Avoiding slack variables in the solving of linear diophantine equations and inequations

Farid Ajili, Evelyne Contejean
1997 Theoretical Computer Science  
In this paper, we present an algorithm for solving &ire& 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 (1994) for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher (Clausen and Fortenbacher, 1989) for solving a single linear Diophantine equation. All
more » ... he 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 hounded stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm.
doi:10.1016/s0304-3975(96)00195-8 fatcat:4jaelx75ozabpj24i5qwzohqem