LEADER 04477nam 22005535 450 001 9910480269303321 005 20200630055724.0 010 $a1-4757-2693-7 024 7 $a10.1007/978-1-4757-2693-0 035 $a(CKB)2660000000024264 035 $a(SSID)ssj0001297082 035 $a(PQKBManifestationID)11721707 035 $a(PQKBTitleCode)TC0001297082 035 $a(PQKBWorkID)11353930 035 $a(PQKB)10559420 035 $a(DE-He213)978-1-4757-2693-0 035 $a(MiAaPQ)EBC3084218 035 $a(PPN)238032590 035 $a(EXLCZ)992660000000024264 100 $a20130305d1997 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIdeals, Varieties, and Algorithms$b[electronic resource] $eAn Introduction to Computational Algebraic Geometry and Commutative Algebra /$fby David Cox, John Little, DONAL OSHEA 205 $a2nd ed. 1997. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1997. 215 $a1 online resource (XIII, 538 p. 44 illus.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-94680-2 311 $a1-4757-2695-3 320 $aIncludes bibliographical references and index. 327 $a1. 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 -- Appendix A. Some Concepts from Algebra -- §1 Fields and Rings -- §2. Groups -- §3. Determinants -- Appendix B. Pseudocode -- §1. Inputs, Outputs, Variables, and Constants -- §2. Assignment Statements -- §3. Looping Structures -- §4. Branching Structures -- Appendix C. Computer Algebra Systems -- §1. AXIOM -- §2. Maple -- §3. Mathematica -- §4. REDUCE -- §5. Other Systems -- Appendix D. Independent Projects -- §1. General Comments -- §2. Suggested Projects -- References. 330 $aAlgebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing a new edition of Ideals, Varieties and Algorithms the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple , Mathematica and REDUCE. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aMathematical logic 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 615 0$aMathematical logic. 615 14$aMathematical Logic and Foundations. 676 $a511.3 700 $aCox$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$012499 702 $aLittle$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aOSHEA$b DONAL$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910480269303321 996 $aIdeals, varieties and algorithms$9375303 997 $aUNINA