Parameterization of nice polynomials

Parameterization of nice polynomials

A univariable polynomial p(x) is said to be nice if all of its coefficients as well as all of the roots of both p(x) and its derivative p0(x) are integers. p(x) is called Q-nice polynomial if the coefficients, roots, and critical points are rational numbers. This research concentrates on findi...

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Main Author: Anton, Hozjee
Format: Thesis
Language:English
Published: 2018
Subjects:
Polynomials
Number theory
Online Access:http://psasir.upm.edu.my/id/eprint/77123/1/IPM%202018%2015%20-%20IR.pdf
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spelling my-upm-ir.771232020-02-07T07:25:19Z Parameterization of nice polynomials 2018-07 Anton, Hozjee A univariable polynomial p(x) is said to be nice if all of its coefficients as well as all of the roots of both p(x) and its derivative p0(x) are integers. p(x) is called Q-nice polynomial if the coefficients, roots, and critical points are rational numbers. This research concentrates on finding parameterized families of symmetric polynomial with four, five, and seven roots. The relations between the roots and critical points of polynomials with four, five, and seven roots are considered respectively. By using the technique of parameterization and substitution, the pattern of solutions of the polynomials in the field of integer, rational, and Q(px) are observed. Then, based on the pattern of solutions, theorems will be constructed. Parameterized families of symmetric polynomials with four and five roots in the field of integral and rational numbers are obtained. Meanwhile, the roots and critical points for symmetric polynomials with seven roots are studied in the field of Q(px). Hence, parameterized families of symmetric polynomials with seven roots are found. Polynomials Number theory Geometry, Algebraic 2018-07 Thesis http://psasir.upm.edu.my/id/eprint/77123/ http://psasir.upm.edu.my/id/eprint/77123/1/IPM%202018%2015%20-%20IR.pdf text en public masters Universiti Putra Malaysia Polynomials Number theory Geometry, Algebraic Sapar, Siti Hasana
institution Universiti Putra Malaysia
collection PSAS Institutional Repository
language English
advisor Sapar, Siti Hasana
topic Polynomials
Number theory
Polynomials
spellingShingle Polynomials
Number theory
Polynomials
Anton, Hozjee
Parameterization of nice polynomials
description A univariable polynomial p(x) is said to be nice if all of its coefficients as well as all of the roots of both p(x) and its derivative p0(x) are integers. p(x) is called Q-nice polynomial if the coefficients, roots, and critical points are rational numbers. This research concentrates on finding parameterized families of symmetric polynomial with four, five, and seven roots. The relations between the roots and critical points of polynomials with four, five, and seven roots are considered respectively. By using the technique of parameterization and substitution, the pattern of solutions of the polynomials in the field of integer, rational, and Q(px) are observed. Then, based on the pattern of solutions, theorems will be constructed. Parameterized families of symmetric polynomials with four and five roots in the field of integral and rational numbers are obtained. Meanwhile, the roots and critical points for symmetric polynomials with seven roots are studied in the field of Q(px). Hence, parameterized families of symmetric polynomials with seven roots are found.
format Thesis
qualification_level Master's degree
author Anton, Hozjee
author_facet Anton, Hozjee
author_sort Anton, Hozjee
title Parameterization of nice polynomials
title_short Parameterization of nice polynomials
title_full Parameterization of nice polynomials
title_fullStr Parameterization of nice polynomials
title_full_unstemmed Parameterization of nice polynomials
title_sort parameterization of nice polynomials
granting_institution Universiti Putra Malaysia
publishDate 2018
url http://psasir.upm.edu.my/id/eprint/77123/1/IPM%202018%2015%20-%20IR.pdf
_version_ 1747813204760723456

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