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Symbolic Summation of Polynomials in Linear Space and Quadratic Time

  • Jose Torres-Jimenez
  • Laura Cruz
  • Nelson Rangel-Valdez
Part of the Advances in Soft Computing book series (AINSC, volume 50)

Summary

Artificial Intelligence (AI) is the core of many current technologies with diverse applications like: a) systems that understand the spoken languages; b) intelligent tutors that assist in the process of learning new concepts; c) systems that detect patterns in huge amounts of data; etc. Also AI has originated many spin-off technologies that are seen as part of our daily lives, v.gr. a) the mouse; b) symbolic programming languages; c) symbolic computation systems like Macsyma. This work is related to the field of symbolic computation, specifically we present an optimized algorithm that is able to compute symbolic summation of polynomials. The algorithm is based on the solution of a system of simultaneous equations that delivers the coefficients of the resulting polynomial.

Keywords

Symbolic Summation Algorithm Analysis 

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References

  1. 1.
    Fasenmyer, S.M.C.: Some generalized hypergeometric polynomials. PhD thesis, University of Michigan (1945)Google Scholar
  2. 2.
    Gosper Jr., R.W.: Indefinite hypergeometric sums in macsyma. In: Proceedings of the MACSYMA User’s Conference Berkeley, pp. 237–251 (1977)Google Scholar
  3. 3.
    Graham, R., Knuth, D., Patashnik, O.: Concrete mathematics. Addison-Wesley, Reading (1989)zbMATHGoogle Scholar
  4. 4.
    Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press and McGraw-Hill (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jose Torres-Jimenez
    • 1
  • Laura Cruz
    • 2
  • Nelson Rangel-Valdez
    • 1
  1. 1.CINVESTAV-TamaulipasCd. VictoriaMéxico
  2. 2.Tecnológico de Cd. MaderoCd. MaderoMéxico

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