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An algorithm for constructing the basis of the solution set for systems of linear Diophantine equations over the ring of integers

A polynomial algorithm is proposed to construct the minimal generating set of solutions and the basis of the solution set for systems of linear Diophantine equations over the ring of integer. The algorithm is based on a modified TSS method.

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Correspondence to S. L. Kryvyi.

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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 36–41, November–December 2009.

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Kryvyi, S.L. An algorithm for constructing the basis of the solution set for systems of linear Diophantine equations over the ring of integers. Cybern Syst Anal 45, 875 (2009). https://doi.org/10.1007/s10559-009-9160-y

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  • DOI: https://doi.org/10.1007/s10559-009-9160-y

Keywords

  • ring of integers
  • linear Diophantine equation
  • prebasis
  • basis of a solution set