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

Pluecker, Julius      693
Plumbing knee      12—14 663
PMS      18
Pochhammer, Leo, symbol      634
Pocklington, Henry Cabourn      81 187 721
Poe, Edgar Allan      490 692
Poilly, Francois      689
Point at infinity      532 535 538 541
Pollack, Richard      707 711 722
Pollard $\rho$ method      515 516 519 521 522 541 543 699
Pollard and Strassen method      515 518 526 543
Pollard p — 1 method      515 531 538 541 542
Pollard, John Michael      235 266 509 516 519 541—543 701 716 721
Polynomial addition      31
Polynomial calculus system      661
Polynomial equation      1 3 4 81 206 253 256 260 418 565 588 595 658 661
Polynomial factorization      see “Factorization”
Polynomial ideal      472 565—595 641
Polynomial interpolation      see “Interpolation”
Polynomial multiplication      see “Multiplication”
Polynomial part      86 599—601
Polynomial remainder sequence, primitive      188
Polynomial remainder sequence, reduced      188
Polynomial remainder sequence, subresultant      188
Polynomial representation of the Frobenius map      374 383
Polynomial ring      2 672
Polynomial summation      3 609 613 614 622
Polynomial time, $\mathcal{P}$       504 555 590 685 686—688
Polynomial, annihilating      319
Polynomial, continuant      59 60 86
Polynomial, cyclotomic, $\Phi_n$       see “Cyclotomic polynomial”
Polynomial, degree of a polynomial      30 672 673
Polynomial, elementary symmetric      155
Polynomial, error locator      201
Polynomial, monic      30 33 38 45 672 674
Polynomial, normalized      46 50 134 140—142 153 299
Polynomial, permutation      400
Polynomial, separable      373
Polynomial, splitting      360 361 363
Polynomial, squarefree      353 373 402 427
Polynomial, Swinnerton — Dyer      408 415 416 417 439 440 442
Polynomial, Taylor      115
Polynomial, weight of a polynomial      40
Polynomial-time equivalent      551 553 686
Polynomial-time reducible      551 553 686
Pomerance, Carl      494 502 504 507 530 541 543 555 698 699 702 704 714—716 718 720 721
Pope Gregory XIII      77
POSSO      592
Pottier, Eugene      691
Power series      61 75 87 112 114 123 261 277 321 423 592 634 636 672
Powers, Raymond Earnest      543 715
PP      see “Primitive part”
Prange, Eugene      394 405 721
Pratt certificate      513
Pratt witness      513
Pratt, Vaughan Ronald      504 509 513 721
Pretend field technique      532
Primality test      3 70 272 487 491 492—494 497 498 504 505 507—510 517 528
Primality test, cyclotomic      508
Primality test, Fermat      493 494 495 497 509
Primality test, Lehmann      504 512 513
Primality test, Lucas — Lehmer      see “Lucas — Lehmer test”
Primality test, probabilistic      15 183 503 517
Primality test, Solovay and Strassen      see “Solovay and Strassen”
Primality test, strong pseudo      494 495 497 504 507 511
Primality, witness of      509
Prime      139 671 672
Prime element      139 254 671 672
Prime factorization      98 122 277 492 503 510 524 528
Prime field      675
Prime finding      497 499 501
Prime number      15 24 104 179 186 397 487 491 491—513 531 539 670
Prime number theorem      89 349 408 497 498 500 502 507 508 511 527 530
Prime power modular algorithm      see “Modular algorithm”
Prime, Fermat      215 239 505 511
Prime, Fourier      91 231 233 502 511
Prime, Mersenne      491 505 506 508 510
Prime, relatively      44 671
Prime, single precision      63 104 105 230 233 502 511
Prime, twin      76 209 234
PRIMES      504 509 513 685 686 688
Primitive EEA      181
Primitive element      605 676
Primitive Euclidean Algorithm      180 181 183—186 188 195
Primitive part, pp      137 138—140 142 152 167 180 181 189 407 408
Primitive polynomial      137 138 140 152 156 157 159 180 188 189 191 195 311 407 659
Primitive polynomial remainder sequence      188
Primitive root of unity      see “Root of unity”
Primitive, polynomial, greatest common divisor of polynomial primitives      142
Pritchard, Paul Andrew      508 721
Private key      see “Secret key”
Probabilistic algorithm      151 157 165 166 190 193 329 354 396—398 408 412 511 543 550 686
Probabilistic primality test      15 183 503 517
Probabilistically checkable proof      81
probability distribution      682
Probability function      681
Probability function, uniform      682
Probability theory      3 348 486 681
Probability, $prob(\cdot)$       682
Probability, conditional      646 682
Probability, finite probability space      667 681 682 683
Proclus      22
Product rule      252 610 635 638
Program checking      35
Projection      450 457
Projective curve      541 542
Projective geometry      541
Projective plane, $\mathbb{P}^2$       541
PROLOG      642
Proof certificate      648
Proof system      641 661
Proof, probabilistically checkable      81
Propositional calculus      641 687
Propositional formula      642 643
Propositional proof system      641 642
Pseudo-division      36 173 180 186 188 193 195
Pseudoprimality test      see “Primality test”
Pseudoprime      497
Pseudorandom number generator      477 479 483 504 548 552 555
Ptolemy, Claudius      22
Public key      14 15 477 483 549 551—553 555 557
Public key cryptography      3 14 15 477 549 547—557
Pudlak, Pavel      661 700 702
Purdy, George Barry      556 721
Putnam, Hilary Whitehall      642
Pythagorean      79 492
Pythagorean triple      541 544
q-norm, $\|\cdot\|_q$       680 681
QR-decomposition      315
Quadratic character      528 535
Quadratic sieve      531 541
Quadratic sieve, multiple polynomial      541
Quadratic time      33
Quadratic, law of quadratic reciprocity      348 503 512 560
Quantifier elimination      4
Quantum group      19
Queen Anne      207
Quicksort      209
Quisquater, Jean-Jacques      701 719
Quotient in the Euclidean Algorithm      47 48 52 53 295 296 299 300 302 303
Quotient rule      635
Quotient, multivariate      574
Quotient, quo      36 38 39 44 247 671
Rabin cryptosystem      547 553
Rabin, Michael Oser      122 203 396 399 507 508 720 722
Rabinowitsch, J.L.      592 722
Rackoff, Charles Weill      6 541 544
Radford, David Eugene      19 715
Radix conversion      250
Radix representation      27 31 39 120

Raghavan, Prabhakar      81 187 719
RAM      30
Ramanujan, Srinivasa Aiyangar      510 608 635 649 701 705 710 720
Ramos, Bartolome      79 722
Random element      95 166 399 509 519
Random polynomial      86 188 296 355 386 394 402 404 435 436
Random squares method      see “Dixon random squares method”
Random variable      151 520 536 646 682 683 686
Random variable, Bernoulli      683
Random walk      536 545
Random, pseudo random number generator      477 479 483 504 548 552 555
Rank of a matrix      662 678 679
Raphson, Joseph      207 689 690 719 722
Ratdolt, Erhard      23 689
Rate of a code      197 198
Rational approximation of $\pi$       75
Rational function      674
Rational function integration      3 600 604
Rational function reconstruction      106 109 110 115 116 303
Rational function, canonical form of a rational function      108 110 112 113 115 129
Rational interpolation      93 110 111 123
Rational number reconstruction      93 116 128 136 177—179 309
Rational number, canonical form of a rational number      117 118
Rational part      599 607
Rational root      431 441
Ray-Chaudhuri, Dwijendra Kumar      203 701 717
Razborov, Aleksandr Aleksandrovich      661 702 722
Reachability problem      644 645 661
Recio Muniz, Tomas Jesus      6 593 711
Recorde, Robert      42 476 690 692 693 754
Rectangular matrix multiplication      330
Recurrence      1
Recursion order      321 322 323 332
Recursively enumerable      82
Reduce      18
Reduce      18
Reduced basis      272 452 453 454 456 462 466 471 472 478 480 482
Reduced basis      272 452 453 454 456 462 466 471 472 478 480 482
Reduced element      585
Reduced element      585
Reduced Groebner basis      see “Groebner basis”
Reduced Groebner basis      see “Groebner basis”
Reduced polynomial remainder sequence      188
Reduced polynomial remainder sequence      188
Reducible      671
Reducible      671
Refutation      642 643
Refutation      642 643
Reichel, Horst      717
Reichel, Horst      717
Reid, Constance      561 722
Reid, Constance      561 722
Reif, John Henry      593 700
Reiner, Irving      716
Reiner, Irving      716
Reischert, Daniel      6 265 310 722
Reischert, Daniel      6 265 310 722
Reisig, Wolfgang      661 722
Reisig, Wolfgang      661 722
Reitwiesner, George Walter      76 722
Reitwiesner, George Walter      76 722
Remainder in the Euclidean Algorithm      46 47 52 56 186 188 295 303 309
Remainder, division with      2 24 35 36 37 92 122 243 247 248 268 296 382 419
Remainder, multivariate      573 574 575 582 584
Remainder, multivariate      573 574 575 582 584
Remainder, rem      36 38 39 44 46 51 247 302 575 671
Remainder, rem      36 38 39 44 46 51 247 302 575 671
Remmers, Harry      394 717
Remmers, Harry      394 717
Renegar, James      593 722
Renegar, James      593 722
Repeated squaring      15 69 70 71 81 86 250 276 357 361 365 368 378—380 383 399 493 495 512
Repeated squaring      15 69 70 71 81 86 250 276 357 361 365 368 378—380 383 399 493 495 512
Representative symmetric, system of representatives      66 102 410
Representative symmetric, system of representatives      66 102 410
Representative, canonical      374
Representative, canonical      374
Representative, system of representatives      66 670 673
Representative, system of representatives      66 670 673
Repunit      506
Repunit      506
Research Institute for Symbolic Computation (RISC)      592
Research Institute for Symbolic Computation (RISC)      592
Residue class ring      65 66 69 85 86 153 248 305 374 670
Residue class ring      65 66 69 85 86 153 248 305 374 670
Residue class, mod      65 66 374 670
Residue class, mod      65 66 374 670
Resolution      642
Resolution      642
Resultant, res      13 145 147 131—195 306 309—311 408 409 427 588 593 602 605 607 625 627 658
Resultant, res      13 145 147 131—195 306 309—311 408 409 427 588 593 602 605 607 625 627 658
Reversal, rev      192 244 248 272 321 400
Reversal, rev      192 244 248 272 321 400
Reynaud, Antoine Andre Louis      56 722
Reynaud, Antoine Andre Louis      56 722
Rhind papyrus      75
Rhind papyrus      75
Richardson, Daniel      606 722
Richmond, Lawrence Bruce      394 396 720
Riemann hypothesis      482 507 710 711 718
Riemann hypothesis      482 507 710 711 718
Riemann Hypothesis, Extended (ERH)      see “Extended Riemann”
Riemann zeta function, $\zeta$       57 209 482 507 508 616 648 717 720
Riemann, Georg Friedrich Bernhard      349 507 722
Riemann, Georg Friedrich Bernhard      349 507 722
Right ideal      669
Right ideal      669
Rigid conformation of cyclohexane      10 13 14 662
Rigid conformation of cyclohexane      10 13 14 662
Ring      30 669 675
Ring      30 669 675
Ring homomorphism      96 99 124 279 286 669 670 673
Ring homomorphism      96 99 124 279 286 669 670 673
Ring homomorphism, canonical      66 96 102 670 673
Ring isomorphism      669
Ring of algebraic integers      671 672
Ring of algebraic integers      671 672
Ring of constants      598
Ring of constants      598
Ring of polynomials      2 672
Ring of polynomials      2 672
Ring operation      see “Arithmetic operation”
Ring operation      see “Arithmetic operation”
Ring, characteristic of a ring      370 371 373 390 434 532 535 556 597 600 604 622 629 674 676
Ring, characteristic of a ring      370 371 373 390 434 532 535 556 597 600 604 622 629 674 676
Ring, commutative      669 670 673 675 677
Ring, factorial      671
Ring, factorial      671
Ring, invariant      591
Ring, Noetherian      579
Ring, Noetherian      579
Rink, Friedrich Theodor      690
Rioboo, Renaud      606 715 719
Risch, Robert H.      606 722
Risch, Robert H.      606 722
Rising factorial      611 634 637
Rising factorial      611 634 637
Ritt, Joseph Fels      593 606 707 722
Rivest, Ronald Linn      14 39 344 483 550 703 704 722
Robbiano, Lorenzo      591 593 705 709
Robot      565 566
Robot      565 566
Robot kinematics      589 662
Robot kinematics      589 662
Rodger, Christopher A.      203 711
Rodger, Christopher A.      203 711
Rogers, Leonard James, — Ramanujan identity      635 649 705 720
Rogers, Leonard James, — Ramanujan identity      635 649 705 720
Roggenkamp, Klaus Wilhelm      716
Rolletschek, Heinrich Franz      123 712

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