LEADER 05254nam 22006615 450 001 9911022157503321 005 20250930123424.0 010 $a9783031918414$b(electronic bk.) 010 $z9783031918407 024 7 $a10.1007/978-3-031-91841-4 035 $a(MiAaPQ)EBC32270595 035 $a(Au-PeEL)EBL32270595 035 $a(CKB)40410624500041 035 $a(DE-He213)978-3-031-91841-4 035 $a(EXLCZ)9940410624500041 100 $a20250823d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIdeals, Varieties, and Algorithms $eAn Introduction to Computational Algebraic Geometry and Commutative Algebra /$fby David A. Cox, John Little, Donal O'Shea 205 $a5th ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (665 pages) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 311 08$aPrint version: Cox, David A. Ideals, Varieties, and Algorithms Cham : Springer,c2025 9783031918407 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 careful attention to their 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?there are chapters on polynomial and rational functions between varieties, robotics and geometric theorem proving, invariant theory of finite groups, projective algebraic geometry, dimension theory, and progress made over the last decades in computing Gröbner bases. The fifth edition builds on the fourth edition in two main ways. First, a number of typographical errors, found by readers and by the authors since 2018, have been corrected. Second, new material on toric varieties, monomial curves, and other topics of current interest in algebraic geometry has been added. This enhances the opportunities for active learning through new examples, new exercises, and new projects in Appendix D, all supplemented by additional references. The book also includes updated computer algebra material in Appendix C. The book may be used for a first or second course in undergraduate abstract algebra and, with some augmentation perhaps, for beginning graduate courses in algebraic geometry or computational commutative 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 SageMath, 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 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,$x2197-5604 606 $aGeometry, Algebraic 606 $aCommutative algebra 606 $aCommutative rings 606 $aLogic, Symbolic and mathematical 606 $aComputer software 606 $aAlgebraic Geometry 606 $aCommutative Rings and Algebras 606 $aMathematical Logic and Foundations 606 $aMathematical Software 615 0$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 $a516.3/5 700 $aCox$b David A$058032 701 $aLittle$b John$0351000 701 $aO'Shea$b Donal$0441007 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9911022157503321 996 $aIdeals, Varieties, and Algorithms$94429440 997 $aUNINA