Parametric families of polynomials : construction and applications

• Main Author: Lavallee, Melisa Jean
• Language: English
• Published: University of British Columbia 2013
• Online Access: http://hdl.handle.net/2429/44655

The focus of this thesis is on the study of parametric families of polynomials and in particular, their construction and applications. A method in constructing a family of parametric sextic trinomials defining sextic fields containing any cubic subfield is presented. We then show two applications of our parametrization to obtain already established parameterizations of sextic trinomials defining sextic fields containing either a cyclic or pure cubic subfield. We then present three chapters illustrating the applications obtained from a parametric family of polynomials. Two such chapters illustrate that such families may yield an infinite number of monogenic fields. The other illustrates that such families may yield an infinite number of intersective polynomials.