03416nam 22005655 450 991025408820332120200706002415.03-319-43601-510.1007/978-3-319-43601-2(CKB)3710000000872817(DE-He213)978-3-319-43601-2(MiAaPQ)EBC5587385(PPN)195513851(EXLCZ)99371000000087281720160906d2016 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierComputational Linear and Commutative Algebra /by Martin Kreuzer, Lorenzo Robbiano1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XVIII, 321 p. 1 illus.) 3-319-43599-X Includes bibliographical references and index.Foreword -- 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.This 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.Commutative algebraCommutative ringsMatrix theoryAlgebraCommutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Commutative algebra.Commutative rings.Matrix theory.Algebra.Commutative Rings and Algebras.Linear and Multilinear Algebras, Matrix Theory.512.24Kreuzer Martinauthttp://id.loc.gov/vocabulary/relators/aut730461Robbiano Lorenzoauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254088203321Computational Linear and Commutative Algebra2044174UNINA