Non-commutative Computer Algebra with applications

Name: Non-commutative Computer Algebra with applications
Brand: Sudwestdeutscher Verlag Fur Hochschulschriften AG
SKU: 9783838127521
Price: 73.12 EUR
Availability: InStock

Автор: Oleksandr Motsak

Език:

Корици: С меки корици

Издател: Sudwestdeutscher Verlag Fur Hochschulschriften AG

Наличност: Външен склад

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73.12 € 143.01 лв

This book that represents the author's Ph.D. thesis is devoted to constructive module theory of poly...

Информация за книгата

Автор

Oleksandr Motsak

Език

Немски език

Корици

Книга - С меки корици

Издадена

2011

страници

168

EAN

9783838127521

ISBN

3838127528

Enbook ID

06957582

Издател

Sudwestdeutscher Verlag Fur Hochschulschriften AG

Теглоt

254

Размери

152 x 229 x 10

Пълно описание

This book that represents the author's Ph.D. thesis is devoted to constructive module theory of polynomial graded commutative algebras over a field. It treats the theory of Gröbner bases, standard bases (SB) and syzygies as well as algorithms and their implementations over graded commutative algebras, which naturally unify exterior and commutative polynomial algebras. They are graded non-commutative, associative unital algebras over fields and may contain zero-divisors. In this book we try to make the most use out of a-priori knowledge about their characteristic (super-commutative) structure in developing direct symbolic methods, algorithms and implementations, which are intrinsic to these algebras and practically efficient. We also tackle their central localizations by generalizing a variation of Mora algorithm. In this setting we prove a generalized Buchberger's criterion, which shows that syzygies of leading terms play the utmost important role in SB and syzygy computations. We develop a variation of the La Scala-Stillman free resolution algorithm. Benchmarks show that our new algorithms and implementation are efficient. We give some applications of the developed framework.

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Non-commutative Computer Algebra with applications

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