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

, harmonic number      440 609 614 615 616
, “soft Oh”      250 251 303 685 688
, nth prime      497
$V(\cdot)$ , variety      568
$V(\cdot)$ , variety      568
$\Delta$ , difference operator      610 611 624 635 637
$\lambda$ , Carmichael function      510
$\lambda$ , length of an integer      28 53 132
$\Lambda\Upsilon\Omega$ (Lambda-Upsilon-Omega)      661
$\mathbb{F}_p$ , finite prime field      67 396 403 437 445 542
$\mathbb{F}_q$ , finite field      67 675
$\mathbb{P}^2$ , projective plane      541
$\mathbb{Z}$ -module      327 447
$\mathbb{Z}_(p)$ , p-adic integers      261 423
$\mathbb{Z}_m$ , integers mod m      66
$\mathcal{BPP}$       504 555 590 685 686—688
$\mathcal{EXPEXPTIME}$       687
$\mathcal{EXPSPACE}$       590 661 687
$\mathcal{EXPTIME}$       687
$\mathcal{NP}$       203 448 477 478 483 504 509 550 553—555 590 686 687
$\mathcal{O}$ , neutral element of an elliptic curve      532
$\mathcal{PSPACE}$       590 591 687
$\mathcal{P}$ , polynomial time      504 555 590 685 686—688
$\mathcal{RP}$       504 686 687
$\mathcal{ZPP}$       492 504 686 687 688
$\mu$ , Moebius function      385 404 482
$\omega$ , feasible matrix multiplication exponent      315
$\Phi$ , totient function for polynomials      86
$\phi_n$ , cyclotomic polynomial      388
$\pi$       62 74—76 82 83 187 209 235 562 674
$\pi$ , rational approximation of      75
$\pi(\cdot)$ , number of primes      497
$\varphi$       see “Euler totient function”
, transpose      679
3-adic FFT      229 230 234 239 240
3-adic FFT      229 230 234 239 240
AAECC      19
Abel, Niels Henrik      349 698
Abelian group      668
Abramov, Sergei Aleksandrovich      635 639 698
Abramson, Michael      702
Achilles      151
Active attack      554
Adams, Douglas Noel      693
Addition chain      81
Additive group      238 552 667 677
Adleman, Leonard Max      14 397 483 504 506 550 554 698
Affine part      542
Affine variety      587 588
Agnew, Gordon B.      554 698
Aho, Alfred Vaino      272 310 698
Ajtai, Miklos      554 555 698 699 709
al-Hajjaj      see “Hajjaj”
al-Hajjaj ben Yusuf ben Matar      23
Al-Kashi      see “Kashi”
al-Kashi, Ghiyath al-Din Jamshld ben Mas’ud ben Mahmud      0 76 83 272 717
al-Khwarizmi      see “Khwarizmi”
al-Khwarizmi, Abu Ja’far Muhammad ben Musa      62 82 242 272 690 691 704 707 723
Albanese, Andres      203 699
Albert, Abraham Adrian      546 692
Alford, William Robert (Red)      502 507 699
Algebra, fundamental theorem of      348
Algebra, homomorphism      218
algebraic      674
Algebraic closure      680
Algebraic complexity theory      230 316 685
Algebraic computation problem      89
Algebraic curve      9 161 163 164 660
Algebraic equation      660
Algebraic field extension      see “Field extension”
Algebraic geometry      532 542 569
Algebraic integers      671
Algebraic number      192 605 627
Algebraic number field      265 354 447 508
Algebraic variety      162 187 560 565 587
Algebraic, degree of an algebraic element      674
Algebraic, geometry computational      4 565 569 593
Algebraic, integers ring of      671 672
Algebraically closed      161 569 591 595 675
ALICE      14—16 477 478 547 548 551—554
Alon, Noga      203 699
Alquie, Ferdinand      693
Amerbach, Bonifatius      23
Amoroso, Francesco      592 699
Amplitude      336 338
Analog signal      336
Analysis of Algorithms      27 263 661
Analytic number theory      482 497 507 616
Analytical engine      294
Andrews, George Eyre      608 661 693 699
Ankeny, Nesmith Cornett      505 699
Annihilating polynomial      319
Annihilator, $Ann(\cdot)$       320
Annus confusionis      77
Antoniou, Andreas      330 699
Antoniszoon, Adrian (Metius)      75
Apery number      648
Apery, Roger      635 648 661 721
Apollonius of Perga      187
Apostol, Tom Mike      57 699
Archimedean valuation      260
Archimedes of Syracuse      22 75 76 206 278 334 348 350 596 699
Aristotle      22
Arithmetic circuit      34 37 40 81 93 211 212 222 223 235 239 240 469 593
Arithmetic circuit representation      469 471 475
Arithmetic, hardware      265 269
Arithmetic, operation      29 30 32 33 38
Artin, Emil      542 710
Arwin, Axel      393 699
Aryabhata      55 82
Aryabhatiya      272
Ascending chain condition      578 579 584
Asmuth, Charles A.      122 699
Associate      44 137 492 671 672
Associated sequence      633 634
Asymmetric cryptosystem      14 549
Asymptotic complexity      6 316
Atkin, Arthur Oliver Lonsdale      507 509 699
Authentication      550 552
Automorphism      415 677 678 679
Automorphism, Frobenius      373 374 395 440 677
Average      682
Average depth of a Huffman tree      292
Average depth of a stochastic mobile      290 291 292
Average-case analysis      151
Avicenna      81
Axiom      18 22
Axiom in a proof system      641 642 643
Axiom of Choice      58
Azra, Jean-Pierre      707
B-number      524 525—527 530 531 542
Babai, Laszlo      187 688 699
Babbage, Charles      294 640 689 691 693
Baby step/giant step strategy      518
Babylonians      272 276
Bach, Carl Eric      6 55 272 396 397 502 505—508 510 541 542 699
Bach, Johann Sebastian      79 699
Bachet, Claude Gaspard, sieur de Meziriac      55 487 699
Bachmann, Paul Gustav Heinrich      507 688
Back-tracking      642
Bacon, Lord Francis      0 689
Bailey, David Harold      2 76 315 700 701
Baker, George Allen, Jr.      123 700
Ball, Walter William Rouse      508 700
Bareiss, Erwin Hans      123 700
Barrau, Theophile      689
Barrow, Isaac      206
Basis of a lattice      447 451
Basis of a vector space      197 200 449 628 679 681
Basis of an ideal      567 575 582 670

Basis orthogonal      449 452 681
Basis reduced      272 452 453 454 456 462 466 471 472 478 480 482
Basis reduction      449 452 453 454 458 462 467 470 471 473 474 477 479—483 550
Basis standard      565
Basis, Hilbert basis theorem      560 575 578 579 580 591
Basis, normal      70 555
Baur, Walter      330 700
Baxter, Rodney James      715
Bayer, David      592 700
BCH code      3 197 198 199 200—203 304 310 353 387 391 392 717
BCH code, designed distance of a BCH code      200 201
BCH code, generator polynomial of a BCH code      199 200 202 203 391
Beame, Paul William      6 661 700
Becker, Thomas      592 700
Bell, Eric Temple (John Taine)      8 88 207 608 689 690 693 700
Beltrami, Eugenio      693 698
Ben-Or, Michael      386 396 472 593 700 720
Benecke, Christof      662 700
Berenstein, Carlos Alberto      592 700
Berggren, Lennart      83 692 699—701 711 713 715 722 724
Berkeley, George      596 692
Berlekamp algebra      372 378 379 395 399 402 403 405
Berlekamp algorithm      151 187 313 377 378 380—382 395 399 403 404 504 707 712
Berlekamp matrix      see “Petr — Berlekamp matrix”
Berlekamp — Massey algorithm      304 705
Berlekamp, Elwyn Ralph      187 203 313 318 330 377 380 381 393—396 403 437 440 441 504 700
Berman, Benjamin P.      606 700
Bernardin, Laurent      444
Bernoulli number      614 633 636
Bernoulli polynomial      636
Bernoulli random variable      683
Bernstein, Daniel Julius      235 272 330 700
Bert      126
Bertossi, Leopoldo      6
Bertrand, Joseph Louis Francois, postulate      499
Beth, Thomas      709 721
Bezier curve      128
Bezier, Pierre Etienne      128 700
Bezout coefficients      42 55 131 143 145 151 186 303 304
Bezout matrix      186 189
Bezout theorem      147 162 163 164 187 533 656
Bezout, Etienne      162 186 564 688 692 700
Bible      22 207 675
Biermann, Gottlieb      689
Big Oh, $O(\cdot)$       2 28 30 667 679 684 685 687 688
Big prime modular algorithm      see “Modular algorithm”
Bijective      668 669
Bilinear complexity      315 316
Bilinear map      332
Bimberg, Guido      726
Binary calendar      78
Binary Euclidean algorithm      60
Binary rational      188
Binary representation      69 81 92 248 269 383 478
Binary tree      280 287 289—291 293
Binet, Jacques Philippe Marie      56 701
Bini, Dario Andrea      330
binomial      590
Binomial coefficient      70 155 633 634 648 677
Binomial ideal      590 645 661
Binomial theorem      70 631 633 637
Bipolar      3 18 265 267—269 435 436
Birch, Thomas      690
Birthday problem      520 522
Bit operation      30
Bivariate factorization      407 432 434 467 468 470 471 560
Bivariate interpolation      125
Bivariate modular EEA      see “Modular EEA”
Bivariate modular gcd      see “Modular gcd”
Bivariate polynomial      131 151 167 172 175 191 193 195 234 241 274 310 432 447 468
Black Box      93 318 329 330 333 470 472
Black box linear algebra      313 312 323 329 330 380 382
Black box representation of a polynomial      470
Blakley, George Robert (Bob)      122 699
Blau, Peter      6
Blocking strategy      397 436
Bloemer, Johannes Friedrich      203 699
Boat conformation      see “Cyclohexane conformation”
Bob      14 15 477 547 548 551—554
Boltzmann, Ludwig      596 692
Bolyai de Bolya, Janos (Johann)      350
Bolyai, Wolfgang      350
Bombieri, Enrico      82 701
Bonnet, Ossian Pierre      350
Boole, George      633 701 726
Boolean circuit      30
Boolean variable      642
Borodin, Allan Bertram      6 272 290 472 701 718
Borwein, Jonathan Michael      76 83 692 699—701 711 713 715 722 724
Borwein, Peter Benjamin      76 83 699—701 711 713 715 722 724
Bose, Nirmal Kumar      702
Bose, Raj Chandra      203 701 717
Bosma, Wiebren      6 508 701
Bound, Hasse      482 536 538 539 703
Bound, Weil      542 699
Bourgne, Robert      707
Bouyer, Martine      76
Boyar, Joan      479 701
Boyle, Robert      42 690
Brassard, Gilles      39 684 701
Bratley, Paul      39 684 701
Brauer, Alfred Theodore      701
Brent, Richard Peirce      83 310 330 331 516 541 701
Brickell, Ernest F.      483 701
Brieskorn, Egbert      542 701
Brillhart, John David      515 516 542 701 719
Broda, Engelbert      692
Bronstein, Manuel      606 607 701
Brook, Clifford Hardman (Clive)      693
Brown, William Stanley      55 187 188 310 701
Brownawell, Woodrow Dale      592 701
Brun, Viggo      719
Bshouty, Nader Hanna      330 713
Bubble sort      209
Bucciarelli, Louis      6
Buchberger algorithm      565 582 583 584 585 586 591 709
Buchberger, Bruno      19 565 583 591 592 701 702 712 714 718
Buchmann, Johannes      18
Budach, Lothar      723
Buergisser, Peter      81 210 272 316 330 590 702
Buettner, J.G.      348
Buhler, Joe Peter      718—720 724
Bunch, James Raymond      330 702
Burrus, Charles Sydney      234 711
Buss, Samuel Rudolph      661 702
Butler, Michael Charles Richard      395 702
Butterfly operation      222 223
Cade, John J.      550 702
Caesar cipher      547 548 555
Caesar, Gaius Julius      77 78 549
calendar      9 63 77
Calendar Gregorian      78 84
Calendar Julian      22 84
Calendar lunar      72
Calendar lunisolar      77
Caliph Harun al-Rashid      23
Camion, Paul Frederic Roger      394 395 702
Cancellation law      670
Canfield, Earl Rodney      541 702
Caniglia, Leandro      592 593 702
Cannon, John      18
Canny, John Francis      593 662 702 720
Canonical form of a rational function      108 110 112 113 115 129
Canonical form of a rational number      117 118
Canonical representative      374
Canonical ring homomorphism      66 96 102 670 673
Cantor and Zassenhaus algorithm      358 382
Cantor multiplication algorithm      267 269 272
Cantor, David Geoffrey      232 234 265—267 269 272 381 393 702
Caratheodory, Constantin      560

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