國立虎尾科技大學 |

Ideals, Varieties, and Algorithms = An Introduction to Computational Algebraic Geometry and Commutative Algebra /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Ideals, Varieties, and Algorithms/ by David A. Cox, John Little, Donal O'Shea.
其他題名:	An Introduction to Computational Algebraic Geometry and Commutative Algebra /
作者:	Cox, David A.
其他作者:	Little, John.
面頁冊數:	XVI, 646 p. 95 illus., 10 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebraic geometry. -
電子資源:	https://doi.org/10.1007/978-3-319-16721-3
ISBN:	9783319167213

Ideals, Varieties, and Algorithms = An Introduction to Computational Algebraic Geometry and Commutative Algebra /
Cox, David A.

Ideals, Varieties, and AlgorithmsAn Introduction to Computational Algebraic Geometry and Commutative Algebra /[electronic resource] :by David A. Cox, John Little, Donal O'Shea. - 4th ed. 2015. - XVI, 646 p. 95 illus., 10 illus. in color.online resource. - Undergraduate Texts in Mathematics,0172-6056. - Undergraduate Texts in Mathematics,.

Preface -- Notation for Sets and 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. .

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 Gröbner 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.

ISBN: 9783319167213

Standard No.: 10.1007/978-3-319-16721-3doiSubjects--Topical Terms:

1255324
Algebraic geometry.

LC Class. No.: QA564-609

Dewey Class. No.: 516.35

Ideals, Varieties, and Algorithms = An Introduction to Computational Algebraic Geometry and Commutative Algebra /
LDR:04397nam a22004095i 4500 001 966492
003 DE-He213
005 20200706112937.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319167213 $9 978-3-319-16721-3
024 7 $a 10.1007/978-3-319-16721-3 $2 doi
035 $a 978-3-319-16721-3
050 4 $a QA564-609
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
100 1 $a Cox, David A. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 672007
245 1 0 $a Ideals, Varieties, and Algorithms $h [electronic resource] : $b An Introduction to Computational Algebraic Geometry and Commutative Algebra / $c by David A. Cox, John Little, Donal O'Shea.
250 $a 4th ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a XVI, 646 p. 95 illus., 10 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Undergraduate Texts in Mathematics, $x 0172-6056
505 0 $a Preface -- Notation for Sets and 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. .
520 $a 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 Gröbner 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.
650 0 $a Algebraic geometry. $3 1255324
650 0 $a Commutative algebra. $3 672047
650 0 $a Commutative rings. $3 672474
650 0 $a Mathematical logic. $2 bicssc $3 810627
650 0 $a Computer software. $3 528062
650 1 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Commutative Rings and Algebras. $3 672054
650 2 4 $a Mathematical Logic and Foundations. $3 669393
650 2 4 $a Mathematical Software. $3 672446
700 1 $a Little, John. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 672008
700 1 $a O'Shea, Donal. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1262105
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319167206
776 0 8 $i Printed edition: $z 9783319167220
776 0 8 $i Printed edition: $z 9783319374277
830 0 $a Undergraduate Texts in Mathematics, $x 0172-6056 $3 1253653
856 4 0 $u https://doi.org/10.1007/978-3-319-16721-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)