000 03593nam a22005175i 4500
001 978-0-387-27105-7
003 DE-He213
005 20161121230924.0
007 cr nn 008mamaa
008 100301s2005 xxu| s |||| 0|eng d
020 _a9780387271057
_9978-0-387-27105-7
024 7 _a10.1007/b138611
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
082 0 4 _a516.35
_223
100 1 _aCox, David A.
_eauthor.
245 1 0 _aUsing Algebraic Geometry
_h[electronic resource] /
_cby David A. Cox, John Little, Donal O’shea.
250 _aSecond Edition.
264 1 _aNew York, NY :
_bSpringer New York,
_c2005.
300 _aXII, 575 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v185
505 0 _aSolving Polynomial Equations -- Resultants -- Computation in Local Rings -- Modules -- Free Resolutions -- Polytopes, Resultants, and Equations -- Polyhedral Regions and Polynomials -- Algebraic Coding Theory -- The Berlekamp-Massey-Sakata Decoding Algorithm.
520 _aIn recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gröbner bases and resultants. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gröbner bases. The book does not assume the reader is familiar with more advanced concepts such as modules. For the new edition, the authors have added a unified discussion of how matrices can be used to specify monomial orders; a revised presentation of the Mora normal form algorithm; two sections discussing the Gröbner fan of an ideal and the Gröbner Walk basis conversion algorithm; and a new chapter on the theory of order domains, associated codes, and the Berlekamp-Massey-Sakata decoding algorithm. They have also updated the references, improved some of the proofs, and corrected typographical errors. David Cox is Professor of Mathematics at Amherst College. John Little is Professor of Mathematics at College of the Holy Cross. Dona l O’Shea is the Elizabeth T. Kennan Professor of Mathematics and Dean of Faculty at Mt. Holyoke College. These authors also co-wrote the immensely successful book, Ideals, Varieties, and Algorithms.
650 0 _aMathematics.
650 0 _aComputer science
_xMathematics.
650 0 _aAlgebraic geometry.
650 0 _aAlgorithms.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aSymbolic and Algebraic Manipulation.
650 2 4 _aAlgorithms.
700 1 _aLittle, John.
_eauthor.
700 1 _aO’shea, Donal.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387207063
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v185
856 4 0 _uhttp://dx.doi.org/10.1007/b138611
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c505971
_d505971