Determining the minimal polynomial of cos(2\pi/n) over Q with Maple


Özgür B., YURTTAŞ A. , CANGÜL İ. N.

FRONTIERS OF FUNDAMENTAL AND COMPUTATIONAL PHYSICS, vol.1479, pp.368-370, 2012 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 1479
  • Publication Date: 2012
  • Doi Number: 10.1063/1.4756140
  • Title of Journal : FRONTIERS OF FUNDAMENTAL AND COMPUTATIONAL PHYSICS
  • Page Numbers: pp.368-370

Abstract

The number lambda(q) = 2cos pi/q, q is an element of N, q >= 3, appears in the study of Hecke groups which are Fuchsian groups, and in the study of regular polyhedra. There are many results about the minimal polynomial of this algebraic number and in some of these methods, the minimal polynomials of several algebraic numbers are used. Here we obtain the minimal polynomial of one of those numbers, cos(2 pi/n), over the field of rationals by means of the better known Chebycheff polynomials for odd q and give some of their properties. We calculated this minimal polynomial for n is an element of N by using the Maple language and classifying the numbers n is an element of N into different classes.