LEADER 03416nam 22005655 450 001 9910254088203321 005 20200706002415.0 010 $a3-319-43601-5 024 7 $a10.1007/978-3-319-43601-2 035 $a(CKB)3710000000872817 035 $a(DE-He213)978-3-319-43601-2 035 $a(MiAaPQ)EBC5587385 035 $a(PPN)195513851 035 $a(EXLCZ)993710000000872817 100 $a20160906d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComputational Linear and Commutative Algebra /$fby Martin Kreuzer, Lorenzo Robbiano 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XVIII, 321 p. 1 illus.) 311 $a3-319-43599-X 320 $aIncludes bibliographical references and index. 327 $aForeword -- Introduction -- 1 Endomorphisms -- 2 Families of Commuting Endomorphisms -- 3 Special Families of Endomorphisms -- 4 Zero-Dimensional Affine Algebras -- 5 Computing Primary and Maximal Components -- 6 Solving Zero-Dimensional Polynomial Systems -- Notation -- References -- Index. 330 $aThis book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations. 606 $aCommutative algebra 606 $aCommutative rings 606 $aMatrix theory 606 $aAlgebra 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aMatrix theory. 615 0$aAlgebra. 615 14$aCommutative Rings and Algebras. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 676 $a512.24 700 $aKreuzer$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut$0730461 702 $aRobbiano$b Lorenzo$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254088203321 996 $aComputational Linear and Commutative Algebra$92044174 997 $aUNINA