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Cohen H.A. — A Course in Computational Algebraic Number Theory
Cohen H.A. — A Course in Computational Algebraic Number Theory



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Название: A Course in Computational Algebraic Number Theory

Автор: Cohen H.A.

Аннотация:

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 563

Добавлена в каталог: 28.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
MLLL algorithm      96
MOD      7
Modular equation      386
Modular forms      234 390
Modular functions      379
Modular invariant      377
Modular multiplication      4
Module      188
Module,denominator      188
Modules, product of      189
Montgomery, P.      5 429 489 492
Morain, F.      445 471 474
Mordell, L.      375
MPQS      490
MPQS, self-initializing      494
Multi-precision      2
Nagao, K.      394
Narrow class group      228
Neumann, W.      102
Newton polygon      313
Newton’s Formulas      163
Newton’s method      38 45
NFS      495
Non-split multiplicative degeneracy      373
Norm of a fractional ideal      187
Norm of an element      162
Norm of an ideal      182
Normal closure      157
NP-complete      103
NUCOMP      247
NUDUPL      247
Number field      154
Number field, primitive      335
Odlyzko, A.      254 465
Oesterle, J.      295
Olivier, M.      171 175 254 288 313 329 333 352 513
Order      181
Order of a group element      24
Orthogonal basis      82
Orthogonal matrix      81
p(z)      368
p-adic factorisation      363
p-adic regulator      300
p-adic valuation      186
p-maximal      303
p-radical      303
PARI      2 508
Partial quotients      22
Period lattice      368 398
Permutation matrix      50
PID      183
Pivot      48 65
Place, finite      187
Place, infinite      187
Place, of a number field      187
Pohst, M.      96 304
Pollard, J.      426 439 495
Polya — Vinogradov inequality      301 476
Polynomial time      2
Pomerance, C.      445 465 481 490 501
Powering algorithms      8 42 466
Powers, R.      478
Powersmooth number      439
Primality certificate      470
Prime element      114
Prime form      252
Prime ideal      184
Prime ideal theorem      215
Prime number theorem      215
Primitive algebraic integer      274
Primitive algebraic number      497
Primitive element      155
Primitive element problem      181
Primitive ideal      225
Primitive part      116
Primitive polynomial      116
Primitive quadratic form      225
Primitive root      24
Principal ideal      183 287
Principal ideal domain      114 183
Principal minors      53
Probabilistic algorithm      2
Product of ideals      182
Projective geometry over $\mathbb{Z}/N\mathbb{Z}$      485
Pseudo-division      112
Pseudo-prime      422
q      378
QS      490
Quadratic form      79 225
Quadratic form, positive definite      80
Quadratic reciprocity law      27
Quer, J.      297
Rabin, M.      421
Ramification index      197
Ramified prime      197
Rank      66
Rank of an elliptic curve      375
Reduce      2 507
Reduced basis      84
Reduced ideal      300
Reduced quadratic form      231 262
Reduction of quadratic forms      243
Regular primes      209
Regular representation      160
Regulator      211
Regulator, elliptic      411
Relative extensions      329
Residual degree      197
Resolvent polynomial      323
Resultant      119
Ribet, K.      392
Roots of unity      209
Row vector      7
Rubin, K.      394
Rumely, R.      445
Schnorr, C.      91 481
Schonhage, A.      3 150
Schoof, R.      32 405 469
Separable extension      166
Serre, J.-P.      392
Shanks, D.      32 241 247 251 279 288 433 434
Shimura, G.      392
Side exit      65
Signature      155
Silverman, J.      367
Simath      508
Singular number      501
Size of a polynomial      168
Small prime variation      494
Smith normal form      67 75
Smooth number      439
SNF      67 75
Solovay, R.      421
Spar      481
Sparse matrix      254 480
Sparse representation      109
Special subset      486
Split multiplicative degeneracy      373
Splitting      419
Square form      434
Square root in $\mathbb{Z}$      38
Square root modulo p      31
Standard fundamental domain      231
Standard representation      159
Stark, H.      382
Stickelberger, L.      167 198
Strassen, V.      3 421
Strong pseudo-prime      422
Sturm, J.      155
Sub-exponential algorithm      2
Sub-resultant algorithm      118 122
Subfield problem      174
Supersingular      382
Supplement      61
Swinnerton-Dyer, H.      392
Sylvester’s matrix      120
Symmetric function      162
Taniyama — Weil conjecture      391
Taniyama, T.      391
Tate — Shafarevitch group      393
Tate, J.      407
Taylor, R.      392
Titanic numbers      471
Torsion subgroup      66 375
Totally complex      155
Totally real      155
Trace      162
Transitive      323
Trial division      419
Triple Jacobi sum      460
Tschirnhausen transformation      324
Two element representation      193
Ubasic      2 508
UFD      114
Unique factorization domain      114
UNIT      114 209
Unramified prime      197
Upper half-plane      378
Vallee, B.      84
Valuation      201
van der Hulst, P.      466
Weber class polynomial      417
Weber functions      474
Weierstrass equation      370
Weierstrass equation, minimal      370 406
Weil Conjectures      387
Weil curve      392
Weil, A.      375 387 391
Wiedemann, D.      254
Wieferich congruence      459
Wiles, A.      392
Williams, H.      279 285
Winter, D.      445
Wolstenholme’s Theorem      476
Zagier, D.      216 234 236 385 394
Zassenhaus, H.      127 304
Zeta function of a number field      214
Zeta function of a variety      388
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