Abstract
We describe through an algebraic and geometrical study, a new method for solving systems of linear diophantine equations. This approach yields an algorithm which is intrinsically parallel. In addition to the algorithm, we give a geometrical interpretation of the satisfiability of an homogeneous system, as well as upper bounds on height and length of all minimal solutions of such a system. We also show how our results apply to inhomogeneous systems yielding necessary conditions for satisfiability and upper bounds on the minimal solutions.
This work was partly supported by the GRECO de programmation (CNRS)
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Domenjoud, E. (1991). Solving systems of linear diophantine equations: An algebraic approach. In: Tarlecki, A. (eds) Mathematical Foundations of Computer Science 1991. MFCS 1991. Lecture Notes in Computer Science, vol 520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54345-7_57
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DOI: https://doi.org/10.1007/3-540-54345-7_57
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