An algorithm for solving a diophantine equation with lower and upper bounds on the variables
نویسندگان
چکیده
We develop an algorithm for solving a diophantine equation with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction, and rst nds short vectors satisfying the diophantine equation. The next step is to branch on linear combinations of these vectors, which either yields a vector that satis es the bound constraints or provides a proof that no such vector exists. The research was motivated by the need for solving constrained diophantine equations as subproblems when designing integrated circuits for video signal processing. Our algorithm is tested with good result on real-life data. Subject classi cation: Primary: 90C10. Secondary: 45F05, 11Y50.
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