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International Journal of Mathematics and Mathematical Sciences
Volume 2018, Article ID 7495964, 6 pages
https://doi.org/10.1155/2018/7495964
Research Article

-Adic Polynomials and Partial Fraction Decomposition of Proper Rational Functions over or

1Departments of Mathematics and Computer Science, Queensborough Community College, 222-05 56th Avenue, Bayside, NY 11364, USA
2Zicklin School of Business, Baruch College, One Bernard Baruch Way, New York, NY 10010, USA

Correspondence should be addressed to Kwang Hyun Kim; ude.ynuc.ccq@mikk

Received 15 October 2017; Accepted 20 February 2018; Published 2 April 2018

Academic Editor: Adolfo Ballester-Bolinches

Copyright © 2018 Kwang Hyun Kim and Xin Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The partial fraction decomposition technique is very useful in many areas including mathematics and engineering. In this paper we present a new and simple method on the partial fraction decomposition of proper rational functions which have completely factored denominators over or . The method is based on a recursive computation of the -adic polynomial in commutative algebra which is a generalization of the Taylor polynomial. Since its computation requires only simple algebraic operations, it does not require a computer algebra system to be programmed.