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Shoup V.A. — Computational Introduction to Number Theory and Algebra
Shoup V.A. — Computational Introduction to Number Theory and Algebra

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Название: Computational Introduction to Number Theory and Algebra

Автор: Shoup V.A.

Язык: en

Рубрика: Математика/Алгебра/Вычислительная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 517

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\delta$-uniform      136
$\mathbb{C}$      212
$\mathbb{Q}$      9
$\mathbb{R}$      212
$\mathbb{Z}$      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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