Extended Quotient-Remainder Theorem on a Polynomial Ring
- Issued Date
- 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 , D. Bini and V. Pan introduced various known polynomial division algorithms(see , , , ), 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
- 제주대학교 대학원
- 대학원 수학과
- 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
- 이정현. (2013). Extended Quotient-Remainder Theorem on a Polynomial Ring
Appears in Collections:
- General Graduate School > Mathematics
- Authorize & License
- Files in This Item:
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.