The Cosmic Computer by H. Beam Piper

Forty years ago, when the war between the Earth Federation and the System States Alliance ended, the Federation hastily abandoned their staging base on the planet Poictesme. Ever since, the people of the planet have made do by salvaging old military equipment and earning meagre profits on locally-produced brandy and tobacco. Local legend tells of a military supercomputer named Merlin that had once existed on the planet, and though nobody has ever found a trace of its existence, the rumors have grown to a near religious level of fervour.
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