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Computation of the central elements and centralizers of sets of elements in non-commutative polynomial algebras

  • In this thesis we present the implementation of libraries center.lib and perron.lib for the non-commutative extension Plural of the Computer Algebra System Singular. The library center.lib was designed for the computation of elements of the centralizer of a set of elements and the center of a non-commutative polynomial algebra. It also provides solutions to related problems. The library perron.lib contains a procedure for the computation of relations between a set of pairwise commuting polynomials. The thesis comprises the theory behind the libraries, aspects of the implementation and some applications of the developed algorithms. Moreover, we provide extensive benchmarks for the computation of elements of the center. Some of our examples were never computed before.

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Author:Oleksandr Motsak
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16934
Document Type:Diploma Thesis
Language of publication:English
Year of Completion:2006
Year of Publication:2006
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2011/04/11
Tag:Algebraische Abhängigkeit der kommutierende Elementen; Computeralgebra System
Algebraic dependence of commuting elements; Computer Algebra System
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):13-XX COMMUTATIVE RINGS AND ALGEBRAS / 13Pxx Computational aspects and applications [See also 14Qxx, 68W30] / 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
16-XX ASSOCIATIVE RINGS AND ALGEBRAS (For the commutative case, see 13-XX) / 16Sxx Rings and algebras arising under various constructions / 16S30 Universal enveloping algebras of Lie algebras [See mainly 17B35]
16-XX ASSOCIATIVE RINGS AND ALGEBRAS (For the commutative case, see 13-XX) / 16Zxx Computational aspects of associative rings / 16Z05 Computational aspects of associative rings [See also 68W30]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) / 68Wxx Algorithms (For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx) / 68W30 Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011