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Symbolic Summation of Polynomials in Linear Space and Quadratic Time

  • Conference paper
International Symposium on Distributed Computing and Artificial Intelligence 2008 (DCAI 2008)

Part of the book series: Advances in Soft Computing ((AINSC,volume 50))

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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.

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References

  1. Fasenmyer, S.M.C.: Some generalized hypergeometric polynomials. PhD thesis, University of Michigan (1945)

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  2. Gosper Jr., R.W.: Indefinite hypergeometric sums in macsyma. In: Proceedings of the MACSYMA User’s Conference Berkeley, pp. 237–251 (1977)

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  3. Graham, R., Knuth, D., Patashnik, O.: Concrete mathematics. Addison-Wesley, Reading (1989)

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  4. Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press and McGraw-Hill (2001)

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Author information

Authors and Affiliations

  1. CINVESTAV-Tamaulipas, Cd. Victoria, Tamaulipas, México

    Jose Torres-Jimenez & Nelson Rangel-Valdez

  2. Tecnológico de Cd. Madero, Cd. Madero, Tamaulipas, México

    Laura Cruz

Authors
  1. Jose Torres-Jimenez
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  2. Laura Cruz
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  3. Nelson Rangel-Valdez
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Editor information

Juan M. Corchado Sara Rodríguez James Llinas José M. Molina

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© 2009 Springer-Verlag Berlin Heidelberg

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Torres-Jimenez, J., Cruz, L., Rangel-Valdez, N. (2009). Symbolic Summation of Polynomials in Linear Space and Quadratic Time. In: Corchado, J.M., Rodríguez, S., Llinas, J., Molina, J.M. (eds) International Symposium on Distributed Computing and Artificial Intelligence 2008 (DCAI 2008). Advances in Soft Computing, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85863-8_77

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  • DOI: https://doi.org/10.1007/978-3-540-85863-8_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85862-1

  • Online ISBN: 978-3-540-85863-8

  • eBook Packages: EngineeringEngineering (R0)

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