제주대학교 Repository

Extended Quotient-Remainder Theorem on a Polynomial Ring

Metadata Downloads
Author(s)
이정현
Issued Date
2013
URI
http://dcoll.jejunu.ac.kr/jsp/common/DcLoOrgPer.jsp?sItemId=000000006271
Abstract
There have been many researches on the polynomial division. With the fast development of computer calculation, the classical problem of a polynomial division with a remainder has been changed to find fast algorithms to computing the coefficients of the quotients and of remainder on the division of by , . In [3], D. Bini and V. Pan introduced various known polynomial division algorithms(see [2], [4], [5], [8]), and compared them with their new algorithm. From these algorithms, we obtain motivation to consider extended division algorithm of polynomials with related to the remainder theorem.
In this thesis, we shall be interested in the dividing by of degree higher than 1. Moreover, we use the determinant of coefficient matrix to obtain extended quotient and remainder theorems in a polynomial ring. The main theorem is the following.
Extended Quotient-Remainder Theorem :
If are all distinct, and we divide by
, then we obtain quotient
and remainder
where .
Affiliation
제주대학교 대학원
Department
대학원 수학과
Advisor
Seok Zun Song
Awarded Date
2013. 2
Table Of Contents
Ⅰ.Introduction and Preliminaries 1
Ⅱ.The remainder on dividing by 7
Ⅲ.The quotient on dividing by 15
Ⅳ.The remainders on dividing by the factors of 20
Ⅴ.Extended Quotient-Remainder Theorem 24
Ⅵ.References 27
Degree
Master
Publisher
제주대학교
Citation
이정현. (2013). Extended Quotient-Remainder Theorem on a Polynomial Ring
Type
Dissertation
Appears in Collections:
General Graduate School > Mathematics
Authorize & License
  • AuthorizeOpen
Files in This Item:

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.