Complete Solving of Linear Diophantine Equations and Inequations without adding Variables

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 [2] for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher [1] for solving a single linear Diophantine equation. All the nice properties of the algorithm of Contejean and Devie are still satisfied by the new algorithm: it is complete, i.e. provides a (finite) description of the set of solutions, it can be implemented with a bounded stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm.

References

[1]

M. Clausen and A. Fortenbacher. Efficient solution of linear diophantine equations. Journal of Symbolic Computation, 8(1&2):201–216, 1989.

[2]

E. Contejean and H. Devie. An efficient algorithm for solving systems of diophantine equations. Information and Computation, 113(1):143–172, Aug. 1994.

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