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Könyv Non-commutative Computer Algebra with applications Oleksandr Motsak

Non-commutative Computer Algebra with applications

Szerző: Oleksandr Motsak
Nyelv: Német
Kötés: Puha kötésű
Kiadó: Sudwestdeutscher Verlag Fur Hochschulschriften AG
Elérhetőség: Beszállítói készleten
Küldés 5-8 napon belül
26 671 Ft
This book that represents the author's Ph.D. thesis is devoted to constructive module theory of poly...

Információk a könyvről

Szerző
Oleksandr Motsak
Nyelv
Német
Kötés
Könyv - Puha kötésű
Kiadva
2011
oldal
168
EAN
9783838127521
ISBN
3838127528
Enbook ID
06957582
Kiadó
Sudwestdeutscher Verlag Fur Hochschulschriften AG
Súly
254
Méretek
152 x 229 x 10

Teljes leírás

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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