Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula

摘要

ISSAC 2005 is a continuation of a well-established series ofinternational conferences for the presentation of the latestadvances in the field of Symbolic and Algebraic Computation. Thefirst meeting of the series (1966) was held in Washington, DC, andsponsored by the Association for Computing Machinery (ACM). Sincethen, the abbreviated name of the meeting has evolved from SYMSAM,SYMSAC, EUROSAM, EUROCAL to finally settle on the present nameISSAC. This 30th meeting was hosted by the Key Laboratory ofMathematics Mechanization, Chinese Academy of Sciences, Beijing,China from July 24 to July 27.>The topics of the conference include, but are not limitedto:ulliAlgorithmic mathematics. Algebraic, symbolicand symbolic-numeric algorithms. Simplification, functionmanipulation, equations, summation, integration, ODE/PDE, linearalgebra, number theory, group and geometriccomputing./liliComputer Science. Theoretical andpractical problems in symbolic computation. Systems, problemsolving environments, user interfaces, software, libraries,parallel/distributed computing and programming languages forsymbolic computation, concrete analysis, benchmarking, theoreticaland practical complexity of computer algebra algorithms, automaticdifferentiation, code generation, mathematical data structures andexchange protocols./liliApplications. Problemtreatments using algebraic, symbolic or symbolic-numericcomputation in an essential or a novel way. Engineering, economicsand finance, physical and biological sciences, computer science,logic, mathematics, statistics,education./li/ul>Following tradition, ISSAC 2005 featured invited talks,contributed papers, tutorials, poster sessions, softwareexhibitions, and satellite workshops. This volume contains all thecontributed papers which were presented at the meeting as well asthe abstracts of the invited talks.>The picture on the front cover shows a page from the classicChinese math book bearing the title "Jade Mirrors of Four Elements"by Zhu Shijie, written in 1303 AD during the Yuan Dynasty. In thispage, a system of equations of three unknowns and degree three isreduced to a univariate equation by eliminating variables.