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

Division with remainder      2 24 35 36 37 92 122 243 247 248 268 296 382 419
Division with remainder, fast      209 247 250 268 272 317
Division with remainder, multivariate      570 572 573 574 575 578 579
Division, exact      40 191 238 247 274 293
Division, trial      365 515 518 526
Dixon random squares method      318 515 523 524 525 530—532 541 543 544 553
Dixon, Alfred Cardew      635
Dixon, John Douglas      543 705
DL, Discrete Logarithm Problem      553 555 557
Dodson, Bruce      516 543 705
Don Quixote de la Mancha      82 703
Dornstetter, Jean Louis      203 705
Double-precision integer      27
Doughty, Herb      719
Doyle, Sir Arthur Conan      546 666 692 693
Dozier, Lamont      692
Dresden, Arnold      693
Dress, Andreas      472 703
du Bois-Reymond, Emil      562
Dube, Thomas William      592 705
Dubner, Harvey Allen      505 727
Dubois, Raymond      507 705
Dupre, Athanase      56 705
Dwork, Cynthia      555 699 709
Dynamical systems theory      262
d’Alembert, Jean le Rond      640 693
E, shift operator      610 612 623 624 635
Early abort      358
Eberly, Wayne      6 331 705
Edmonds, Jeffrey Allen      203 643 699 703
Edmonds, John Robert (Jack)      123 705
EEA      see “Extended Euclidean Algorithm”
Effective univariate factorization      see “Factorization”
Eigenvalue      680
Eisenbud, David      591 661 705
Eisenstein theorem      441
Eisenstein, Ferdinand Gotthold Max      349 508 705
Ekhad, Shalosh B.      661 705
Eleatics      22
Elementary functions      597
Elementary symmetric polynomial      155
Elements (Euclid)      22 23 24 492 506 688 689
Elgamal cryptosystem      547 553 554
ElGamal, Taher      555 707
Elimination of variables      161
Elkenbracht-Huizing, Reina Marije      516 543 704
Ellipsoid method      447
Elliptic curve      482 509 532 531—542 545 554
Elliptic curve cryptosystem      547 554 555
Elliptic curve factoring method      272 509 515—517 537 531—541 545
Elliptic curve primality test      509
Elliptic curve, size of an elliptic curve      535 539
Elliptic curve, smooth      532 533
Emiris, Ioannis Zacharias      662 705
Encamacion, Mark James      440 704
Encke, Johann Franz      709
Encoding map      197
Encryption      14 15 547—557
Encryption rate      554
Endomorphism      678 679
Endomorphism, Frobenius      374 377 380 403 677 708
Enestroem, Gustav      705 706
Engel, Friedrich      692
ENIGMA      548
entropy      281
Equal-degree factorization      363 353—397 400 435 437 528 553
Equal-degree splitting      361 363 399
Equivalence relation      84 296 310 405 637 671
Erasmus of Rotterdam      23
Erasure code      16 203
Eratosthenes of Cyrene      22 492
Eratosthenes sieve      161 501 506 508 526 530
Erdmann, Johann Eduard      690
Erdoes, Pal      486 541 702
ERH      see “Extended Riemann Hypothesis”
ERNIE      126
Error correcting code      16 197
Error locator polynomial      201
Euchner, Martin      471 723
Euclid      3 22 23 24 42 67 86 492 506 688 689 711
Euclidean algorithm      3 4 23 43—195 295—311 503 586 590 606 671 701 705 715 717 724
Euclidean Algorithm with least absolute remainders      61
Euclidean Algorithm, binary      60
Euclidean Algorithm, classical      45 46 87 91
Euclidean Algorithm, Extended (EEA)      see “Extended Euclidean”
Euclidean Algorithm, fast      3 167 249 299 295—311 322 600
Euclidean Algorithm, monic      47 55 174—176 181 185 186
Euclidean Algorithm, primitive      180 181 183—186 188 195
Euclidean Algorithm, quotient in the Euclidean Algorithm      see “Quotient”
Euclidean Algorithm, remainder in the Euclidean Algorithm      see “Remainder”
Euclidean Domain      43 43—87 89 96 97 126 137 148 149 176 243 569 671 672—675
Euclidean engine      187
Euclidean function      44 45 47 57—59 243 671
Euclidean function, minimal      52
Euclidean length      47 53—55 61 129 299 301
Euclidean norm, two-norm, $\|\cdot\|_2$       10 147 154 447 448 454 461 555 681
Euclidean number field      688 716
Euclidean representation      59
Eudoxus of Cnidus      22
Euler constant, $\gamma$       508 615
Euler number      633
Euler theorem      15 492 551 668
Euler totient function, $\varphi$       15 68 69 99 122 127 238 388 492 510 551
Euler, Leonhard      55 57 70 81—84 122 123 125 186 187 348 394 487 494 507 516 560 608 634 699 705 706 714 721
Evaluation homomorphism      99 673
Evaluation map      95 203 279
Evaluation multipoint      17 89—95 219 221 266 279 280 283—285 292 310 375 382 435
Evaluation multipoint, fast      219 279 282 283 292 375 519
Evaluation of a matrix      318 324 326 329 330
Evdokimov, Sergei Alekseevich      397 706
Eve      14 547 554 557
Event      682
Eventually positive      684
Exact division      40 191 238 247 274 293
Expected value      173 194 386 646 682
Explicit linear algebra      313 329 382
Extended Euclidean Algorithm (EEA)      15 47 43—195 202 230 269 288 295—311 322 382 427 432 463 479 551 674
Extended Euclidean Algorithm, big prime modular      178 179 183 195
Extended Euclidean Algorithm, bivariate modular      178
Extended Euclidean Algorithm, modular      172 176 195 305 309
Extended Euclidean Algorithm, primitive      181
Extended Euclidean Algorithm, small primes modular      see “Modular EEA”
Extended Riemann Hypothesis (ERH)      397 504 505 507 508 513 706 720
EZ-GCD      435 441
Factor base      524 531
Factor combination      408—110 415 428 430 432 437 440 463 466 470
Factor group      668
Factor tree      424 425—427 429—432 444
Factorial ring      671
Factorial, falling      611 613 618 634 637
Factorial, greatest factorial factorization, gff      see “Greatest factorial”
Factorial, rising      611 634 637
Factorization      2 18
Factorization by continued fraction method      515 542
Factorization by elliptic curve method      see “Elliptic curve”
Factorization of integers      3 15 16 210 313 318 329 331 479 487 491 494 506—508 515 515—545 551—554
Factorization of multivariate polynomials      467 471 475
Factorization of polynomials      2 4 13 18 138 257 269 272 348 349 353 353—475 479 487 560 562
Factorization of polynomials over $\mathbb{Z}$ and $\mathbb{Q}$       35 92 154 243 349 414 407—445 447 448 461—475 499 501
Factorization of polynomials over finite fields      3 70 265 269 318 330 365 353—405 435—437 462 467 543 688
Factorization of sparse polynomials      471
Factorization pattern      409 416 417 437 439—442
Factorization, bivariate      407 432 434 467 468 470 471 560
Factorization, distinct-degree      349 357 353—397 435—437
Factorization, effective univariate      432 434 447 467 475
Factorization, greatest factorial, gff      see “Greatest factorial”
Factorization, irreducible      see “Irreducible factorization”
Factorization, prime      98 122 277 492 503 510 524 528
Factorization, squarefree      353 355 365 369 371 373 391 401 622
Factorization, unique      670 671

Faddeev, Dmitrii Konstantinovich      394
Falling factorial      611 613 618 634 637
Fano, Robert Mario      291 706
Fast convolution      223 227 231 237 238 239 240 241
Fast CRA      see “Chinese Remainder Algorithm”
Fast division with remainder      see “Division”
Fast Euclidean Algorithm      3 167 249 299 295—311 322 600
Fast exponentiation      349 555
Fast Fourier transform (FFT)      3 17 76 199 221 209—241 267 339 340 349 398 704 706 709 711 721
Fast Fourier Transform arithmetic circuit      222
Fast Fourier Transform multiplication      3 93 225 231 235 237 239 248 264—266 269 311
Fast Fourier Transform, 3-adic      229 230 234 239 240
Fast Fourier Transform, Fermat number      269—271
Fast Fourier Transform, support the Fast Fourier Transform      223 225 232 238 280 310 311
Fast Fourier Transform, three primes      231 233 235 269 270
Fast integer multiplication      209—241
Fast interpolation      219 285 279—293 309
Fast matrix multiplication      314 315 318
Fast modular composition      316 317 395
Fast multipoint evaluation      see “Evaluation”
Fast polynomial multiplication      209—241
Fast sorting      220
Fateman, Richard J.      606 700
Faugere, Jean-Charles      593 706
Faulhaber, Johann      634 713
Feasible matrix multiplication exponent      315 316 330
Feisel, Sandra      6 187 704
Felkel, Anton      514
Feller, William      681 706
Ferdinand von Fuerstenberg      488 689
Ferdinand, Duke of Braunschweig      348
Fermat last theorem      488 569 721 726
Fermat liar      493 509
Fermat little theorem      70 71 81 355 356 374 487 492 494 506 668 676 677 705 706
Fermat number      70 81 233 234 487 494 505 513 516 701 716
Fermat number FFT      269—271
Fermat Pierre      3 22 70 81 86 206 486 487 488 494 505 524 596 689 702 704 705 724 726
Fermat polynomial      467
Fermat primality test      493 494 495 497 509
Fermat prime      215 239 505 511
Fermat witness      493 494 496 497 509
Feynman, Richard Phillips      208 514 690 692
FFT      see “Fast Fourier Transform”
Fibonacci sequence      60 319 321
Fibonacci, Leonardo Pisano, son of Bonaccio number      53—56 60 61 82 705
Fich, Faith Ellen      6
Fiduccia, Charles (Chuck) M.      290 330 706
Field      30 672 674 675
Field extension      68 374 384 387 627 674 675—677
Field extension, algebraic      165 321 354 360 468 601 606 674 675
Field extension, degree of a field extension      360 605 674 675
Field extension, finite      674
Field extension, Galois      441
Field extension, normal      374
Field of constants      601 623
Field of fractions      40 73 137 139 140 142 147 167 176 181 188 189 261 277 407 474 674
Field operation      see “Arithmetic operation”
Field perfect      373
Field splitting      167 402 404 415 601 602 605 606 675
Field, algebraic number      440
Field, difference      623 624 638
Field, differential      598 599
Field, finite, $\mathbb{F}_q$       see “Finite field”
Field, Hilbertian      471
Fields, John Charles, medal      565
Finck, Piene Joseph Etienne      56 707
Fingerprinting      64 81 84
Finite duration      339 345
Finite extension of a field      674
Finite field, $\mathbb{F}_q$       2 16 18 67 69 70 81 217 252 272 333 353—405 675 676 677
Finite field, irreducibility test over a finite field      383
Finite field, root finding over      353 368 393 403
Finite prime field, $\mathbb{F}_p$       67 396 403 437 445 542
Finite probability space      667 681 682 683
Finite-dimensional vector space      674 678
Finitely generated ideal      567 577 578 591
Finitely vector space      678
Fish, Daniel W.      514 692
Fitch, John      703 709 719
Fitchas, Noai      593 707
Flaccus, Aules Persius      663 693
Flajolet, Philippe Patrick Michel      394 661 707 720 724 726
Fleischer, Jochem      700 711 720
Flexible conformation      see “Cyclohexane conformation”
Floating point arithmetic      18 76 269 471
Floating point number      30 272 315
Floating point representation      92
Floyd cycle detection trick      520 521 522 541
Floyd, Robert W.      521
Fluxions      206
FOCS      19
Folkerts, Menso      272 691 707
Ford, Garrett      693
Fourier coefficient      338 345
Fourier prime      91 231 233 502 511
Fourier series      337 704
Fourier transform      234 335 337—339 344 487
Fourier transform, continuous      335 337 338
Fourier Transform, Discrete (DFT)      see “Discrete Fourier”
Fourier transform, fast (FFT)      see “Fast Fourier Transform”
Fourier, Jean Baptiste Joseph      234 334 691 707
Fractal      214 262 263
Freeman, Timothy Scott      472 707
Frege — Hilbert proof      642
Frege, Friedrich Ludwig Gottlob      562 702
Freivalds, Rusins      81 707
Frenicle de Bessy, Bernard      487
frequency      78 79 335 336 337—339 341 342
Frequency analysis      548
Friedman, Philip      446 546 692
Frieze, Alan Michael      479 707
FRISCO      592
Frise, Adolf      691
Frobenius automorphism      373 374 395 440 677
Frobenius density theorem      415 416 417 440
Frobenius endomorphism      374 377 380 403 672 708
Frobenius endomorphism polynomial, representation of the      374 383
Frobenius, Ferdinand Georg      123 186 415 440 707
Frobenius, iterated Frobenius algorithm      see “Iterated Frobenius”
Froehlich, Albrecht      395 707 714
ftp directory      265 516 661
Fuchssteiner, Benno      18
Fulton, William      542 707
functional decomposition      550 555 556
Fundamental lemma about gff      621 622 625
Fundamental period      344
Fundamental theorem of algebra      348 675
Fundamental theorem of calculus      611
Fundamental theorem of number theory      353 492
Fundamental theorem on subresultants      306 307 310
Galileo Galilei      476
Galligo, Andre      592 593 702 707
Gallo, Giovanni      593 707
Galois extension      441
Galois field      see “Finite field”
Galois group      349 374 397 415—417 440 722
Galois theory      374 390 415 677
Galois, Evariste      187 352 393 396 688 691 692 707
Gamer, Harvey Louis      123 708
Gamma function, $\Gamma$       623 624 634 637
Gao, Shuhong      6 81 382 394—396 555 707 708
Garey, Michael Randolph      483 687 708
Gauss bell curve      348
Gauss lemma      131 136 137 138 146 180 407 412
Gauss period      70 349 555 707 708
Gauss theorem      139 673
Gauss, Carl Friedrich      3 22 55 122 123 138 186 234 242 334 348 349 350 352 393 394 396 418 440 471 503 507 514 560 634 663 688 689 691—693 708 709 711
Gaussian elimination      101—105 122 123 128 179 317 349 377 379 449 586 595 601 630 679 680 688 700 725
Gaussian elimination, unimodular      81
Gaussian integers      44 59 671

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