### Decomposition of ordinary difference polynomials

Mingbo Zhang, Xiao-Shan Gao
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
In this paper, we present a complete algorithm to decompose nonlinear differential polynomials in one variable and with coefficients in a computable differential field K of characteristic zero. The algorithm provides an efficient reduction of the problem to the factorization of LODOs over the same coefficient field. Besides arithmetic operations, the algorithm needs decomposition of algebraic polynomials, factorization of multi-variable polynomials, and solution of algebraic linear equation
more &raquo; ... ems. The algorithm is implemented in Maple for the constant field case. The program can be used to decompose differential polynomials with thousands of terms effectively. Keywords Decomposition · Differential polynomial · Pseudo linear differential polynomial · Differential degree Introduction The study on functional decomposition algorithms started with the decomposition of univariate polynomials. The first algorithm to find decompositions of polynomials was presented by and Alagar-Tanh [1]. This was soon followed by the work of Kozen and Landau [17] who proposed a polynomial time decomposition algorithm. Gutierrez et al. gave an almost quadratic complexity decomposition
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jsc.2009.04.001">doi:10.1016/j.jsc.2009.04.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5rpquxk4mvdpxhmga5xs26alla">fatcat:5rpquxk4mvdpxhmga5xs26alla</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190204032239/http://www.mmrc.iss.ac.cn:80/~xgao/paper/08-aaecc.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c1/46/c1461022bdb98368ee21ad74d72a6af6811418ef.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jsc.2009.04.001"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>