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Non-commutative Computer Algebra with applications: Graded commutative algebra and related structures in Singular with applications (German Edition) - Softcover
Synopsis
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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About the Author
Dr. Oleksandr Motsak was born in Kyiv, Ukraine in 1982. He received his Ph.D. degree from the University of Kaiserslautern, Germany in 2010. Currently he is a Postdoctoral Researcher at the University of Kaiserslautern. His scientific interests include computer science, homological algebra and computer algebra.
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- PublisherSüdwestdeutscher Verlag für Hochschulschriften
- Publication date2011
- ISBN 10 3838127528
- ISBN 13 9783838127521
- BindingPaperback
- LanguageGerman
- Number of pages168
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Non-commutative Computer Algebra with applications
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Südwestdeutscher Verlag Für Hochschulschriften AG Co. KG Jul 2015, 2015
ISBN 10: 3838127528
ISBN 13: 9783838127521
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Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 168 pp. Deutsch. Seller Inventory # 9783838127521
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Non-commutative Computer Algebra with applications : Graded commutative algebra and related structures in Singular with applications
Published by
Südwestdeutscher Verlag Für Hochschulschriften AG Co. KG, 2011
ISBN 10: 3838127528
ISBN 13: 9783838127521
New
Taschenbuch
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Seller Inventory # 9783838127521
Quantity: 1 available
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Non-commutative Computer Algebra with applications
Published by
Südwestdeutscher Verlag für Hochschulschriften, 2011
ISBN 10: 3838127528
ISBN 13: 9783838127521
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Motsak OleksandrDr. Oleksandr Motsak was born in Kyiv, Ukraine in 1982. He received his Ph.D. degree from the University of Kaiserslautern, Germany in 2010. Currently he is a Postdoctoral Researcher at the University of Kaiserslauter. Seller Inventory # 5407065
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Non-commutative Computer Algebra with applications | Graded commutative algebra and related structures in Singular with applications
Published by
Südwestdeutscher Verlag für Hochschulschriften AG Co. KG, 2015
ISBN 10: 3838127528
ISBN 13: 9783838127521
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Taschenbuch. Condition: Neu. Non-commutative Computer Algebra with applications | Graded commutative algebra and related structures in Singular with applications | Oleksandr Motsak | Taschenbuch | Paperback | 168 S. | Deutsch | 2015 | Südwestdeutscher Verlag für Hochschulschriften AG Co. KG | EAN 9783838127521 | Verantwortliche Person für die EU: Südwestdt. Verl. f. Hochschulschrift., Brivibas Gatve 197, 1039 RIGA, LETTLAND, customerservice[at]vdm-vsg[dot]de | Anbieter: preigu. Seller Inventory # 106853312
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