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Computational linear and commutative algebra

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Computational linear and commutative algebra/ by Martin Kreuzer, Lorenzo Robbiano.
作者:	Kreuzer, Martin.
其他作者:	Robbiano, Lorenzo.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xviii, 321 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Algebras, Linear. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-43601-2
ISBN:	9783319436012

Computational linear and commutative algebra
Kreuzer, Martin.

Computational linear and commutative algebra[electronic resource] /by Martin Kreuzer, Lorenzo Robbiano. - Cham :Springer International Publishing :2016. - xviii, 321 p. :ill., digital ;24 cm.

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.

ISBN: 9783319436012

Standard No.: 10.1007/978-3-319-43601-2doiSubjects--Topical Terms:

528115
Algebras, Linear.

LC Class. No.: QA184.2

Dewey Class. No.: 512.5

Computational linear and commutative algebra
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300 $a xviii, 321 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a 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.
650 0 $a Algebras, Linear. $3 528115
650 0 $a Commutative algebra. $3 672047
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Commutative Rings and Algebras. $3 672054
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 672090
700 1 $a Robbiano, Lorenzo. $3 672535
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