Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
[1995]
|
| Edition: | Corr. 3. print. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 499 - 501 |
| Physical Description: | XI, 513 S. graph. Darst. |
| ISBN: | 354097847X 038797847X |
Staff View
MARC
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| 100 | 1 | |a Cox, David A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ideals, varieties, and algorithms |b an introduction to computational algebraic geometry and commutative algebra |c David Cox ; John Little ; Donal O'Shea |
| 250 | |a Corr. 3. print. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c [1995] | |
| 300 | |a XI, 513 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate texts in mathematics | |
| 500 | |a Literaturverz. S. 499 - 501 | ||
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Record in the Search Index
| _version_ | 1807773944580669440 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
PREFACE
.
VII
CHAPTER
1
GEOMETRY,
ALGEBRA,
AND
ALGORITHMS
.
1
§1.
POLYNOMIALS
AND
AFFINE
SPACE
.
1
§2.
AFFINE
VARIETIES
.
5
§3.
PARAMETRIZATIONS
OF
AFFINE
VARIETIES
.
14
§4.
IDEALS
.
29
§5.
POLYNOMIALS
OF
ONE
VARIABLE
.
37
CHAPTER
2
GROEBNER
BASES
.
48
§1.
INTRODUCTION
.
48
PROBLEMS
.
48
§2.
ORDERINGS
ON
THE
MONOMIALS
IN
,.
,X
N
]
.
53
§3.
A
DIVISION
ALGORITHM
IN
60
§4.
MONOMIAL
IDEALS
AND
DICKSON
'
S
LEMMA
.
68
§5.
THE
HILBERT
BASIS
THEOREM
AND
GROEBNER
BASES
.
74
§6.
PROPERTIES
OF
GROEBNER
BASES
.
80
§7.
BUCHBERGER
'
S
ALGORITHM
.
87
§8.
FIRST
APPLICATIONS
OF
GROEBNER
BASES
.
94
THE
IDEAL
MEMBERSHIP
PROBLEM
.
94
THE
PROBLEM
OF
SOLVING
POLYNOMIAL
EQUATIONS
.
95
THE
IMPLICITIZATION
PROBLEM
.
97
§9.
(OPTIONAL)
IMPROVEMENTS
ON
BUCHBERGER
'
S
ALGORITHM
.
101
CHAPTER
3
ELIMINATION
THEORY
.
113
§
1.
THE
ELIMINATION
AND
EXTENSION
THEOREMS
.
113
§2.
THE
GEOMETRY
OF
ELIMINATION
.
121
§3.
IMPLICITIZATION
.
126
§4.
SINGULAR
POINTS
AND
ENVELOPES
.
135
SINGULAR
POINTS
.
135
ENVELOPES
.
139
§5.
UNIQUE
FACTORIZATION
AND
RESULTANTS
.
147
IRREDUCIBLE
POLYNOMIALS
AND
UNIQUE
FACTORIZATION
.
147
RESULTANTS
.
150
§6.
RESULTANTS
AND
THE
EXTENSION
THEOREM
.
159
X
TABLE
OF
CONTENTS
CHAPTER
4
THE
ALGEBRA-GEOMETRY
DICTIONARY
.
168
§1.
HILBERT
'
S
NULLSTELLENSATZ
.
168
§2.
RADICAL
IDEALS
AND
THE
IDEAL-VARIETY
CORRESPONDENCE
.
174
§3.
SUMS,
PRODUCTS,
AND
INTERSECTIONS
OF
IDEALS
.
181
SUMS
OF
IDEALS
.
182
PRODUCTS
OF
IDEALS
.
183
INTERSECTIONS
OF
IDEALS
.
184
§4.
ZARISKI
CLOSURE
AND
QUOTIENTS
OF
IDEALS
.
191
§5.
IRREDUCIBLE
VARIETIES
AND
PRIME
IDEALS
.
196
§6.
DECOMPOSITION
OF
A
VARIETY
INTO
IRREDUCIBLES
.
201
§7.
(OPTIONAL)
PRIMARY
DECOMPOSITION
OF
IDEALS
.
207
§8.
SUMMARY
.
211
CHAPTERS
POLYNOMIAL
AND
RATIONAL
FUNCTIONS
ON
A
VARIETY
.
213
§1.
POLYNOMIAL
MAPPINGS
.
213
§2.
QUOTIENTS
OF
POLYNOMIAL
RINGS
.
220
§3.
ALGORITHMIC
COMPUTATIONS
IN
,.,
X
N
}/I
.
228
§4.
THE
COORDINATE
RING
OF
AN
AFFINE
VARIETY
.
235
§5.
RATIONAL
FUNCTIONS
ON
A
VARIETY
.
245
CHAPTER
6
ROBOTICS
AND
AUTOMATIC
GEOMETRIC
THEOREM
PROVING
.
255
§1.
GEOMETRIC
DESCRIPTION
OF
ROBOTS
.
255
§2.
THE
FORWARD
KINEMATIC
PROBLEM
.
261
§3.
THE
INVERSE
KINEMATIC
PROBLEM
AND
MOTION
PLANNING
.
269
§4.
AUTOMATIC
GEOMETRIC
THEOREM
PROVING
.
280
§5.
WU
'
S
METHOD
.
296
STEP
1.
REDUCTION
TO
TRIANGULAR
FORM
.
299
STEP
2.
SUCCESSIVE
PSEUDODIVISION
.
301
CHAPTER
7
INVARIANT
THEORY
OF
FINITE
GROUPS
.
306
§1.
SYMMETRIC
POLYNOMIALS
.
306
§2.
FINITE
MATRIX
GROUPS
AND
RINGS
OF
INVARIANTS
.
316
§3.
GENERATORS
FOR
THE
RING
OF
INVARIANTS
.
325
§4.
RELATIONS
AMONG
GENERATORS
AND
THE
GEOMETRY
OF
ORBITS
.
333
CHAPTER
8
PROJECTIVE
ALGEBRAIC
GEOMETRY
.
345
§1.
THE
PROJECTIVE
PLANE
.
345
§2.
PROJECTIVE
SPACE
AND
PROJECTIVE
VARIETIES
.
356
§3.
THE
PROJECTIVE
ALGEBRA-GEOMETRY
DICTIONARY
.
366
§4.
THE
PROJECTIVE
CLOSURE
OF
AN
AFFINE
VARIETY
.
374
§5.
PROJECTIVE
ELIMINATION
THEORY
.
381
§6.
THE
GEOMETRY
OF
QUADRIC
HYPERSURFACES
.
395
TABLE
OF
CONTENTS
XI
CHAPTER
9
THE
DIMENSION
OF
A
VARIETY
.
409
§1.
THE
VARIETY
OF
A
MONOMIAL
IDEAL
.
409
§2.
THE
COMPLEMENT
OF
A
MONOMIAL
IDEAL
.
413
§3.
THE
HILBERT
FUNCTION
AND
THE
DIMENSION
OF
A
VARIETY
.
426
THE
DIMENSION
OF
AN
AFFINE
VARIETY
.
427
THE
DIMENSION
OF
A
PROJECTIVE
VARIETY
.
432
§4.
ELEMENTARY
PROPERTIES
OF
DIMENSION
.
438
§5.
DIMENSION
AND
ALGEBRAIC
INDEPENDENCE
.
447
§6.
DIMENSION
AND
NONSINGULARITY
.
454
§7.
THE
TANGENT
CONE
.
465
APPENDIX
A
SOME
CONCEPTS
FROM
ALGEBRA
.
479
§1.
FIELDS
AND
RINGS
.
479
§2.
GROUPS
.
480
§3.
DETERMINANTS
.
481
APPENDIX
B
PSEUDOCODE
.
483
§1.
INPUTS,
OUTPUTS,
VARIABLES,
AND
CONSTANTS
.
483
§2.
ASSIGNMENT
STATEMENTS
.
484
§3.
LOOPING
STRUCTURES
.
484
§4.
BRANCHING
STRUCTURES
.
485
APPENDIX
C
COMPUTER
ALGEBRA
SYSTEMS
.
487
§1.
MAPLE
.
487
§2.
MATHEMATICA
.
489
§3.
REDUCE
.
491
§4.
OTHER
SYSTEMS
.
493
APPENDIX
D
INDEPENDENT
PROJECTS
.
495
§1.
GENERAL
COMMENTS
.
495
§2.
SUGGESTED
PROJECTS
.
495
REFERENCES
.
499
INDEX
.
503 |
| any_adam_object | 1 |
| author | Cox, David A. Little, John B. O'Shea, Donal 1952- |
| author_GND | (DE-588)113289731 |
| author_facet | Cox, David A. Little, John B. O'Shea, Donal 1952- |
| author_role | aut aut aut |
| author_sort | Cox, David A. |
| author_variant | d a c da dac j b l jb jbl d o do |
| building | Verbundindex |
| bvnumber | BV010387545 |
| classification_rvk | SK 240 |
| classification_tum | MAT 140f DAT 535f MAT 130f |
| ctrlnum | (OCoLC)634466125 (DE-599)BVBBV010387545 |
| discipline | Informatik Mathematik |
| edition | Corr. 3. print. |
| format | Book |
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| id | DE-604.BV010387545 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:32:59Z |
| institution | BVB |
| isbn | 354097847X 038797847X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006916501 |
| oclc_num | 634466125 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XI, 513 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Cox, David A. Verfasser aut Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra David Cox ; John Little ; Donal O'Shea Corr. 3. print. New York [u.a.] Springer [1995] XI, 513 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Literaturverz. S. 499 - 501 Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Computeralgebra (DE-588)4010449-7 s DE-604 Kommutative Algebra (DE-588)4164821-3 s Datenverarbeitung (DE-588)4011152-0 s 1\p DE-604 Algorithmische Geometrie (DE-588)4130267-9 s 2\p DE-604 Little, John B. Verfasser aut O'Shea, Donal 1952- Verfasser (DE-588)113289731 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916501&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cox, David A. Little, John B. O'Shea, Donal 1952- Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra Datenverarbeitung (DE-588)4011152-0 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4011152-0 (DE-588)4130267-9 (DE-588)4164821-3 (DE-588)4001161-6 (DE-588)4010449-7 |
| title | Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra |
| title_auth | Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra |
| title_exact_search | Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra |
| title_full | Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra David Cox ; John Little ; Donal O'Shea |
| title_fullStr | Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra David Cox ; John Little ; Donal O'Shea |
| title_full_unstemmed | Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra David Cox ; John Little ; Donal O'Shea |
| title_short | Ideals, varieties, and algorithms |
| title_sort | ideals varieties and algorithms an introduction to computational algebraic geometry and commutative algebra |
| title_sub | an introduction to computational algebraic geometry and commutative algebra |
| topic | Datenverarbeitung (DE-588)4011152-0 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Kommutative Algebra (DE-588)4164821-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Datenverarbeitung Algorithmische Geometrie Kommutative Algebra Algebraische Geometrie Computeralgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916501&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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