Abstract
Given a system gs of linear diophantine equations and inequations of the form Li#i Mi, i=I, ⋯, n, where #i ∈ {=,<,>,≠,≥,≤} we compute a finite set S of numerical and parametric solutions describing the set of all the solutions of gs (i.e. its general solution). Our representation of the general solution gives direct and simple functions generating the set of all the solutions: this is obtained by giving all the nonnegative natural values to the integer variables of the right hand-side of the parametric solutions, without any linear combination. In particular, unlike the usual representation based on minimal solutions, our representation of the general solution is nonambiguous: given any solution s of gs, it can be deduced from a unique numerical or parametric solution of S.
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Abdulrab, H., Maksimenko, M. (1995). General solution of systems of linear diophantine equations and inequations. In: Hsiang, J. (eds) Rewriting Techniques and Applications. RTA 1995. Lecture Notes in Computer Science, vol 914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59200-8_68
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DOI: https://doi.org/10.1007/3-540-59200-8_68
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