A course in computational algebraic number theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1995
|
| Edition: | 2. corr. print. |
| Series: | Graduate texts in mathematics
138 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 517 - 528 |
| Physical Description: | XXII, 534 S. |
| ISBN: | 3540556400 0387556400 |
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MARC
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| 100 | 1 | |a Cohen, Henri |d 1947- |e Verfasser |0 (DE-588)1018621717 |4 aut | |
| 245 | 1 | 0 | |a A course in computational algebraic number theory |c Henri Cohen. [Ed. board: J. H. Ewing ...] |
| 250 | |a 2. corr. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1995 | |
| 300 | |a XXII, 534 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 138 | |
| 500 | |a Literaturverz. S. 517 - 528 | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Algebraic number theory |x Data processing | |
| 650 | 0 | 7 | |a Algebraische Zahlentheorie |0 (DE-588)4001170-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Datenverarbeitung |0 (DE-588)4011152-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algorithmische Zahlentheorie |0 (DE-588)4314054-3 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Graduate texts in mathematics |v 138 |w (DE-604)BV000000067 |9 138 | |
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| _version_ | 1807502656558596096 |
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CONTENTS
CHAPTER
1
FUNDAMENTAL
NUMBER-THEORETIC
ALGORITHMS
1
1.1
INTRODUCTION
.
1
1.1.1
ALGORITHMS
.
1
1.1.2
MULTI-PRECISION
.
2
1.1.3
BASE
FIELDS
AND
RINGS
.
5
1.1.4
NOTATIONS
.
6
1.2
THE
POWERING
ALGORITHMS
.
8
1.3
EUCLID
'
S
ALGORITHMS
.
12
1.3.1
EUCLID
'
S
AND
LEHMER
'
S
ALGORITHMS
.
12
1.3.2
EUCLID
'
S
EXTENDED
ALGORITHMS
.
16
1.3.3
THE
CHINESE
REMAINDER
THEOREM
.
19
1.3.4
CONTINUED
FRACTION
EXPANSIONS
OF
REAL
NUMBERS
.
21
1.4
THE
LEGENDRE
SYMBOL
.
24
1.4.1
THE
GROUPS
(Z/NZ)*
.
24
1.4.2
THE
LEGENDRE-JACOBI-KRONECKER
SYMBOL
.
27
1.5
COMPUTING
SQUARE
ROOTS
MODULO
P
.
31
1.5.1
THE
ALGORITHM
OF
TONELLI
AND
SHANKS
.
32
1.5.2
THE
ALGORITHM
OF
CORNACCHIA
.
34
1.6
SOLVING
POLYNOMIAL
EQUATIONS
MODULO
P
.
36
1.7
POWER
DETECTION
.
38
1.7.1
INTEGER
SQUARE
ROOTS
.
38
1.7.2
SQUARE
DETECTION
.
39
1.7.3
PRIME
POWER
DETECTION
.
41
1.8
EXERCISES
FOR
CHAPTER
1
.
42
XVI
CONTENTS
CHAPTER
2
ALGORITHMS
FOR
LINEAR
ALGEBRA
AND
LATTICES
45
2.1
INTRODUCTION
.
45
2.2
LINEAR
ALGEBRA
ALGORITHMS
ON
SQUARE
MATRICES
.
46
2.2.1
GENERALITIES
ON
LINEAR
ALGEBRA
ALGORITHMS
.
46
2.2.2
GAUSSIAN
ELIMINATION
AND
SOLVING
LINEAR
SYSTEMS
.
47
2.2.3
COMPUTING
DETERMINANTS
.
49
2.2.4
COMPUTING
THE
CHARACTERISTIC
POLYNOMIAL
.
52
2.3
LINEAR
ALGEBRA
ON
GENERAL
MATRICES
.
56
2.3.1
KERNEL
AND
IMAGE
.
56
2.3.2
INVERSE
IMAGE
AND
SUPPLEMENT
.
59
2.3.3
OPERATIONS
ON
SUBSPACES
.
61
2.3.4
REMARKS
ON
MODULES
.
63
2.4
Z-MODULES
AND
THE
HERMITE
AND
SMITH
NORMAL
FORMS
.
.
65
2.4.1
INTRODUCTION
TO
Z-MODULES
.
65
2.4.2
THE
HERMITE
NORMAL
FORM
.
66
2.4.3
APPLICATIONS
OF
THE
HERMITE
NORMAL
FORM
.
72
2.4.4
THE
SMITH
NORMAL
FORM
AND
APPLICATIONS
.
74
2.5
GENERALITIES
ON
LATTICES
.
78
2.5.1
LATTICES
AND
QUADRATIC
FORMS
.
78
2.5.2
THE
GRAM-SCHMIDT
ORTHOGONALIZATION
PROCEDURE
.
81
2.6
LATTICE
REDUCTION
ALGORITHMS
.
83
2.6.1
THE
LLL
ALGORITHM
.
83
2.6.2
THE
LLL
ALGORITHM
WITH
DEEP
INSERTIONS
.
89
2.6.3
THE
INTEGRAL
LLL
ALGORITHM
.
91
2.6.4
LLL
ALGORITHMS
FOR
LINEARLY
DEPENDENT
VECTORS
.
94
2.7
APPLICATIONS
OF
THE
LLL
ALGORITHM
.
96
2.7.1
COMPUTING
THE
INTEGER
KERNEL
AND
IMAGE
OF
A
MATRIX
.
96
2.7.2
LINEAR
AND
ALGEBRAIC
DEPENDENCE
USING
LLL
.
99
2.7.3
FINDING
SMALL
VECTORS
IN
LATTICES
.
102
2.8
EXERCISES
FOR
CHAPTER
2
.
105
CHAPTER
3
ALGORITHMS
ON
POLYNOMIALS
.
108
3.1
BASIC
ALGORITHMS
.
108
3.1.1
REPRESENTATION
OF
POLYNOMIALS
.
108
3.1.2
MULTIPLICATION
OF
POLYNOMIALS
.
109
3.1.3
DIVISION
OF
POLYNOMIALS
.
110
3.2
EUCLID
'
S
ALGORITHMS
FOR
POLYNOMIALS
.
112
3.2.1
POLYNOMIALS
OVER
A
FIELD
.
112
3.2.2
UNIQUE
FACTORIZATION
DOMAINS
(UFD
'
S)
.
113
3.2.3
POLYNOMIALS
OVER
UNIQUE
FACTORIZATION
DOMAINS
.
115
3.2.4
EUCLID
'
S
ALGORITHM
FOR
POLYNOMIALS
OVER
A
UFD
.
116
CONTENTS
XVII
3.3
THE
SUB-RESULTANT
ALGORITHM
.
117
3.3.1
DESCRIPTION
OF
THE
ALGORITHM
.
117
3.3.2
RESULTANTS
AND
DISCRIMINANTS
.
118
3.3.3
RESULTANTS
OVER
A
NON-EXACT
DOMAIN
.
122
3.4
FACTORIZATION
OF
POLYNOMIALS
MODULO
P
.
123
3.4.1
GENERAL
STRATEGY
.
123
3.4.2
SQUAREFREE
FACTORIZATION
.
124
3.4.3
DISTINCT
DEGREE
FACTORIZATION
.
125
3.4.4
FINAL
SPLITTING
.
126
3.5
FACTORIZATION
OF
POLYNOMIALS
OVER
Z
OR
Q
.
132
3.5.1
BOUNDS
ON
POLYNOMIAL
FACTORS
.
133
3.5.2
A
FIRST
APPROACH
TO
FACTORING
OVER
Z
.
134
3.5.3
FACTORIZATION
MODULO
P
E
:
HENSEL
'
S
LEMMA
.
136
3.5.4
FACTORIZATION
OF
POLYNOMIALS
OVER
Z
.
138
3.5.5
DISCUSSION
.
140
3.6
ADDITIONAL
POLYNOMIAL
ALGORITHMS
.
141
3.6.1
MODULAR
METHODS
FOR
COMPUTING
GCD
'
S
IN
Z[X]
.
141
3.6.2
FACTORIZATION
OF
POLYNOMIALS
OVER
A
NUMBER
FIELD
.
142
3.6.3
A
ROOT
FINDING
ALGORITHM
OVER
C
.
145
3.7
EXERCISES
FOR
CHAPTER
3
.
147
CHAPTER
4
ALGORITHMS
FOR
ALGEBRAIC
NUMBER
THEORYL
151
4.1
ALGEBRAIC
NUMBERS
AND
NUMBER
FIELDS
.
151
4.1.1
BASIC
DEFINITIONS
AND
PROPERTIES
OF
ALGEBRAIC
NUMBERS
.
151
4.1.2
NUMBER
FIELDS
.
152
4.2
REPRESENTATION
AND
OPERATIONS
ON
ALGEBRAIC
NUMBERS
.
.
156
4.2.1
ALGEBRAIC
NUMBERS
AS
ROOTS
OF
THEIR
MINIMAL
POLYNOMIAL
.
156
4.2.2
THE
STANDARD
REPRESENTATION
OF
AN
ALGEBRAIC
NUMBER
.
157
4.2.3
THE
MATRIX
(OR
REGULAR)
REPRESENTATION
OF
AN
ALGEBRAIC
NUMBER
.
158
4.2.4
THE
CONJUGATE
VECTOR
REPRESENTATION
OF
AN
ALGEBRAIC
NUMBER
.
.
159
4.3
TRACE,
NORM
AND
CHARACTERISTIC
POLYNOMIAL
.
160
4.4
DISCRIMINANTS,
INTEGRAL
BASES
AND
POLYNOMIAL
REDUCTION
.
163
4.4.1
DISCRIMINANTS
AND
INTEGRAL
BASES
.
163
4.4.2
THE
POLYNOMIAL
REDUCTION
ALGORITHM
.
166
4.5
THE
SUBFLELD
PROBLEM
AND
APPLICATIONS
.
172
4.5.1
THE
SUBFIELD
PROBLEM
USING
THE
LLL
ALGORITHM
.
172
4.5.2
THE
SUBFIELD
PROBLEM
USING
LINEAR
ALGEBRA
OVER
C
.
173
4.5.3
THE
SUBFIELD
PROBLEM
USING
ALGEBRAIC
ALGORITHMS
.
175
4.5.4
APPLICATIONS
OF
THE
SOLUTIONS
TO
THE
SUBFIELD
PROBLEM
.
177
XVIII
CONTENTS
4.6
ORDERS
AND
IDEALS
.
179
4.6.1
BASIC
DEFMITIONS
.
179
4.6.2
IDEALS
OF
.
184
4.7
REPRESENTATION
OF
MODULES
AND
IDEALS
.
186
4.7.1
MODULES
AND
THE
HERMITE
NORMAL
FORM
.
186
4.7.2
REPRESENTATION
OF
IDEALS
.
188
4.8
DECOMPOSITION
OF
PRIME
NUMBERS
I
.
193
4.8.1
DEFINITIONS
AND
MAIN
RESULTS
.
194
4.8.2
A
SIMPLE
ALGORITHM
FOR
THE
DECOMPOSITION
OF
PRIMES
.
196
4.8.3
COMPUTING
VALUATIONS
.
198
4.8.4
IDEAL
INVERSION
AND
THE
DIFFERENT
.
202
4.9
UNITS
AND
IDEAL
CLASSES
.
205
4.9.1
THE
CLASS
GROUP
.
205
4.9.2
UNITS
AND
THE
REGULATOR
.
206
4.9.3
CONCLUSION:
THE
MAIN
COMPUTATIONAL
TASKS
OF
ALGEBRAIC
NUMBER
THEORY
.
214
4.10
EXERCISES
FOR
CHAPTER
4
.
215
CHAPTER
5
ALGORITHMS
FOR
QUADRATIC
FIELDS
.
218
5.1
DISCRIMINANT,
INTEGRAL
BASIS
AND
DECOMPOSITION
OF
PRIMES
218
5.2
IDEALS
AND
QUADRATIC
FORMS
.
220
5.3
CLASS
NUMBERS
OF
IMAGINARY
QUADRATIC
FIELDS
.
226
5.3.1
COMPUTING
CLASS
NUMBERS
USING
REDUCED
FORMS
.
226
5.3.2
COMPUTING
CLASS
NUMBERS
USING
MODULAR
FORMS
.
229
5.3.3
COMPUTING
CLASS
NUMBERS
USING
ANALYTIC
FORMULAS
.
232
5.4
CLASS
GROUPS
OF
IMAGINARY
QUADRATIC
FIELDS
.
235
5.4.1
SHANKS
'
S
BABY
STEP
GIANT
STEP
METHOD
.
235
5.4.2
REDUCTION
AND
COMPOSITION
OF
QUADRATIC
FORMS
.
238
5.4.3
CLASS
GROUPS
USING
SHANKS
'
S
METHOD
.
245
5.5
MCCURLEY
'
S
SUB-EXPONENTIAL
ALGORITHM
.
:
.
.
247
5.5.1
OUTLINE
OF
THE
ALGORITHM
.
247
5.5.2
DETAILED
DESCRIPTION
OF
THE
ALGORITHM
.
250
5.5.3
ATKIN
'
S
VARIANT
.
255
5.6
CLASS
GROUPS
OF
REAL
QUADRATIC
FIELDS
.
257
5.6.1
COMPUTING
CLASS
NUMBERS
USING
REDUCED
FORMS
.
257
5.6.2
COMPUTING
CLASS
NUMBERS
USING
ANALYTIC
FORMULAS
.
261
5.6.3
A
HEURISTIC
METHOD
OF
SHANKS
.
263
CONTENTS
XIX
5.7
COMPUTATION
OF
THE
FUNDAMENTAL
UNIT
AND
OF
THE
REGULATOR
.
264
5.7.1
DESCRIPTION
OF
THE
ALGORITHMS
.
264
5.7.2
ANALYSIS
OF
THE
CONTINUED
FRACTION
ALGORITHM
.
266
5.7.3
COMPUTATION
OF
THE
REGULATOR
.
273
5.8
THE
INFRASTRUCTURE
METHOD
OF
SHANKS
.
274
5.8.1
THE
DISTANCE
FUNCTION
.
274
5.8.2
DESCRIPTION
OF
THE
ALGORITHM
.
278
5.8.3
COMPACT
REPRESENTATION
OF
THE
FUNDAMENTAL
UNIT
.
280
5.8.4
OTHER
APPLICATION
AND
GENERALIZATION
OF
THE
DISTANCE
FUNCTION
.
282
5.9
BUCHMANN
'
S
SUB-EXPONENTIAL
ALGORITHM
.
283
5.9.1
OUTLINE
OF
THE
ALGORITHM
.
284
5.9.2
DETAILED
DESCRIPTION
OF
BUCHMANN
'
S
SUB-EXPONENTIAL
ALGORITHM
.
286
5.10
THE
COHEN-LENSTRA
HEURISTICS
.
289
5.10.1
RESULTS
AND
HEURISTICS
FOR
IMAGINARY
QUADRATIC
FIELDS
.
290
5.10.2
RESULTS
AND
HEURISTICS
FOR
REAL
QUADRATIC
FIELDS
.
292
5.11
EXERCISES
FOR
CHAPTER
5
.
293
CHAPTER
6
ALGORITHMS
FOR
ALGEBRAIC
NUMBER
THEORYLL
297
6.1
COMPUTING
THE
MAXIMAL
ORDER
.
297
6.1.1
THE
POHST-ZASSENHAUS
THEOREM
.
297
6.1.2
THE
DEDEKIND
CRITERION
.
299
6.1.3
OUTLINE
OF
THE
ROUND
2
ALGORITHM
.
302
6.1.4
DETAILED
DESCRIPTION
OF
THE
ROUND
2
ALGORITHM
.
305
6.2
DECOMPOSITION
OF
PRIME
NUMBERS
II
.
306
6.2.1
NEWTON
POLYGONS
.
307
6.2.2
THEORETICAL
DESCRIPTION
OF
THE
BUCHMANN-LENSTRA
METHOD
.
309
6.2.3
MULTIPLYING
AND
DIVIDING
IDEALS
MODULO
P
.
311
6.2.4
SPLITTING
OF
SEPARABLE
ALGEBRAS
OVER
F
P
.
312
6.2.5
DETAILED
DESCRIPTION
OF
THE
ALGORITHM
FOR
PRIME
DECOMPOSITION
.
314
6.3
COMPUTING
GALOIS
GROUPS
.
316
6.3.1
THE
RESOLVENT
METHOD
.
316
6.3.2
DEGREE
3
.
319
6.3.3
DEGREE
4
.
319
6.3.4
DEGREE
5
.
322
6.3.5
DEGREE
6
.
323
6.3.6
DEGREE
7
.
325
6.3.7
A
LIST
OF
TEST
POLYNOMIALS
.
327
XX
CONTENTS
6.4
EXAMPLES
OF
FAMILIES
OF
NUMBER
FIELDS
.
328
6.4.1
MAKING
TABLES
OF
NUMBER
FIELDS
.
328
6.4.2
CYCLIC
CUBIC
FIELDS
.
330
6.4.3
PURE
CUBIC
FIELDS
.
337
6.4.4
DECOMPOSITION
OF
PRIMES
IN
PURE
CUBIC
FIELDS
.
341
6.4.5
GENERAL
CUBIC
FIELDS
.
345
6.5
COMPUTING
THE
CLASS
GROUP,
REGULATOR
AND
FUNDAMENTAL
UNITS
.
346
6.5.1
IDEAL
REDUCTION
.
346
6.5.2
COMPUTING
THE
RELATION
MATRIX
.
348
6.5.3
COMPUTING
THE
REGULATOR
AND
A
SYSTEM
OF
FUNDAMENTAL
UNITS
.
.351
6.5.4
THE
GENERAL
CLASS
GROUP
AND
UNIT
ALGORITHM
.
352
6.5.5
THE
PRINCIPAL
IDEAL
PROBLEM
.
354
6.6
EXERCISES
FOR
CHAPTER
6
.
356
CHAPTER
7
INTRODUCTION
TO
ELLIPTIC
CURVES
.
360
7.1
BASIC
DEFINITIONS
.
360
7.1.1
INTRODUCTION
.
360
7.1.2
ELLIPTIC
INTEGRALS
AND
ELLIPTIC
FUNCTIONS
.
360
7.1.3
ELLIPTIC
CURVES
OVER
A
FIELD
.
362
7.1.4
POINTS
ON
ELLIPTIC
CURVES
.
365
7.2
COMPLEX
MULTIPLICATION
AND
CLASS
NUMBERS
.
369
7.2.1
MAPS
BETWEEN
COMPLEX
ELLIPTIC
CURVES
.
370
7.2.2
ISOGENIES
.
372
7.2.3
COMPLEX
MULTIPLICATION
.
374
7.2.4
COMPLEX
MULTIPLICATION
AND
HILBERT
CLASS
FIELDS
.
377
7.2.5
MODULAR
EQUATIONS
.
378
7.3
RANK
AND
L-FUNCTIONS
.
379
7.3.1
THE
ZETA
FUNCTION
OF
A
VARIETY
.
380
7.3.2
L-FUNCTIONS
OF
ELLIPTIC
CURVES
.
381
7.3.3
THE
TANIYAMA-WEIL
CONJECTURE
.
383
7.3.4
THE
BIRCH
AND
SWINNERTON-DYER
CONJECTURE
.
385
7.4
ALGORITHMS
FOR
ELLIPTIC
CURVES
.
387
7.4.1
ALGORITHMS
FOR
ELLIPTIC
CURVES
OVER
C
.
387
7.4.2
ALGORITHM
FOR
REDUCING
A
GENERAL
CUBIC
.
392
7.4.3
ALGORITHMS
FOR
ELLIPTIC
CURVES
OVER
F
P
.
396
7.5
ALGORITHMS
FOR
ELLIPTIC
CURVES
OVER
Q
.
399
7.5.1
TATE
'
S
ALGORITHM
.
399
7.5.2
COMPUTING
RATIONAL
POINTS
.
402
7.5.3
ALGORITHMS
FOR
COMPUTING
THE
L-FUNCTION
.
405
CONTENTS
XXI
7.6
ALGORITHMS
FOR
ELLIPTIC
CURVES
WITH
COMPLEX
MULTIPLICATION
.
407
7.6.1
COMPUTING
THE
COMPLEX
VALUES
OF
J(R)
.
407
7.6.2
COMPUTING
THE
HILBERT
CLASS
POLYNOMIALS
.
408
7.6.3
COMPUTING
WEBER
CLASS
POLYNOMIALS
.
408
7.7
EXERCISES
FOR
CHAPTER
7
.
409
CHAPTER
8
FACTORING
IN
THE
DARK
AGES
.
412
8.1
FACTORING
AND
PRIMALITY
TESTING
.
412
8.2
COMPOSITENESS
TESTS
.
414
8.3
PRIMALITY
TESTS
.
416
8.3.1
THE
POCKLINGTON-LEHMER
N
-
1
TEST
.
416
8.3.2
BRIEFLY,
OTHER
TESTS
.
417
8.4
LEHMAN
'
S
METHOD
.
418
8.5
POLLARD
'
S
P
METHOD
.
419
8.5.1
OUTLINE
OF
THE
METHOD
.
419
8.5.2
METHODS
FOR
DETECTING
PERIODICITY
.
420
8.5.3
BRENT
'
S
MODIFIED
ALGORITHM
.
422
8.5.4
ANALYSIS
OF
THE
ALGORITHM
.
423
8.6
SHANKS
'
S
CLASS
GROUP
METHOD
.
426
8.7
SHANKS
'
S
SQUFOF
.
427
8.8
THE
P
-
1-METHOD
.
431
8.8.1
THE
FIRST
STAGE
.
432
8.8.2
THE
SECOND
STAGE
.
433
8.8.3
OTHER
ALGORITHMS
OF
THE
SAME
TYPE
.
434
8.9
EXERCISES
FOR
CHAPTER
8
.
435
CHAPTER
9
MODERN
PRIMALITY
TESTS
.
437
9.1
THE
JACOBI
SUM
TEST
.
438
9.1.1
GROUP
RINGS
OF
CYCLOTOMIC
EXTENSIONS
.
438
9.1.2
CHARACTERS,
GAUSS
SUMS
AND
JACOBI
SUMS
.
440
9.1.3
THE
BASIC
TEST
.
442
9.1.4
CHECKING
CONDITION
P
.
447
9.1.5
THE
USE
OF
JACOBI
SUMS
.
449
9.1.6
DETAILED
DESCRIPTION
OF
THE
ALGORITHM
.
455
9.1.7
DISCUSSION
.
457
9.2
THE
ELLIPTIC
CURVE
TEST
.
459
9.2.1
THE
GOLDWASSER-KILIAN
TEST
.
459
9.2.2
ATKIN
'
S
TEST
.
463
9.3
EXERCISES
FOR
CHAPTER
9
.
467
XXII
CONTENTS
CHAPTER
10
MODERN
FACTORING
METHODS
.
469
10.1
THE
CONTINUED
FRACTION
METHOD
.
469
10.2
THE
CLASS
GROUP
METHOD
.
473
10.2.1
SKETCH
OF
THE
METHOD
.
473
10.2.2
THE
SCHNORR-LENSTRA
FACTORING
METHOD
.
474
10.3
THE
ELLIPTIC
CURVE
METHOD
.
476
10.3.1
SKETCH
OF
THE
METHOD
.
476
10.3.2
ELLIPTIC
CURVES
MODULO
N
.
477
10.3.3
THE
ECM
FACTORING
METHOD
OF
LENSTRA
.
479
10.3.4
PRACTICAL
CONSIDERATIONS
.
481
10.4
THE
MULTIPLE
POLYNOMIAL
QUADRATIC
SIEVE
.
482
10.4.1
THE
BASIC
QUADRATIC
SIEVE
ALGORITHM
.
483
10.4.2
THE
MULTIPLE
POLYNOMIAL
QUADRATIC
SIEVE
.
484
10.4.3
IMPROVEMENTS
TO
THE
MPQS
ALGORITHM
.
486
10.5
THE
NUMBER
FIELD
SIEVE
.
487
10.5.1
INTRODUCTION
.
487
10.5.2
DESCRIPTION
OF
THE
SPECIAL
NFS
WHEN
H(K)
=
1
.
488
10.5.3
DESCRIPTION
OF
THE
SPECIAL
NFS
WHEN
TI(AE')
1
.
492
10.5.4
DESCRIPTION
OF
THE
GENERAL
NFS
.
493
10.5.5
MISCELLANEOUS
IMPROVEMENTS
TO
THE
NUMBER
FIELD
SIEVE
.
495
10.6
EXERCISES
FOR
CHAPTER
10
.
496
APPENDIX
A
PACKAGES
FOR
NUMBER
THEORY
.
498
APPENDIX
B
SOME
USEFUL
TABLES
.
503
B.L
TABLE
OF
CLASS
NUMBERS
OF
COMPLEX
QUADRATIC
FIELDS
.
.
503
B.2
TABLE
OF
CLASS
NUMBERS
AND
UNITS
OF
REAL
QUADRATIC
FIELDS
.
505
B.3
TABLE
OF
CLASS
NUMBERS
AND
UNITS
OF
COMPLEX
CUBIC
FIELDS
.
509
B.4
TABLE
OF
CLASS
NUMBERS
AND
UNITS
OF
TOTALLY
REAL
CUBIC
FIELDS
.
511
B.5
TABLE
OF
ELLIPTIC
CURVES
.
514
BIBLIOGRAPHY
.
517
INDEX
.
529 |
| any_adam_object | 1 |
| author | Cohen, Henri 1947- |
| author_GND | (DE-588)1018621717 |
| author_facet | Cohen, Henri 1947- |
| author_role | aut |
| author_sort | Cohen, Henri 1947- |
| author_variant | h c hc |
| building | Verbundindex |
| bvnumber | BV009924039 |
| callnumber-first | Q - Science |
| callnumber-label | QA247 |
| callnumber-raw | QA247 |
| callnumber-search | QA247 |
| callnumber-sort | QA 3247 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| classification_tum | MAT 120f DAT 120f MAT 679f DAT 532f |
| ctrlnum | (OCoLC)31517711 (DE-599)BVBBV009924039 |
| dewey-full | 512/.74/028551 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74/028551 |
| dewey-search | 512/.74/028551 |
| dewey-sort | 3512 274 528551 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. corr. print. |
| format | Book |
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| id | DE-604.BV009924039 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-16T00:40:59Z |
| institution | BVB |
| isbn | 3540556400 0387556400 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006574293 |
| oclc_num | 31517711 |
| open_access_boolean | |
| owner | DE-29T DE-91 DE-BY-TUM DE-11 |
| owner_facet | DE-29T DE-91 DE-BY-TUM DE-11 |
| physical | XXII, 534 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Cohen, Henri 1947- Verfasser (DE-588)1018621717 aut A course in computational algebraic number theory Henri Cohen. [Ed. board: J. H. Ewing ...] 2. corr. print. Berlin [u.a.] Springer 1995 XXII, 534 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 138 Literaturverz. S. 517 - 528 Datenverarbeitung Algebraic number theory Data processing Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Algorithmische Zahlentheorie (DE-588)4314054-3 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Algorithmische Zahlentheorie (DE-588)4314054-3 s Datenverarbeitung (DE-588)4011152-0 s 1\p DE-604 Graduate texts in mathematics 138 (DE-604)BV000000067 138 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006574293&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cohen, Henri 1947- A course in computational algebraic number theory Graduate texts in mathematics Datenverarbeitung Algebraic number theory Data processing Algebraische Zahlentheorie (DE-588)4001170-7 gnd Datenverarbeitung (DE-588)4011152-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Algorithmische Zahlentheorie (DE-588)4314054-3 gnd |
| subject_GND | (DE-588)4001170-7 (DE-588)4011152-0 (DE-588)4128130-5 (DE-588)4314054-3 |
| title | A course in computational algebraic number theory |
| title_auth | A course in computational algebraic number theory |
| title_exact_search | A course in computational algebraic number theory |
| title_full | A course in computational algebraic number theory Henri Cohen. [Ed. board: J. H. Ewing ...] |
| title_fullStr | A course in computational algebraic number theory Henri Cohen. [Ed. board: J. H. Ewing ...] |
| title_full_unstemmed | A course in computational algebraic number theory Henri Cohen. [Ed. board: J. H. Ewing ...] |
| title_short | A course in computational algebraic number theory |
| title_sort | a course in computational algebraic number theory |
| topic | Datenverarbeitung Algebraic number theory Data processing Algebraische Zahlentheorie (DE-588)4001170-7 gnd Datenverarbeitung (DE-588)4011152-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Algorithmische Zahlentheorie (DE-588)4314054-3 gnd |
| topic_facet | Datenverarbeitung Algebraic number theory Data processing Algebraische Zahlentheorie Numerisches Verfahren Algorithmische Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006574293&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT cohenhenri acourseincomputationalalgebraicnumbertheory |