MARC Record from marc_columbia

LEADER: 03365fam a2200421 a 4500
001 1965409
005 20220609040325.0
008 960402t19971997nyua b 001 0 eng
010 $a 96008023
020 $a0387946802 (alk. paper)
035 $a(OCoLC)34547266
035 $a(OCoLC)ocm34547266
035 $9AMG9011CU
035 $a(NNC)1965409
035 $a1965409
040 $aDLC$cDLC$dDLC$dOrLoB-B
050 00 $aQA564$b.C688 1997
082 00 $a516.3/5$220
100 1 $aCox, David A.$0http://id.loc.gov/authorities/names/n88167261
245 10 $aIdeals, varieties, and algorithms :$ban introduction to computational algebraic geometry and commutative algebra : with 91 illustrations /$cDavid Cox, John Little, Donal O'Shea.
250 $a2nd ed.
260 $aNew York :$bSpringer,$c[1997], ©1997.
300 $axiii, 536 pages :$billustrations ;$c25 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aUndergraduate texts in mathematics
504 $aIncludes bibliographical references (p. 523-526) and index.
505 00 $g1.$tGeometry, Algebra, and Algorithms --$g2.$tGroebner Bases --$g3.$tElimination Theory --$g4.$tThe Algebra-Geometry Dictionary --$g5.$tPolynomial and Rational Functions on a Variety --$g6.$tRobotics and Automatic Geometric Theorem Proving --$g7.$tInvariant Theory of Finite Groups --$g8.$tProjective Algebraic Geometry --$g9.$tThe Dimension of a Variety --$gApp. A.$tSome Concepts from Algebra --$gApp. B.$tPseudocode --$gApp. C.$tComputer Algebra Systems --$gApp. D.$tIndependent Projects.
520 $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?
520 8 $aThe 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.
520 8 $aThe 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 1960s. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century.
520 8 $aThis has changed in recent years, and new algorithms, coupled with the power of fast computers, have led to some interesting applications - for example, in robotics and in geometric theorem proving.
650 0 $aGeometry, Algebraic$xData processing.
650 0 $aCommutative algebra$xData processing.
700 1 $aLittle, John B.$0http://id.loc.gov/authorities/names/n88121494
700 1 $aO'Shea, Donal.$0http://id.loc.gov/authorities/names/n92032739
830 0 $aUndergraduate texts in mathematics.$0http://id.loc.gov/authorities/names/n42025566
852 00 $bmat$hQA564$i.C688 1997