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→Applications: algorithms don't prove theorems, so it is more proper to say the SNF serves to find invariant factors than to prove the structure theorem |
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== Applications ==
The Smith normal form is useful for computing the [[homology (mathematics)|homology]] of a [[chain complex]] when the chain modules of the chain complex are [[Finitely generated module|finitely generated]]. For instance, in [[topology]], it can be used to compute the homology of a [[simplicial complex]] or [[CW complex]] over the integers, because the boundary maps in such a complex are just integer matrices. It can also be used to
== Example ==
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