Computational Linear and Commutative Algebra

Martin Kreuzer and Lorenzo Robbiano

Springer Int. Publ., Cham 2016

Fields: Symbolic Computation; Linear Algebra; Computer Algebra; Computational Mathematics; Commutative Algebra Keywords: Commuting endomorphisms, generalized eigenspace, multiplication map, zero-dimensional ring, primary decomposition, polynomial system


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Computational Linear and Commutative Algebra 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 Millenium, 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 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.