Polynomials Generating Maximal Real Subfields of Circular Fields

Abstract

We have constructed recurrence formulas for polynomials qn(x) ɕ Q[x], any root of which generates the maximal real subfield of circular field K2n. It has been shown that all real subfields of fixed field K2n can be described by using polynomial qn(x) and its Galois group. Furthermore, a methodology has been developed for presentation of square radical d1/2, d ɕ N, d > 1 in the form of a polynomial with rational coefficients relative to 2cos(π/n) at the corresponding n. The theoretical results have been verified by a number of examples.

Keywords

• algebraic number
• minimal polynomial
• circular fields and their subfields
• Galois group