\(h\)-Adic Polynomials and Partial Fraction Decomposition of Proper Rational Functions over \(\mathbb{R}\) or \(\mathbb{C}\)

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 $\mathbb{R}$ or $\mathbb{C}$. The method is based on a recursive computation of the $h$-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.