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SparseArrays are atomic objects, but they do have a FullForm which reveals information about them.

What is the meaning of the various elements in the full form of a SparseArray? Did the structure change between Mathematica versions, and is it documented anywhere?

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It seems to be the same as InputForm which is mentioned: Whenever a sparse array is evaluated, it is automatically converted to an optimized standard form But it doesn't have much detalis – ssch Jan 19 at 21:34
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I can't tell much about the changes from version to version, but the "API" I use in many of my answers,e.g. here gives some idea. I give more details on the meaning of these parts here. – Leonid Shifrin Jan 19 at 21:48
Based on ElisionsDump`HeldSparseArrayData it looks like SparseArray[data_,dims_,def_,{___,elems_}], where dims is the dimensions and elems is number of non-default elements. I'm not sure about def and data. – Szabolcs Jan 19 at 22:50
def is the "background", or default, value. data seems always to be Automatic, and I don't know what it represents. – Oleksandr R. Jan 20 at 6:12

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I have described the details here and here. The second post describes the version number of the sparse array implementation, which is still at version 1. So no big changes since it's introduction and V9.

If you like to read about sparse arrays I can recommend this from Tim Davis.

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