LEADER 05533nam0 22007093i 450 001 VAN00235057 005 20260626022053.541 010 $a978-33-19-16720-6 035 40$a934130554 100 $a20211124d2015 |0itac50 ba 101 $aeng 102 $aCH 105 $a|||| ||||| 181 $ai$b e 182 $ab 183 $acr 200 1 $aIdeals, varieties, and algorithms$ean introduction to computational algebraic geometry and commutative algebra$fDavid Cox, John Little, Donal O'Shea 205 $a4. ed 210 $a[Cham]$cSpringer$d2015 215 $aXVI, 646 p.$cill.$d24 cm 327 $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 levelcourses 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. Readers who are teaching from Ideals, Varieties, and Algorithms, or are studying the book on their own, may obtain a copy of the solutions manual by sending an email to jlittle@holycross.edu. 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 1$1001VAN00024019$12001 $aUndergraduate texts in mathematics$1210 $aBerlin [etc.]$cSpringer$d1958- 500 1$3VAN00235056$aIdeals, varieties, and algorithms$91745125 606 $a13-XX$xCommutative algebra [MSC 2020]$3VANC019732$2MF 606 $a13Pxx$xComputational aspects and applications [MSC 2020]$3VANC029095$2MF 606 $a14-XX$xAlgebraic geometry [MSC 2020]$3VANC019702$2MF 610 $aAlgebraic Geometry$9KW:K 610 $aAlgorithms Algebraic Geometry$9KW:K 610 $aCoCoA Algebraic Geometry$9KW:K 610 $aComputational Algebraic Geometry$9KW:K 610 $aGröbner basis$9KW:K 610 $aHilbert basis theorem$9KW:K 610 $aInvariant theory$9KW:K 610 $aMacaulay2 algebraic geometry$9KW:K 610 $aMaple algebraic geometry$9KW:K 610 $aMathematica algebraic geometry$9KW:K 610 $aProjective geometry$9KW:K 610 $aSage algebraic geometry$9KW:K 620 $aCH$dCham$3VANL001889 700 1$aCox$bDavid A.$3VANV030543$058032 701 1$aLittle$bJohn B.$3VANV043520$059605 701 1$aO'Shea$bDonal B.$3VANV043522$0441007 712 $aSpringer $3VANV108073$4650 790 1$aCox, David$zCox, David A.$3VANV093603 790 1$aCox, D. A.$zCox, David A.$3VANV264526 790 1$aCox, D.A.$zCox, David A.$3VANV264527 790 1$aCox, David Archibald$zCox, David A.$3VANV264528 790 1$aLittle, John Brittain$zLittle, John B.$3VANV264533 790 1$aLittle, J. B.$zLittle, John B.$3VANV264534 790 1$aLittle, J.B.$zLittle, John B.$3VANV264535 790 1$aLittle, John$zLittle, John B.$3VANV264536 790 1$aO'Shea, D.$zO'Shea, Donal B.$3VANV043523 790 1$aO'Shea, Don$zO'Shea, Donal B.$3VANV264531 790 1$aO'Shea, Donal Bartholomew$zO'Shea, Donal B.$3VANV264532 801 $aIT$bSOL$c20260911$gRICA 856 4 $uhttp://dx.doi.org/10.1007/978-3-319-16721-3$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN00235057 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08DLOAD e-book 0245 $e08eMF245 20211124 996 $aIdeals, varieties, and algorithms$91745125 997 $aUNICAMPANIA