hasse — Teichmueller”
Derivative trivial      598 606
DERIVE      18
Descartes, Rene      312 486 596 691 693 754
Designed distance of a BCH code      200 201
Determinant Gramian      456 458 681
Determinant modular      101 105 499
Determinant modular big prime      102 104 157 435 500
Determinant modular small primes      see “Modular determinant”
Determinant, det      50 92 101—104 127 147 162 186 188 193 194 307 313 315 652 679 680
DFT      see “Discrete Fourier Transform”
DH      see “Diffie — Hellman problem”
Diatonic scale      80
Diaz, Angel Luis      187 472 704 705
Dickman, Karl Daniel, $\rho$ -function      527
Dickson lemma      576 577 578 594
Dickson, Leonard Eugene      565
Difference equation      624 633 639
Difference field      623 624 638
Difference operator, $\Delta$       610 611 624 635 637
Differential algebra      597 598 606
Differential equation      1 4 82 330 403 606 607 617 633 648
Differential field      598 599
Differential operator, D      598 633 637
Diffie — Hellman key exchange      547 552 553 717
Diffie — Hellman problem      553 555 557
Diffie, Bailey Whitfield      477 549 550 552 555 556 705
Digital filter      330
Digital signal      234 335 339 344
Digital signature      552
Dimension formula      678
Dimension of a code      197 198 199
Dimension of a lattice      448 454
Dimension of a vector space      326 377 638 649 652 662 674 675 678
Diophantine approximation      3 73 74 79 83 447 471 479 723
Diophantine approximations simultaneous      80 477 479 481—483 554 714
Diophantine equation      486 724 726
Diophantine equation linear      63 71 72 81 86
Diophantus of Alexandria      487 488 715 717
Direct product of finite probability spaces      682
Direct product of groups      668
Direct product of rings      670
Directed graph      398 442 643
DISCO      19
Discrete cosine transform (DCT)      339 339—345
Discrete Cosine Transform, Inverse (IDCT)      339 342 345
Discrete Fourier transform (DFT)      217 209—241 248 318 329 330 338 335—345
Discrete logarithm      553—555
Discrete Logarithm Problem (DL)      553 555 557
Discrete signal      335 336—340 344 345
Discriminant, disc      146 409 417 428 429 441 445 512 655
Dispersion, dis      639
Distinct-degree decomposition      357 368 376 397
Distinct-degree factorization      349 357 353—397 435—437
Distributed computing      17 91 541
Distributed data structures      16 17
Divide-and-conquer      275 282 284 293 299 331
Division property      670 671 673
Division time, D      282

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