Postdoctoral Associate in Experimental Symbolic Computation

小行星9405068 要进行的研究是在一般领域的算法集成有限项（即不确定或符号集成），特别强调的发展和实施的算法，涉及特殊功能。 在过去的几十年里，在有限项积分算法方面取得了实质性的进展。 里施的工作达到高潮超过一个世纪的工作整合的基本职能。 几乎立即注意力转向涉及更大类的功能，包括特殊功能的集成。 第一个真实的进步，在这方面是延长刘维定理一类特殊职能的辛格，桑德斯和Caviness后，樱桃和诺尔斯开发的算法集成integands包含错误的功能和对数积分的条款。 然而，这项工作并没有涵盖在许多应用中出现的重要功能和相关功能。 Baddoura的工作提供了一个优雅的方式来整合方面的双对数。 本项目将继续这一研究方向。 的总体目标是实现所获得的算法，并改善和扩大其范围的集成和各种特殊功能。 ***

9405068 Caviness The research to be carried out is in the general area of algorithms for integration in finite terms (that is, indefinite or symbolic integration) with particular emphasis on the development and implementation of algorithms involving special functions. In the last few decades substantial progress has been made on algorithms for integration in finite terms. Risch's work culminated more than a century of work on integration of elementary functions. Almost immediately attention turned to integration involving larger classes of functions including special functions. The first real advance in this area was the extension of the Liouville theorem for a class of special functions by Singer, Saunders, and Caviness upon which Cherry and Knowles developed algorithms for integrating integrands containing error functions and logarithmic integrals in terms of such. This work however did not cover the important dilogarithms and associated functions that occur in many applications. Baddoura's work has given an elegant way to integrate in terms of the dilogarithm. This project will continue this line of research. The overall objective is to implement the algorithms obtained and to improve and extend their scope for integration of and in terms of various special functions. ***