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von zur Gathen J., Gerhard J. — Modern computer algebra |
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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 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, 504 555 590 685 686—688
Polynomial, annihilating 319
Polynomial, continuant 59 60 86
Polynomial, cyclotomic, 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, 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, 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, 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 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, 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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