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Avoiding slack variables in the solving of linear diophantine equations and inequations. (English) Zbl 0903.11033
Summary: The authors present an algorithm for solving directly linear diophantine systems of both equations and inequalities. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to E. Contejean and H. Devie [Inf. Comput. 113, 143-172 (1994; Zbl 0809.11015)] for solving linear diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher [M. Clausen and A. Fortenbacher, J. Symb. Comput. 8, No. 1/2, 201-216 (1989; Zbl 0674.10011)] 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.

MSC:
11Y50 Computer solution of Diophantine equations
11D04 Linear Diophantine equations
68W30 Symbolic computation and algebraic computation
11D75 Diophantine inequalities
68N17 Logic programming
90C05 Linear programming
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