A REDUCE program for the integration of differential polynomials

Abstract A differential polynomial F[u] is a polynomial expression of the derivatives of the function u(x). A REDUCE program for the integration of differential polynomials is given. The program is tested on the computation of the conserved densities of polynomial evolution equations. Input and output from the test runs are included in the library files. Title of program: INTEG Catalogue Id: ACJG_v1_0 Nature of problem The study of the conserved densities and symmetries of polynomial evolution equations leads to the integration of polynomial expressions of the derivatives of certain functions. Actually differential polynomials have a unique decomposition as "total derivatives" and "functional differential monomials" and integration means finding this decomposition. This cannot be acheived with the standard packages of symbolic programming languages. Versions of this program held in the CPC repository in Mendeley Data ACJG_v1_0; INTEG; 10.1016/0010-4655(92)90013-O This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 微分多项式（differential polynomial）F[u]是函数u(x)各阶导数构成的多项式表达式。本文给出了一款用于微分多项式积分的REDUCE程序。该程序已针对多项式演化方程（polynomial evolution equations）的守恒密度（conserved densities）计算任务进行了测试，测试运行的输入与输出文件已收录至程序库文件中。 程序名称：INTEG 目录编号：ACJG_v1_0 问题本质 对多项式演化方程的守恒密度与对称性开展研究，最终会归约为对特定函数导数构成的多项式表达式进行积分。实际上，微分多项式可唯一分解为“全导数（total derivatives）”与“泛函微分单项式（functional differential monomials）”两类形式，积分过程即指求解该分解式。符号编程语言（symbolic programming languages）的标准程序包无法完成此类任务。 本程序在Mendeley数据平台的CPC程序库中留存的版本信息为：ACJG_v1_0; INTEG; 10.1016/0010-4655(92)90013-O 本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2019）