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Computing Square Roots in Quaternion Algebras

Computing square roots in quaternion algebras
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 27 Oct 2023Embargo end date: 01 Jan 2023 English Publisher:SAGE PublicationsJournal:Fundamenta Informaticae, volume 190, pages 1-15 (issn: 0169-2968, eissn: 1875-8681, Copyright policy )
Authors: Przemyslaw Koprowski;

doi: 10.3233/fi-222163 , 10.48550/arxiv.2301.00743

arXiv: 2301.00743

Computing Square Roots in Quaternion Algebras

Abstract

We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.

Related Organizations
Keywords

Computer Science - Symbolic Computation, FOS: Computer and information sciences, global fields, Algebraic number theory computations, Mathematics - Rings and Algebras, Symbolic Computation (cs.SC), number fields, I.1.2, 68W30, 11Y40, 11R52, Rings and Algebras (math.RA), square root computation, FOS: Mathematics, quaternion algebra, Quaternion and other division algebras: arithmetic, zeta functions, Number-theoretic algorithms; complexity

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    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 1
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
bronze