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Complete solving of linear Diophantine equations and inequations without adding variables

  • Efficient Constraint Handling
  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming — CP '95 (CP 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 976))

Abstract

In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie [9] for solving linear Diophantine systems of equations, which is itself ageneralization of the algorithm of Fortenbacher [6] for solving a single linearDiophantine equation, All the nice properties of the algorithm of Contejeanand Devie are still satisfied by the new algorithmi it is complete, i.e providesa (finite) description of the set of solutions, it can be implemented with abounded stack, and it admits an incremental version. All of these character-istics enable its easy integration in the CLP paradigm.

This work was partly supported by the European Contract SOL HCM No CHRX CT92 0053

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Author information

Authors and Affiliations

  1. INRIA Lorraine & CRIN, 615 rue du jardin botanique, BP 101, 54602, Villers-lès-Nancy Cedex, France

    Farid Ajili

  2. Centre d'Orsay, LRI, CNRS URA 410 Bât 490, Université Paris-Sud, 91405, Orsay Cedex, France

    Evelyne Contejean

Authors
  1. Farid Ajili
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  2. Evelyne Contejean
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Editor information

Ugo Montanari Francesca Rossi

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© 1995 Springer-Verlag Berlin Heidelberg

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Ajili, F., Contejean, E. (1995). Complete solving of linear Diophantine equations and inequations without adding variables. In: Montanari, U., Rossi, F. (eds) Principles and Practice of Constraint Programming — CP '95. CP 1995. Lecture Notes in Computer Science, vol 976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60299-2_1

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  • DOI: https://doi.org/10.1007/3-540-60299-2_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60299-6

  • Online ISBN: 978-3-540-44788-7

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