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On the uniform representation of mathematical data structures

  • Carla Limongelli
  • Marco Temperini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 722)

Abstract

Topics about the integration of the numeric and symbolic computation paradigms are discussed. Mainly an approach through a uniform representation of numbers and symbols is presented, that allows for the application of algebraic algorithms to numeric problems. The p-adic construction is the basis of the unifying representation environment. An integrated version of the Hensel algorithm is presented, which is able to perform symbolic and numeric computations over instances of ground (concrete) and parametric structures, and symbolic computations over instances of abstract structures. Examples are provided to show how the approach outlined and the proposed implementation can treat both cases of symbolic and numeric computations. In the numeric case it is shown that the proposed extension of the Hensel Algorithm can allow for the exact manipulation of numbers. Moreover, such an extension avoids the use of simplification algorithms, since the computed results are already in simplified form.

Keywords

Symbolic Computation Diophantine Equation Abstract Structure Numeric Operation Uniform Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Carla Limongelli
    • 1
  • Marco Temperini
    • 1
  1. 1.Dipartimento Informatica e SistemisticaUniversità “La Sapienza”RomaItaly

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