LEADER 05813nam 22007695 450 001 9910299766603321 005 20250930123540.0 010 $a3-319-16721-9 024 7 $a10.1007/978-3-319-16721-3 035 $a(CKB)3710000000404042 035 $a(SSID)ssj0001501524 035 $a(PQKBManifestationID)11918412 035 $a(PQKBTitleCode)TC0001501524 035 $a(PQKBWorkID)11446777 035 $a(PQKB)10276372 035 $a(DE-He213)978-3-319-16721-3 035 $a(MiAaPQ)EBC6313195 035 $a(MiAaPQ)EBC5577245 035 $a(Au-PeEL)EBL5577245 035 $a(OCoLC)1066179708 035 $a(PPN)185489850 035 $a(EXLCZ)993710000000404042 100 $a20150430d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIdeals, Varieties, and Algorithms $eAn Introduction to Computational Algebraic Geometry and Commutative Algebra /$fby David A. Cox, John Little, Donal O'Shea 205 $a4th ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XVI, 646 p. 95 illus., 10 illus. in color.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-319-16720-0 327 $aPreface -- 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. . 330 $aThis 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. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aGeometry, Algebraic 606 $aCommutative algebra 606 $aCommutative rings 606 $aLogic, Symbolic and mathematical 606 $aComputer software 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aMathematical Software$3https://scigraph.springernature.com/ontologies/product-market-codes/M14042 615 0$aGeometry, Algebraic. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aLogic, Symbolic and mathematical. 615 0$aComputer software. 615 14$aAlgebraic Geometry. 615 24$aCommutative Rings and Algebras. 615 24$aMathematical Logic and Foundations. 615 24$aMathematical Software. 676 $a516.35 700 $aCox$b David A$4aut$4http://id.loc.gov/vocabulary/relators/aut$058032 702 $aLittle$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aO'Shea$b Donal$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299766603321 996 $aIdeals, Varieties, and Algorithms$92508611 997 $aUNINA