A new algorithm for division of polynomials
Lee, H.P. and Kumar, K. (eds.)
In Recent Advances in Computational Science and Engineering: Proceedings of the International Conference on Scientific and Engineering Computation (IC-SEC) 2002.
World Scientific. 5 pp, .
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Division of polynomials has fundamental importance in algorithmic algebra, and is commonly encountered in many areas of mathematics as well as in scientific and engineering applications. The existing classical algorithm for polynomial division fails to provide an explicit way of determining the coefficients of the quotient and the remainder. In this paper, I present a new general theorem about division of polynomials, which provides a new and explicit algorithm for division of any two polynomials. A method of expressing a polynomial in polynomials of lower degrees is also obtained, as a corollary of the algorithm
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