Titlebook: Computational Linear and Commutative Algebra; Martin Kreuzer,Lorenzo Robbiano Textbook 2016 Springer International Publishing Switzerland

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并排上下

https://doi.org/10.1007/978-3-8350-9596-0e are mainly interested in .-rational solutions, we can use an algorithm to find all 1-dimensional joint eigenspaces of the multiplication family: the eigenvalue method, or the eigenvector method. In general, if the base field . is finite, we can still obtain good results by using the techniques of

斷斷續(xù)續(xù)

Endomorphisms,cal theory of eigenvalues and eigenspaces by defining eigenspaces and generalized eigenspaces with respect to every eigenfactor of ., i.e. every irreducible factor of the minimal polynomial. A?further important notion is that of a commendable endomorphism . which is defined by the condition that its

FLASK

Families of Commuting Endomorphisms,tive subalgebra of the ring of the .-endomorphisms of .. Given an ideal . in??, the kernel of . is the intersection of the kernels of all endomorphisms in .. Now it turns out that the joint eigenspaces of ? are precisely the kernels of its maximal ideals, and . is the direct sum of the joint general

高興一回

ENACT

Zero-Dimensional Affine Algebras,zero-dimensional affine algebra . over a field ., the multiplication endomorphisms define a commuting family ?, called the multiplication family. Via the natural isomorphism between . and ?, we get a number of interesting connections: the joint generalized eigenspaces of ? are the local factors of .

打谷工具

Computing Primary and Maximal Components,examine various methods for computing the primary and maximal components of . in the fifth chapter. In addition to the generic approach, i.e., the approach using a generic linear form to get a splitting endomorphism, we use random linear forms, the power of the Frobenius endomorphism over finite bas

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Fermentation

Textbook 2016mensional 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

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