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| Авторизация |
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| Shoup V.A. — Computational Introduction to Number Theory and Algebra |
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| Предметный указатель |
Kayal, N. 489 500
Kernel 194
Kills 206
Kim, S.H. 267
Knuth, D.E. 53 54 73
Kronecker substitution 416
Kung, H.T. 421
Lagrange interpolation formula 372
Las Vegas algorithm 157
Law of Large Numbers 118
Law of quadratic reciprocity 285
lcm, integer 9
lcm, polynomial 370
Leading coefficient 223
Leading coefficient of a reversed formal Laurent series 381
Least common multiple in an integral domain 385
Least common multiple, integer 9
Least common multiple, polynomial 370
Leftover hash lemma 138
Legendre symbol 285
Lehmann, D. 267
Lehmer, D. 356
Leiserson, C.E. 282
LEN 46 399
Length of a polynomial 399
Length of an integer 46
Lenstra, Jr., H.W. 357 488
Levin, L. 147
Li 87
Linear map 303
Linear transformation 440
Linearly dependent 306
Linearly generated sequence 423
Linearly generated sequence of full rank 429
Linearly generated sequence, minimal polynomial of 424
Linearly independent 306
Little-o 33
Littlewood, J.E. 95
LOG xiv
Logarithmic integral 87
Lowest terms 9
Luby, M. 147 179
Markov's inequality 117
Massey, J. 447
Matrix 316
Maurer, U. 267
Maximal ideal 234
Memory cells 36
Menezes, A. 73 179
Mertens' theorem 83
Message authentication scheme 128
Micali, S. 298
Miller, G.L. 266 267
Miller–Rabin test 247
Mills, W. 421 447
Min entropy 137
Minimal polynomial 374
Minimal polynomial of a linear transformation 441
Minimal polynomial of a linearly generated sequence 424
Minimal polynomial of a vector under a linear transformation 442
Minimal polynomial, algorithm for computing 401 438 466
MOD 3 13 17 224 371
Modular square root 283
Modular square root, algorithm for computing 292
Module 299
Modulus 13
Moebius function  29
Moebius inversion formula 30
Monic associate 366
Monic polynomial 223
Monomial 227 229 230
Monte Carlo algorithm 156
Morrison, K. 447
Morrison, M. 356
Multi-variate polynomial 230
Multiple root 226
Multiplication map 194 212 305
Multiplicative function 28
Multiplicative group of units 214
Multiplicative inverse 23
Multiplicative inverse in a ring 214
Multiplicative inverse, modulo integers 15
Multiplicative inverse, modulo polynomials 371
Multiplicative order 26 202
Multiplicative order modulo n 26
Multiplicity 226
Mutually independent events 100
Mutually independent random variables 105
Natural map 197
Newton Interpolation 406
Newton's identities 383
Niven, I. 289
Non-constant polynomial 220
Non-trivial ring 213
Norm 213 458
Normal basis 461
Number field sieve 357
Oesterle, J. 95
One-sided error 157
Order in a module 305
Order of a group element 202
Order of an abelian group 183
Ordered basis 321
Pairwise disjoint xv
Pairwise independent events 100
Pairwise independent hash function 125
Pairwise independent random variables 105
Pairwise relatively prime, integer 9
Pairwise relatively prime, polynomial 370
Partition xv
Penk, M. 73
Perfect power 261
Period 71
Periodic sequence 71
Phi function of Euler 24
PID 388
Pivot element 326
Pivot sequence 324
Pohlig, S. 282
Pollard, J.M. 282 357
Polynomial evaluation map 238 361
Polynomial time 38
Polynomial time, expected 149
Polynomial time, strict 149
Polynomial, associate 366
Polynomial, irreducible 366
Polynomial, monic 223
Polynomial, primitive 392
Polynomial, reducible 366
Pomerance, C. 54 95 267 357 358 500
Power map 194
Pre-image xv
Pre-period 71
Prefix free 150
Primality test, deterministic 489
Primality test, probabilistic 244
Prime ideal 234
Prime in an integral domain 386
Prime number 2
Prime number theorem 86
Prime number theorem, irreducible polynomials over a finite field 453
Primitive polynomial 392
Principal ideal 4 231
Principal ideal domain 388
Probabilistic algorithm 148
Probability distribution, conditional 99
Probability distribution, discrete 141
Probability distribution, finite 96
Probability function 96
Product distribution 98
| PROGRAM 36
Projection 429
Public key cryptography 282
Purely periodic 71
Quadratic formula 226
Quadratic reciprocity 285
Quadratic residue 283
Quadratic residuosity, algorithm for testing 291
Quadratic residuosity, assumption 297
Quadratic sieve 353
Quantum computer 358
Quotient algebra 359
Quotient group 191
Quotient module 303
Quotient ring 232
Quotient space 309
Rabin, M.O. 266
Rackoff, C. 357
RAM 36
Random access machine 36
Random self-reduction 178
Random variable 104
Random variable, conditional distribution of 105
Random variable, conditional expectation 114
Random variable, distribution of 105
Random variable, expected value 111
Random variable, image 104
Random variable, independent 105
Random variable, joint distribution 105
Random variable, k-wise independent 105
Random variable, mutually independent 105
Random variable, pairwise independent 105
Random variable, real 104
Random variable, variance 113
Randomized algorithm 148
Rank 331
Rational function field 366
Rational function reconstruction 410
Rational reconstruction 66
Real random variable 104
Recursion tree 282
Redmond, D. 95
Reduced row echelon form 324
Reducible polynomial 366
Reed, I. 421
Reed–Solomon code 69 412
Relatively prime in an integral domain 385
Relatively prime, integers 6
Relatively prime, polynomials 368
Renyi entropy 137
rep 48 400
Repeated-squaring algorithm 49
Representation 278
Representative of a coset 190
Representative of a residue class 21
Representative of an equivalence class xv
Residue class 20 232
Residue class ring 232
Reversed formal Laurent series 381
Richert, H. 267
Riemann hypothesis 88 90 92 94 266 267 281 298 419 488
Riemann's zeta function 88
Riemann, B. 94
Ring 211
Ring of polynomials 220
Rivest, R.L. 175 179 282
Rogaway, P. 358
Root of a polynomial 224
Rosser, J. 94
Row echelon form 333
Row null space 329
Row rank 331
Row space 329
Row vector 317
RSA cryptosystem 175
Rumely, R.S. 500
Sample mean 118
Sample space 96
Saxena, N. 489 500
scalar 299
Scalar matrix 319
Scalar multiplication 299
Schirokauer, O. 358
Schoenfeld, L. 94
Schoenhage, A. 53 54 73
Scholtz, R. 447
Secret sharing scheme 407
Semaev, I.A. 488
Separating set 484
Shallit, J. 95 289 487
Shamir, A. 52 175 179 421
Shanks, D. 282
Shift register sequence 425
Shor, P. 358
Shoup, V. 281 447 487 488
Shub, M. 73
Sieve of Eratosthenes 85
Simple root 226
Smooth number 336 352
Solomon, G. 421
Solovay, R. 266 298
Solving linear congruences, integer 17
Solving linear congruences, polynomial 371
Sophie Germain prime 93
Splitting field 378
Square root (modular) 283
Square root (modular), algorithm for computing 292
Square-free decomposition algorithm 476 485
Square-free integer 10
Square-free polynomial 449
Standard basis 306
Statistical distance 131
Stein, C. 282
Stein, J. 73
Strassen, V. 54 266 298
Strict polynomial time 149
Subalgebra 360
Subfield 219
Subgroup 185
Subgroup, generated by 202
Submodule 301
Submodule, generated (or spanned) by 302
Subring 218
subspace 309
Surjective xv
Theta function of Chebyshev 76
Total degree 229 230
Trace 458
Transcendental element 377
TRANSPOSE 319
Trial division 244
Trivial ring 213
Twin primes conjecture 94
Two-sided error 157
UFD 384
Ultimately periodic sequence 71
Unique factorization domain 384
Unique factorization in a Euclidean domain 387
Unique factorization in a PID 388
Unique factorization in D[X] 392
Unique factorization in F [X] 367
Unique factorization in Z 2
UNIT 214
Universal family of hash functions 127
van Oorschot, P. 73 179 282
Vandermonde matrix 373
Vanstone, S. 73 179
Variance 113
Vector 299
Vector space 309
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