Computational commutative algebra: 1
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | IX, 321 S. graph. Darst. |
| ISBN: | 354067733X |
Staff View
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Record in the Search Index
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| adam_text | Kreuzer • Robbiano
Computational Commutative
The main topic of this book is that of Groebner bases and
their applications. The main purpose of this book is that of
bridging the current gap in the literature between theory and
real computation. The book can be used by teachers and students
alike as a comprehensive guide to both the theory and the
practice of Computational Commutative Algebra. It has been
made as self-contained as possible, and thus is ideaEy suited as
a textbook for graduate or advanced undergraduate courses.
Numerous applications are described, covering fields as disparate
as algebraic geometry and financial markets. To aid a deeper
understanding of these applications there are
at illustrating how the theory can be used in these cases. The
computational aspects of the tutorials can be carried out with
the computer algebra system
appears in an appendix. Besides the tutorials there are plenty
of exercises, some of a theoretical nature and others more
practical.
Contents
Foreword
Introduction
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.10
0.11
1.
1.1
Tutorial
Tutorial
Tutorial
1.2
Tutorial
Tutorial
Tutorial
1.3
Tutorial
Tutorial
1.4
Tutorial
Tutorial
1.5
Tutorial
Tutorial
Tutorial IS. Newton Polytopes
1.6
Tutorial
Tutorial
1.7
Tutorial
2.
2.1
Tutorial
2.2
Tutorial
2.3
Tutorial
Tutorial
2.4 Gröbner
2.4.A Existence of
2.4.B Normal Forms
2.4.C Reduced
Tutorial
Tutorial
2.5
Tutorial
Tutorial
Tutorial
2.6
2.6.A The Field-Theoretic Version.
2.6.B The Geometric Version
Tutorial
Tutorial
3.
3.1
Tutorial
Tutorial
3.2
3.2.A Intersections
3.2.B Colon Ideals and Annihilators
3.2.C Colon Modules
Tutorial
Tutorial
3.3
3.3.A Kernels, Images, and Liftings of Linear Maps
3.3.B Horn-Modules
Tutorial
Tutorial
Contents
3.4 Elimination............................................195
Tutorial 34- Elimination
Tutorial 35.
Tutorial 36. Diophantine Systems and Integer Programming ... 207
3.5
3.5.A
3.5.B Saturation......................................215
Tutorial 37.
Tutorial 38. Toric Ideals................................222
3.6 Homomorphisms
Tutorial 39.
Tutorial 40. Gröbner Bases and Invariant
Tutorial 41. Subalgebras
3.7 Systems
3.7.A A Bound for the Number of Solutions
3.7.B Radicals of Zero-Dimensional Ideals
3.7.C Solving Systems Effectively
Tutorial
Tutorial
Tutorial
A. How to Get Started with CbCbA
B. How to Program CoCoA
C. A Potpourri of CoCbA Programs
D. Hints for Selected Exercises
Notation
Bibliography
i.
Index
|
| any_adam_object | 1 |
| author | Kreuzer, Martin Robbiano, Lorenzo 1944- |
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| callnumber-first | Q - Science |
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| callnumber-raw | QA251.3 |
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| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)264713281 (DE-599)BVBBV013382624 |
| dewey-full | 512/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.24 |
| dewey-search | 512/.24 |
| dewey-sort | 3512 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:44:51Z |
| institution | BVB |
| isbn | 354067733X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009128257 |
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| physical | IX, 321 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
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| spelling | Kreuzer, Martin Verfasser aut Computational commutative algebra 1 Martin Kreuzer ; Lorenzo Robbiano Berlin [u.a.] Springer 2000 IX, 321 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Anéis e álgebras comutativos larpcal Álgebra computacional larpcal Datenverarbeitung Commutative algebra Data processing Gröbner bases Computeralgebra (DE-588)4010449-7 gnd rswk-swf Computeralgebra (DE-588)4010449-7 s DE-604 Robbiano, Lorenzo 1944- Verfasser (DE-588)122293304 aut (DE-604)BV013382620 1 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009128257&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009128257&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kreuzer, Martin Robbiano, Lorenzo 1944- Computational commutative algebra Anéis e álgebras comutativos larpcal Álgebra computacional larpcal Datenverarbeitung Commutative algebra Data processing Gröbner bases Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4010449-7 |
| title | Computational commutative algebra |
| title_auth | Computational commutative algebra |
| title_exact_search | Computational commutative algebra |
| title_full | Computational commutative algebra 1 Martin Kreuzer ; Lorenzo Robbiano |
| title_fullStr | Computational commutative algebra 1 Martin Kreuzer ; Lorenzo Robbiano |
| title_full_unstemmed | Computational commutative algebra 1 Martin Kreuzer ; Lorenzo Robbiano |
| title_short | Computational commutative algebra |
| title_sort | computational commutative algebra |
| topic | Anéis e álgebras comutativos larpcal Álgebra computacional larpcal Datenverarbeitung Commutative algebra Data processing Gröbner bases Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Anéis e álgebras comutativos Álgebra computacional Datenverarbeitung Commutative algebra Data processing Gröbner bases Computeralgebra |
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