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Parallel Square Modular Computer Algebra

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Book cover Parallel Processing and Applied Mathematics (PPAM 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3019))

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Abstract

The computer algebra of parallel modular operations with a square diapason for a variable is described. The base set of the algebra is a finite dimension metric space of modular integer vectors. Two metrics are introduced. An orthogonal normal basis is employed to reconstruct the value of the integer number corresponding to the vector. An analog of the inner product is used to advance beyond the additive range, and the vector product is defined in two ways. The algebra could serve as the basis for parallel computer arithmetic of unbounded digit integers, a theoretical foundation of parallel computing.

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References

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  3. Inutin, S.A.: A Method of an Inverse Element Computation in a Finite Field. In: Scientific Works of the Surgut State University, vol. 1, pp. 102–107. Regional Publishing House, Surgut (1997)

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  4. Inutin, S.A.: A Modular Calculation in the High Computer Diapason. The Electronics 6, 12–17 (2001)

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  5. Inutin, S.A.: Base Algorithms for Multiple Digits Calculations. Regional Publishing House, Surgut (2002)

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Author information

Authors and Affiliations

  1. Surgut State Pedagogic University, 50 Let VLKSM, 10/2, 628413, Surgut, Russia

    Sergey A. Inutin

Authors
  1. Sergey A. Inutin
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Editor information

Editors and Affiliations

  1. Institute of Computational and Information Sciences, Czestochowa University of Technology,  

    Roman Wyrzykowski

  2. Computer Science Department, University of Tennessee, TN 37996-3450, Knoxville, USA

    Jack Dongarra

  3. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marcin Paprzycki

  4. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2004 Springer-Verlag Berlin Heidelberg

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Inutin, S.A. (2004). Parallel Square Modular Computer Algebra. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2003. Lecture Notes in Computer Science, vol 3019. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24669-5_128

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  • DOI: https://doi.org/10.1007/978-3-540-24669-5_128

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21946-0

  • Online ISBN: 978-3-540-24669-5

  • eBook Packages: Springer Book Archive

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