Verfügbarkeit: Ideals, varieties, and algorithms | Technische Universität München

Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra

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Beteiligte Personen:	Cox, David A. 1948- (VerfasserIn), Little, John (VerfasserIn), O'Shea, Donal 1952- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	Englisch
Veröffentlicht:	Cham [u.a.] Springer 2015
Ausgabe:	4. ed.
Schriftenreihe:	Undergraduate texts in mathematics
Schlagwörter:	Mathematics Geometry, algebraic Algebra Computer software Logic, Symbolic and mathematical Algebraic Geometry Commutative Rings and Algebras Mathematical Logic and Foundations Mathematical Software Mathematik Datenverarbeitung Algebraische Geometrie Algorithmische Geometrie Kommutative Algebra Computeralgebra
Links:	https://doi.org/10.1007/978-3-319-16721-3 https://doi.org/10.1007/978-3-319-16721-3 https://doi.org/10.1007/978-3-319-16721-3 https://doi.org/10.1007/978-3-319-16721-3 https://doi.org/10.1007/978-3-319-16721-3 https://doi.org/10.1007/978-3-319-16721-3 https://doi.org/10.1007/978-3-319-16721-3 https://doi.org/10.1007/978-3-319-16721-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027978508&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027978508&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	1 Online-Ressource (XVI, 646 S.) 95 illus., 10 illus. in color
ISBN:	9783319167213
DOI:	10.1007/978-3-319-16721-3

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Datensatz im Suchindex

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adam_text	IDEALS, VARIETIES, AND ALGORITHMS / COX, DAVID A. : 2015 TABLE OF CONTENTS / INHALTSVERZEICHNIS PREFACE NOTATION FOR SETSAND FUNCTIONS 1. GEOMETRY, ALGEBRA, AND ALGORITHMS 2. GROEBNER BASES 3. ELIMINATION THEORY 4.THE ALGEBRA-GEOMETRY DICTIONARY 5. POLYNOMIAL AND RATIONAL FUNCTIONS ON A VARIETY 6. ROBOTICS AND AUTOMATIC GEOMETRIC THEOREM PROVING 7. INVARIANT THEORY OF FINITE GROUPS 8. PROJECTIVE ALGEBRAIC GEOMETRY 9. THE DIMENSION OF A VARIETY 10.ADDITIONAL GROEBNER BASIS ALGORITHMS APPENDIX A. SOME CONCEPTS FROM ALGEBRA APPENDIX B. PSEUDOCODE APPENDIX C. COMPUTER ALGEBRA SYSTEMS APPENDIX D. INDEPENDENT PROJECTS REFERENCES INDEX DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. IDEALS, VARIETIES, AND ALGORITHMS / COX, DAVID A. : 2015 ABSTRACT / INHALTSTEXT THIS TEXT COVERS TOPICS IN ALGEBRAIC GEOMETRY AND COMMUTATIVE ALGEBRA WITH A STRONG PERSPECTIVE TOWARD PRACTICAL AND COMPUTATIONAL ASPECTS. THE FIRST FOUR CHAPTERS FORM THE CORE OF THE BOOK. A COMPREHENSIVE CHART IN THE PREFACE ILLUSTRATES A VARIETY OF WAYS TO PROCEED WITH THE MATERIAL ONCE THESE CHAPTERS ARE COVERED. IN ADDITION TO THE FUNDAMENTALS OF ALGEBRAIC GEOMETRY—THE ELIMINATION THEOREM, THE EXTENSION THEOREM, THE CLOSURE THEOREM, AND THE NULLSTELLENSATZ—THIS NEW EDITION INCORPORATES SEVERAL SUBSTANTIAL CHANGES, ALL OF WHICH ARE LISTED IN THE PREFACE. THE LARGEST REVISION INCORPORATES A NEW CHAPTER (TEN), WHICH PRESENTS SOME OF THE ESSENTIALS OF PROGRESS MADE OVER THE LAST DECADES IN COMPUTING GROEBNER BASES. THE BOOK ALSO INCLUDES CURRENT COMPUTER ALGEBRA MATERIAL IN APPENDIX C AND UPDATED INDEPENDENT PROJECTS (APPENDIX D).THE BOOK MAY SERVE AS A FIRST OR SECOND COURSE IN UNDERGRADUATE ABSTRACT ALGEBRA AND, WITH SOME SUPPLEMENTATION PERHAPS, FOR BEGINNING GRADUATE LEVEL COURSES IN ALGEBRAIC GEOMETRY OR COMPUTATIONAL ALGEBRA. PREREQUISITES FOR THE READER INCLUDE LINEAR ALGEBRA AND A PROOF-ORIENTED COURSE. IT IS ASSUMED THAT THE READER HAS ACCESS TO A COMPUTER ALGEBRA SYSTEM. APPENDIX C DESCRIBES FEATURES OF MAPLE™, MATHEMATICA, AND SAGE, AS WELL AS OTHER SYSTEMS THAT ARE MOST RELEVANT TO THE TEXT. PSEUDOCODE IS USED IN THE TEXT; APPENDIX B CAREFULLY DESCRIBES THE PSEUDOCODE USED. FROM THE REVIEWS OF PREVIOUS EDITIONS: “…THE BOOK GIVES AN INTRODUCTION TO BUCHBERGER’S ALGORITHM WITH APPLICATIONS TO SYZYGIES, HILBERT POLYNOMIALS, PRIMARY DECOMPOSITIONS. THERE IS AN INTRODUCTION TO CLASSICAL ALGEBRAIC GEOMETRY WITH APPLICATIONS TO THE IDEAL MEMBERSHIP PROBLEM, SOLVING POLYNOMIAL EQUATIONS, AND ELIMINATION THEORY. …THE BOOK IS WELL-WRITTEN.…THE REVIEWER IS SURE THAT IT WILL BE AN EXCELLENT GUIDE TO INTRODUCE FURTHER UNDERGRADUATES IN THE ALGORITHMIC ASPECT OF COMMUTATIVE ALGEBRA AND ALGEBRAIC GEOMETRY.” —PETER SCHENZEL, ZBMATH, 2007 “I CONSIDER THE BOOK TO BE WONDERFUL. ... THE EXPOSITION IS VERY CLEAR, THERE ARE MANY HELPFUL PICTURES, AND THERE ARE A GREAT MANY INSTRUCTIVE EXERCISES, SOME QUITE CHALLENGING ... OFFERS THE HEART AND SOUL OF MODERN COMMUTATIVE AND ALGEBRAIC GEOMETRY.” —THE AMERICAN MATHEMATICAL MONTHLY DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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id	DE-604.BV042544502
illustrated	Illustrated
indexdate	2024-12-20T17:14:00Z
institution	BVB
isbn	9783319167213
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-027978508
oclc_num	910404318
open_access_boolean
owner	DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-20 DE-739 DE-634 DE-861 DE-83
owner_facet	DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-20 DE-739 DE-634 DE-861 DE-83
physical	1 Online-Ressource (XVI, 646 S.) 95 illus., 10 illus. in color
psigel	ZDB-2-SMA UBY_PDA_SMA ZDB-2-SMA_2015
publishDate	2015
publishDateSearch	2015
publishDateSort	2015
publisher	Springer
record_format	marc
series2	Undergraduate texts in mathematics
spellingShingle	Cox, David A. 1948- Little, John O'Shea, Donal 1952- Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra Mathematics Geometry, algebraic Algebra Computer software Logic, Symbolic and mathematical Algebraic Geometry Commutative Rings and Algebras Mathematical Logic and Foundations Mathematical Software Mathematik Datenverarbeitung (DE-588)4011152-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Kommutative Algebra (DE-588)4164821-3 gnd Computeralgebra (DE-588)4010449-7 gnd
subject_GND	(DE-588)4011152-0 (DE-588)4001161-6 (DE-588)4130267-9 (DE-588)4164821-3 (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 A. Cox ; John Little ; Donal O'Shea
title_fullStr	Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra David A. Cox ; John Little ; Donal O'Shea
title_full_unstemmed	Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra David A. 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	Mathematics Geometry, algebraic Algebra Computer software Logic, Symbolic and mathematical Algebraic Geometry Commutative Rings and Algebras Mathematical Logic and Foundations Mathematical Software Mathematik Datenverarbeitung (DE-588)4011152-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Kommutative Algebra (DE-588)4164821-3 gnd Computeralgebra (DE-588)4010449-7 gnd
topic_facet	Mathematics Geometry, algebraic Algebra Computer software Logic, Symbolic and mathematical Algebraic Geometry Commutative Rings and Algebras Mathematical Logic and Foundations Mathematical Software Mathematik Datenverarbeitung Algebraische Geometrie Algorithmische Geometrie Kommutative Algebra Computeralgebra
url	https://doi.org/10.1007/978-3-319-16721-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027978508&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027978508&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
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