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Wearing a ring of slow digestion removes the ordinary consumption of one nutrition per turn. Nutrition consumption from all other sources (such as ring hunger from wearing the ring of slow digestion, jumping, or spellcasting) is unaffected. In practice this means that a non-spellcasting player can go without being hungry twenty times longer than normal. Wearing two such rings is actually counterproductive, but see below.
The ring of slow digestion also defends against monsters with digestion attacks, such as the purple worm. The monster attempts to digest the hero, but "You get regurgitated! Obviously the «foo» didn't like your taste." Since this is the only way to get that message, you can identify ring of slow digestion in this way.
With two rings of slow digestion, and good technique, the player can go indefinitely long without losing any nutrition, because the ring hunger for each hand is calculated on different turns. The process is to wear both rings, but removing one of the rings for the turn that its hunger is calculated. Your left hand hunger is calculated turn 4 (mod 20); right hand hunger is calculated on turn 12 (mod 20). No known ascensions have made use of this trick alone to ascend with the foodless conduct intact.
You can identify a ring of slow digestion by its nutrition-cancelling property alone, though it is a bit clunky if you're testing a lot of rings. As soon as your hunger level (Satiated, Hungry, Weak, Fainting) crosses into a hungrier level, put on the (ideally noncursed) ring and eat something that provides only a little nutrition (such as a 40-nutrition fortune cookie). If you go a long time (for a fortune cookie, as many as 800 turns) without recrossing the boundary, the ring is probably slow digestion.
Dropping a ring of slow digestion into a sink produces the message, "The ring is regurgitated!" and the ring is never consumed.
Attempting to eat a ring of slow digestion while polymorphed into a metallivore (which is the only way to eat a ring) produces the message, "The ring is indigestible! Blecch! Rotten metal!" followed by the normal effects and messages of eating rotten food.