In many cases, the jets method will store its results inside a CacheTable in the base object. When the method is called again with the same or a lower jets order, the result is pulled from the cache.
For polynomial rings, data is stored under *.jet.
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Note also that rings of jets are built as towers from lower to higher jets orders. Therefore it is possible to store a single ring of the highest order computed thus far.
For ideals, data is stored under *.cache.jet. A single matrix is stored containing generators for the highest order of jets computed thus far. Generators for lower orders are recovered from this matrix without additional computations.
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For quotient rings, data is stored under *.jet. Each jets order gives rise to a different quotient that is stored separately under *.jet.jetsRing (order zero jets are always included by default).
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For ring homomorphisms, data is stored under *.cache.jet. A single matrix is stored describing the map for the highest order of jets computed thus far. Lower orders map are recovered from this matrix without additional computations.
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Projective jets data is stored separately under *.projet or *.cache.projet to accommodate for the different grading.
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No data is cached when computing jets of affine varieties and (hyper)graphs, radicals, or principal components.