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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.
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