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| Авторизация |
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| Поиск по указателям |
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| Shoup V.A. — Computational Introduction to Number Theory and Algebra |
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| Предметный указатель |
 -uniform 136
 212
 9
 212
 1
Abel's identity 82
Abelian group 180
Adleman, L.M. 175 179 358 488 500
Agrawal, M. 489 500
Alford, W. 267
Algebra 359
Algebraic element 377
Algebraic extension 377
Apostol, T.M. 95
Approximately computes 155
Arithmetic function 28
Artin's conjecture 72
Associate elements of an integral domain 383
Associate polynomials 366
Associative binary operation xvi
Asymptotic notation 33
Atlantic City algorithm 156
Automorphism algebra 360
Automorphism group 197
Automorphism module 304
Automorphism ring 237
Automorphism vector space 309
Baby step/giant step method 271
Bach, E. 73 95 179 266 281 289 298 487
Basis 306
Bayes' theorem 101
Bellare, M. 358
Ben-Or, M. 487
Berlekamp subalgebra 478
Berlekamp's algorithm 475
Berlekamp, E.R. 447 488
Bernoulli trial 96
Bertrand's postulate 78
Big-O, Big-Omega, Big-Theta 33
Bijection xv
Bijective xv
Binary gcd algorithm 57
Binary operation xvi
Binary relation xv
Binomial distribution 110 116
Binomial theorem 214
Birthday paradox 121
Bivariate polynomial 228
Blum, L. 73
Blum, M. 73
Boneh, D. 179 282
Bonferroni's inequalities 99
Boolean circuits 53
Brent, R.P. 421
Brillhart, J. 356
Buhler, J.P. 357
Burgess, D.A. 298
Cancellation law for integer congruences 16
Cancellation law for polynomial congruences 371
Cancellation law in an integral domain 216
Canfield, E. 357
Canonical representative integer 48
Canonical representative polynomial 400
Cantor — Zassenhaus algorithm 467
Cantor, D.G. 488
Carmichael number 248
Carmichael, R.D. 267
Carter, J.L. 147
Cartesian product xiv
Ceiling function 3
Characteristic of a ring 213
Characteristic polynomial 458
Chebyshev's inequality 118
Chebyshev's theorem 74
Chebyshev's theta function 76
Chernoff bound 119
Chinese remainder theorem, general 242
Chinese remainder theorem, integer 18 62
Chinese remainder theorem, polynomial 372 406
Chistov, A.L. 488
Classification of cyclic groups 202
Collision probability 137
Column null space 331
Column rank 331
Column space 331
Column vector 317
Common divisor in an integral domain 385
Common divisor, integer 5
Common divisor, polynomial 368
Common multiple in an integral domain 385
Common multiple, integer 8
Common multiple, polynomial 370
Commutative binary operation xvi
Commutative ring with unity 211
Companion matrix 322
Complex conjugation 212 240
Composite 2
Conditional distribution 99 105
Conditional expectation 114
Conditional probability 100
Congruence 13 190
Conjugacy class 456
conjugate 456
Constant polynomial 220
Constant term 223
Continued fraction method 356
Coordinate vector 321
Coordinate vector of a projection 429
Coppersmith, D. 357
Cormen, T.H. 282
Coset 190
Crandall, R. 54 95 358
Cyclic 202
Damgard, I. 267 397
Davenport, J. 73
de la Vallee Poussin, C.-J. 94 95
Decisional Diffie — Hellman problem 279
Degree of a polynomial 223
Degree of a reversed formal Laurent series 381
Degree of an element in an extension field 377
Degree of an extension 377
Denny, T. 358
Derivative 227
Deterministic poly-time equivalent 277
Deterministic poly-time reducible 277
Diagonal matrix 319
DICTIONARY 126
Diffie — Hellman key establishment protocol 276
Diffie — Hellman problem 276
Diffie, W. 282
DIMENSION 311
Direct product of algebras 359
Direct product of groups 184
Direct product of modules 300
Direct product of rings 213
Dirichlet inverse 32
Dirichlet product 28
Dirichlet series 90
Dirichlet's theorem 92
Dirichlet, G. 95
Discrete logarithm 268
Discrete logarithm, algorithm for computing 270 337
Discrete probability distribution 141
Discriminant 226
Disjoint xv
Distinct degree factorization 467 483
divides 1 213
Divisible by 1 214
Division with remainder property, integer 3
Division with remainder property, polynomial 224 367
| Divisor 1 214
Dixon, J. 356
Dornstetter, J.L. 447
Dual space 429
Durfee, G. 179
Eisenstein integers 389
Eisenstein's criterion 395
Elementary row operation 325
Elliptic curve method 357
Equal degree factorization 469 475
Equivalence class xv
Equivalence relation xv
Eratosthenes, sieve of 85
Erdoes, P. 357
Error correcting code 69 412
Error probability 155
Euclidean algorithm, extended, integer 58
Euclidean algorithm, extended, polynomial 403
Euclidean algorithm, integer 55
Euclidean Algorithm, polynomial 402
Euclidean Domain 387
Euler's identity 89
Euler's phi function 24
Euler's phi function and factoring 263
Euler's theorem 26
Euler, L. 94
Event 97
execution path 150
EXP xiv
Expected polynomial time 149
Expected running time 149
Expected value 111
EXPONENT 206
Exponent, module 305
Extended Euclidean algorithm, integer 58
Extended Euclidean algorithm, polynomial 403
Extended Gaussian elimination 327
Extension field 219 376
Extension ring 218
Factoring and Euler's phi function 263
Factoring, integer 344 352
Factoring, integer, deterministic 421
Factoring, polynomial 467 475
Factoring, polynomial, deterministic 483
Fast Fourier Transform 417
Fermat's little theorem 27
FFT 417
Field 215
Field of fractions 363
Finite dimensional 311
Finite extension 376
Finite fields, existence 450
Finite fields, subfield structure 454
Finite fields, uniqueness 454
Finite probability distribution 96
Finitely generated abelian group 202
Finitely generated module 306
Fixed field 455
Floor function 3
Floor function, reversed formal Laurent series 382
Formal derivative 227
Formal Laurent series 380
Formal power series 379
Fouvry, E. 500
Frandsen, G. 397
Frobenius map 451
Fundamental Theorem of Arithmetic 2
Fundamental theorem of finite abelian groups 208
Fundamental theorem of finite dimensional F [X]-modules 445
Gauss' lemma 285
Gaussian elimination 325
Gaussian integers 219 240 387 390
gcd, integer 6
gcd, polynomial 368
Generating polynomial 424
Generator 202
Generator, algorithm for finding 268
Geometric distribution 142 145
Gerhard, J. 422 488
Goldwasser, S. 298
Gordon, D.M. 358
Gordon, J. 488
Granville, A. 267
Greatest common divisor in an integral domain 385
Greatest common divisor, integer 6
Greatest common divisor, polynomial 368
Group 180
Guessing probability 137
Guy, M. 73
Hadamard, J. 94
Halberstam, H. 267
Hardy, G.H. 94 95
Hash function 125
Hash function, universal 127
Hash table 126
Heath-Brown, D. 95
Hellman, M. 282
Hensel lifting 294
Homomorphism algebra 360
Homomorphism group 194
Homomorphism module 303
Homomorphism ring 236
Homomorphism vector space 309
Horner's rule 400
Huang, M.-D. 500
Hybrid argument 135
Hypothesis H 93
Ideal 4 231
Ideal, generated by 4 231
Ideal, maximal 234
Ideal, prime 234
Ideal, principal 4 231
Identity element 180
Identity matrix 319
Image xv
Image of a random variable 104
Impagliazzo, R. 147
Inclusion/exclusion principle 99
INDEX 191
Index Calculus method 358
Indicator variable 105
Infinite extension 377
Infinite order 183
Injective xv
Integral domain 215
Inverse function xvi
Inverse of a group element 180
Inverse of a matrix 323
Inverse, multiplicative 214
Invertible matrix 323
Irreducible element 383
Irreducible polynomial 366
Irreducible polynomial, algorithm for generating 464
Irreducible polynomial, algorithm for testing 462
Irreducible polynomial, number of 453
Isomorphism algebra 360
Isomorphism group 197
Isomorphism module 304
Isomorphism ring 236
Isomorphism vector space 309
Iwaniec, H. 281
Jacobi map 289
Jacobi sum test 500
Jacobi symbol 287
Jacobi symbol, algorithm for computing 290
Joint distribution 105
k-wise independent 105
Kalai, A. 179
Kaltofen, E. 488
Karatsuba, A.A. 53
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