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A few related issues to classification are the following.
*The equivalence problem is "given two objects, determine if they are equivalent".
*A [[complete set of invariants]], together with which invariants are realizable, solves the classification problem, and is often a step in solving it.
*A computable [[complete set of invariants]] (together with which invariants are realizable) solves both the classification problem and the equivalence problem.
* A [[canonical form]] solves the classification problem, and is more data: it not only classifies every class, but gives a distinguished (canonical) element of each class.
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