Stam’s Identities Collection: A Case Study for Math Knowledge Bases

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9725)

Abstract

In the frame of the work of the Working Group “Global Digital Mathematical Library”, Jim Pitman proposed Aart Stam’s collection of combinatorial identities as a benchmark for “digitizing” mathematical knowledge. This collection seems to be a challenge for “digitization” because of its size (1300 pages in a .pdf file) and because of the fact that, for the most part, it is hand-written. However, after an in-depth analysis, it turns out that the real challenges are of mathematical and logical nature. In this talk we discuss what digitization of such a piece of mathematics means and report on various tools that may help in this endeavor. The tools range from technical tools for typing formulae all the way to sophisticated algebraic and reasoning algorithms. The experiments for applying these tools to Stam’s collection are currently carried out by two of the working groups at RISC.

References

  1. Buchberger, B., Lichtenberger, F.: Mathematics for Computer Scientists. Springer, Heidelberg (1980). (in German)Google Scholar
  2. Buchberger, B., Mathe is meta. In: Invited Talk at the Summer School “Summation, Integration and Special Functions in Quantum Field Theory”, 9–13 July. RISC. Johannes Kepler University, Castle of Hagenberg, Austria (2012)Google Scholar
  3. Kauers, M., Paule, P.: The Concrete Tetrahedron. Texts and Monographs in Symbolic Computation. Springer, Vienna (2011)CrossRefMATHGoogle Scholar
  4. Maletzky, A.: Formalization of Gröbner Bases Theory in Theorema (working title). Ph.D. thesis, July 2016, to appearGoogle Scholar
  5. Pitman, J.: Personal Communcation to the Working Group “Global Digital Math Library”, December 2015Google Scholar
  6. Risch, R.H.: The problem of integration in finite terms. Trans. Am. Math. Soc. 139, 167–189 (1969)MathSciNetCrossRefMATHGoogle Scholar
  7. Stam, A.: Binomial Identities with Old-fashioned Proofs, Manuscript, University of Groningen (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Research Institute for Symbolic Computation (RISC)Johannes Kepler UniversityLinzAustria

Personalised recommendations