Finding minimal polynomials of algebraic numbers of the form tan<sup>2</sup>(π/n) using Tschirnhausen’s transform

dc.contributor.author	Galyautdinov I.
dc.contributor.author	Lavrentyeva E.
dc.date.accessioned	2018-09-19T22:09:51Z
dc.date.available	2018-09-19T22:09:51Z
dc.date.issued	2016
dc.identifier.issn	1995-0802
dc.identifier.uri	https://dspace.kpfu.ru/xmlui/handle/net/144789
dc.description.abstract	© 2016, Pleiades Publishing, Ltd.Solutions of two problems are proposed based on the Tschirnhausen transform. The first problem is connected with the construction of minimal polynomials of the numbers of the form tan2(π/n) by means of the Tschirnhausen transform for all natural n > 2. The second problem consists in finding the exact roots of the equation x3 − 7x − 7 = 0. A solution of the problem is obtained from the fact that the roots of the equation produce the cyclotomic field Q7. Examples of construction of minimal polynomials are provided.
dc.relation.ispartofseries	Lobachevskii Journal of Mathematics
dc.subject	algebraic numbers
dc.subject	cyclotomic fields and their subfileds
dc.subject	minimal polynomials
dc.subject	Tschirnhausen transform
dc.title	Finding minimal polynomials of algebraic numbers of the form tan<sup>2</sup>(π/n) using Tschirnhausen’s transform
dc.type	Article
dc.relation.ispartofseries-issue	3
dc.relation.ispartofseries-volume	37
dc.collection	Публикации сотрудников КФУ
dc.relation.startpage	342
dc.source.id	SCOPUS19950802-2016-37-3-SID84971613845

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