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Bach E., Shallit J. — Algorithmic Number Theory (том 1)
Bach E., Shallit J. — Algorithmic Number Theory (том 1)

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Название: Algorithmic Number Theory (том 1)

Авторы: Bach E., Shallit J.

Аннотация:

"[Algorithmic Number Theory] is an enormous achievement and an extremely valuable reference." — Donald E. Knuth, Emeritus, Stanford University
Algorithmic Number Theory provides a thorough introduction to the design and analysis of algorithms for problems from the theory of numbers. Although not an elementary textbook, it includes over 300 exercises with suggested solutions. Every theorem not proved in the text or left as an exercise has a reference in the notes section that appears at the end of each chapter. The bibliography contains over 1,750 citations to the literature. Finally, it successfully blends computational theory with practice by covering some of the practical aspects of algorithm implementations. The subject of algorithmic number theory represents the marriage of number theory with the theory of computational complexity. It may be briefly defined as finding integer solutions to equations, or proving their non-existence, making efficient use of resources such as time and space. Implicit in this definition is the question of how to efficiently represent the objects in question on a computer. The problems of algorithmic number theory are important both for their intrinsic mathematical interest and their application to random number generation, codes for reliable and secure information transmission, computer algebra, and other areas. The first volume focuses on problems for which relatively efficient solutions can be found. The second (forthcoming) volume will take up problems and applications for which efficient algorithms are currently not known. Together, the two volumes cover the current state of the art in algorithmic number theory and will be particularly useful to researchers and students with a special interest in theory of computation, number theory, algebra, and cryptography.


Язык: en

Рубрика: Математика/Теория чисел/Вычислительная теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 516

Добавлена в каталог: 21.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathcal{B}\mathcal{P}\mathcal{P}$      50—52 278
$\mathcal{N}\mathcal{C}$      58 59 63 66 151
$\mathcal{N}\mathcal{P}$      12 46—47 49 51
$\mathcal{N}\mathcal{P}$-complete      12 47—49 147
$\mathcal{N}\mathcal{P}$-completeness      7 16 47
$\mathcal{N}\mathcal{P}$-hard      3
$\mathcal{P}$      45 46 51
$\mathcal{P}\mathcal{S}\mathcal{P}\mathcal{A}\mathcal{C}\mathcal{E}$-complete      56 65
$\mathcal{R}\mathcal{P}$      50—52 61 64 278
$\mathcal{Z}\mathcal{P}\mathcal{P}$      51 52 278
2-regular sequence      338
3-conjunctive normal form      48
3-SAT      48
Abbott, W.L.      334
Abel's identity      25 26 38
Abel, N.H.      369
Abelian groups      30 116 138
Abelian groups, fundamental theorem of      138 152
Abramov, S.A.      98
Absolute Berlekamp algebra      164 189 190
Absolutely irreducible      136
Abundant number      93 94
Acceptance      45
Acyclic      57
Adams, W.W.      314 379 382
Addition chains      121
Additive number theory      259
Adleman — Manders — Miller algorithm      161
Adleman, L.M.      13 14 17 64 65 96 122 160 194 195 200 266 285 294 311 316
Admissible sequence      226 243 258
Agnew.G.B.      351
Agou, S.      197
Aho, A.V.      xiii 150 152 326 345
Aieilo, W.      121
Aitken, A.C      347
Akbik, S.      350
Akl, S.G.      15
Akushskit, I.Ya.      312
Alagic, S.      99
Albert, A.A.      4 14 39 148 344 350
Alford, W.R.      251 276 313 315 316
algebraic      33
Algebraic integers      227
Algebraic number theory      xiii 227—233 260—263 266 285
Algebraic number theory, computations      260
Algorithmic number theory      xiv 1 2 9
Algorithms, Atlantic City      51 52 65 278 279 305
Algorithms, Las Vegas      51 52 65 168 278 279 293
Algorithms, Monte Carlo      51 52 65 278 279
Algorithms, polynomial-time      12
Algorithms, randomized      12
Alia,G.      121
ALICE      118
Allard, P.E.      355
Allouche. J.-P.      xv xvi 150 338 339
Alphabet      44
AMM algorithm      160 183
Amo, S.      314 382
Amon, D.      196
Anderson, S.F.      66
Angluin, D.      353
Ankeny's theorem      178 245 253
Ankeny's theorem for number fields      231 262 263
Ankeny's theorem, explicit version      235
Ankeny, N.C      218 245 253
Ansari, A.R.      318
Anti-Chinese remainder theorem      107 122
Apostol, T.M.      38 246 323 335 367 368
Appel, K.I.      2
Approximate equality      26 29
Arbib, M.A.      99
Archibald, R.C.      14 312
Arithmometer      6 15
Arnault, F.      314
Artin symbol      230 262
Artin — Schreier polynomials      179 193
Artin — Scnreier equation      348 362
Artin — Whaples approximation theorem      118 342
Artin's conjecture      152 221 227 255—256
Artin's conjecture for inlinitely many bases      222 256
Artin's conjecture for number fields      263
Artin's conjecture for polynomials      135
Artin's conjecture, prime tuples and      256
Artin's constant      256
Artin's constant, complexity of      256
Artin, E.      118 148 149 152 153 205 221 255 262 342 345 348 353 362
Arwin, A.      196
Aryabhata      4 14
Aryabhatiya      4 98
Asano, Y.      351
Ash,D.W.      351
Associates      32
Associative law      30
Asymptotic differentiation      238
Asymptotic growth of functions, notation for      25
Asymptotic integration      27—28 39
Atkin, A.O.L.      13 314 353
Atlantic City algorithms      51 52 65 278 279 305
Augustine, St.      273
Automatic sequences      150
Averbuch, A.      152
Avizienis, A.      346
Ayoub, R.G.      15
Babai, L.      65
Babbage, H.P.      15
Baby-step giant-step algorithm      161
Bach, E.      99 153 195 198 200 201 253 255 256 264 325 326 328 332 344 352 353 356 359 369—371 373 379 386
Bachmann, P.      38 96 123 246 344
Backlund, R.J.      240 243 249 257 369 374
Bahbage, C.      6
Baillie, R.      253 305 314 382
Baker, C.L.      310
Baker, P.W.      120
Baker, R.C      225 257
Balasubramanian, R.      2 13 310
Bang, T.      318
Bannon, P.J.      14
Baratz, A.E.      315
Barlow. P.      14 96
Bartec, T.C.      148
Baruah, S.K.      342
Basis-factor algorithm      85
Bassalygo, L.A.      150
Bateman — Hom conjecture      259
Bateman, P.T.      14 259 375
Batui, C.      11
Baum, U.      152
Bays, C.      297 317
Bcntardi, D.      11
Beame, P.W.      xv 65
Beard. J.T.B., Jr.      196
Beauchemin, P.      316
Beeger, N.G.W.H.      313
Beiler. A.H.      312
Bell, E.T.      7 15
Ben-Or algorithm      359
Ben-Or, M.      196 198 355 356 359
Benaissa, M.      148
Bengelloun, S.A.      317
Beniley, J.L.      96
Benin, P.      121
Benrand's postulate      225 238
Benrand's postulate for arithmetic progressions      367
Bergeron, R      121
Berlekamp algebra      164 190
Berlekamp algebra, absolute      164 189 190
Berlekamp algorithm      164
Berlekamp's algorithm      164 167 189 190
Berlekamp's algorithm, running time of      165
Berlekamp, E.R.      148 149 164 195—197 200 347 348 352 354 356
Berndt, B.C.      363
Bernoulli numbers      38 240
Bernstein, D.      99 326
Bernstein, L.      98
Berstel, J.      121
Bertrand, J.      225 238 367
Beth, T.      148 351
Bhargava, V.K.      148 351
Bicknell, M.      314 381
Bicycle-chain sieve      9 16
Biermann, O.      347
Biermann. K.-R.      309 310
Big-O notation      25 37 38 42 246
Big-omega notation      25 38
Big-theta notation      25 38
Bilharz, H.      152
Binary gcd algorithm      82—84 92 99
Binary gcd algorithm for polynomials      149
Binary gcd algorithm, extended      93
Binary gcd algorithm, variants of      93
Binary Jacobi algorithm      343
Binary method      102 121
Binary search      48
Binel form for Fibonacci numbers      330
Binet, J.P.M.      98 330
Binomial coefficients      35
Binomial equations in finite fields      155—163 189 195
Birch, B.J.      1 13
Birkhoff, G.      13 39
Bitlingsley. P.      248
Blake, I.E.      351
Blakley, G.R.      120 343
Blankinship, W.A.      96
Bleichcnbacher, D.      314
Block designs      196
Blokh, E.L.      196
Blum, M.      xv 98
Blundon, W.J.      257—258
Bob      118
Boeffgen, R.      361
Bohman. J.      258 318 365 369
Bohr, H.      246
Bojanczyk, A.W.      98
Bokhari, S.H.      318
Bombieri, E.      251
Bond, D.J.      316
Boolean circuits      58 148
boolean formulas      48
Boos, P.      360
Boraing, A.      312
Borcl, E.      373 374
Borel — Cantelli lemma      373 374
Borho, W.      312
Borodin, A.      65 121 149 151 152
Borosh, I.      343
Borrell, D.      198 352
Borwein, P.B.      326
Bos, J.      121
Bose, N.K.      346
Bosma, W.      312 314 316
Bouniakowsky, V.      15 259
Bourbaki, N.      39
Boute, R.T.      38
Boyar, J.      xv 148 372
Boyd, C.      315
Boys, C.V.      15
Bradley, G.R      96
Brahmagupta      4 14
Brancker, T.      1
Brassard, G.      64 316
Brauer, A.      121 318
Brenljes, A.J.      98
Brent, R.P.      39 98 99 149 249 257—259 310 317
Bressoud, D.M.      xiv
Breusch, R.      320
Brewer, B.W.      312
Brezinski, C.      98
Brickell, E.F.      120 121
Briggs, W.E.      369
Brillhart, J.      xv xvi 8 10 14 15 310 311 380 385
Brlek, S.      121
Brodnik, A.      xv
Brooks, A.S.      245
Browder, F.E.      16
Brown, J.      309
Brown, Jr.J.L.      98
Bruckman, P.S.      314
Brun — Titchmarsh theorem      263
Brun. V.      97 206 258 263 317
Bshouty, N.      152
Buchmann, J.A.      99 200 260
Buck, R.C.      318
Buell, D.A      10 16 312
Buhl, J.      312
Buhler, J.P.      2 13 312
Bum's constant      258
Bum's constant, intractability of      258
Bumby, R.T.      353
Burgess, D.A.      123 201 253 255 373
Burthc, Jr., R.J.      253 317
Burtsev. V.M.      312
Butler, M.C.R.      196 198
Cadwell, H.      256 257
Cahen, E.      368
Calculators, mechanical      6 8 15 249
Caldwell, C.K.      312
Callan, D.      319
Calmel, J.      148 198
Calude. C.      315
Cames, R.      xv
Camion, P.R.      149 196
Campbell, D.      311
Campbell-Kelly, M.      16
Canonical representative      101
Canonical representative for gcd of polynomials      130
Canonical representative for multiplicative inverse      102
Cantelli, F.P.      373 374
Cantor — Zassenhaus algorithm      167—168 190
Cantor, D.G.      11 148 151 167 196 197 353 355
Capoeelli, R.M.      122
Cappello, P.R.      122
Cardano, formula of      184—185 200 363
Cardano, G.      200
Carissan, E.      8 15
Carissan, P.      8
Carlitz, L.      152 356 358 360 364
Carmichael lambda function      275
Carmichael lambda function for polynomials      194
Carmichael numbers      227 266 275—279 313 314
Carmichael numbers, infinitely many      276
Carmichael, R.D.      310 312 313
Caron, T.R.      16
Cartier, P.      123
Carvaho, J.      312
Casde, C.M.A.      97
Cassels, J.W.S.      262
Casteran, P.      121
Cataldi, P.      1 308 310
Cauchy principal value      246
Cauchy's theorem      138
Cauchy, A.L.      149 199 200 313 360 363
Caviness, B.E.      98
CayIey, A.      149
CEILING      19
Central limit theorem      256
Cerbone, G.      122
Cerlienco, L.      346
Certificate      279
Cesaro, E.      36 238 324 332 335 367
CFA algorithm      76
1 2 3 4 5 6 7 8 9
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