LEADER 03849nam 22006732 450 001 9910786041303321 005 20151005020621.0 010 $a1-107-23864-1 010 $a1-139-56576-1 010 $a1-107-25588-0 010 $a1-107-30195-5 010 $a1-107-30704-X 010 $a1-107-31259-0 010 $a1-299-00635-3 010 $a1-107-31479-8 010 $a1-107-30924-7 035 $a(CKB)2670000000327068 035 $a(EBL)1113118 035 $a(OCoLC)827210294 035 $a(SSID)ssj0000850078 035 $a(PQKBManifestationID)11531579 035 $a(PQKBTitleCode)TC0000850078 035 $a(PQKBWorkID)10825034 035 $a(PQKB)11609607 035 $a(UkCbUP)CR9781139565769 035 $a(Au-PeEL)EBL1113118 035 $a(CaPaEBR)ebr10649565 035 $a(CaONFJC)MIL431885 035 $a(MiAaPQ)EBC1113118 035 $a(PPN)261277367 035 $a(EXLCZ)992670000000327068 100 $a20141103d2013|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA first course in computational algebraic geometry /$fWolfram Decker and Gerhard Pfister ; with pictures by Oliver Labs$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2013. 215 $a1 online resource (viii, 118 pages) $cdigital, PDF file(s) 225 1 $aAIMS library series 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 320 $aIncludes bibliographical references and index. 327 $aCover; Contents; Preface; Prologue: General Remarks on Computer Algebra Systems; 1 The Geometry-Algebra Dictionary; 1.1 Affine Algebraic Geometry; 1.1.1 Ideals in Polynomial Rings; 1.1.2 Affine Algebraic Sets; 1.1.3 Hilbert's Nullstellensatz; 1.1.4 Irreducible Algebraic Sets; 1.1.5 Removing Algebraic Sets; 1.1.6 Polynomial Maps; 1.1.7 The Geometry of Elimination; 1.1.8 Noether Normalization and Dimension; 1.1.9 Local Studies; 1.2 Projective Algebraic Geometry; 1.2.1 The Projective Space; 1.2.2 Projective Algebraic Sets; 1.2.3 Affine Charts and the Projective Closure 327 $a1.2.4 The Hilbert Polynomial2 Computing; 2.1 Standard Bases and Singular; 2.2 Applications; 2.2.1 Ideal Membership; 2.2.2 Elimination; 2.2.3 Radical Membership; 2.2.4 Ideal Intersections; 2.2.5 Ideal Quotients; 2.2.6 Kernel of a Ring Map; 2.2.7 Integrality Criterion; 2.2.8 Noether Normalization; 2.2.9 Subalgebra Membership; 2.2.10 Homogenization; 2.3 Dimension and the Hilbert Function; 2.4 Primary Decomposition and Radicals; 2.5 Buchberger's Algorithm and Field Extensions; 3 Sudoku; 4 A Problem in Group Theory Solved by Computer Algebra; 4.1 Finite Groups and Thompson's Theorem 327 $a4.2 Characterization of Finite Solvable GroupsBibliography; Index 330 $aA First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments. 410 0$aAIMS library series. 606 $aGeometry, Algebraic$xData processing$vTextbooks 615 0$aGeometry, Algebraic$xData processing 676 $a516.3/5 700 $aDecker$b W.$01479266 702 $aPfister$b Gerhard 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910786041303321 996 $aA first course in computational algebraic geometry$93695312 997 $aUNINA