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*The equivalence problem is "given two objects, determine if they are equivalent".
*A [[complete set of invariants]], together with which invariants are {{clarify span|realizable,|reason=This notion should be introduced.}} solves the classification problem, and is often a step in solving it.
*A {{clarify span|computable complete set of invariants|reason=Shouldn't this be "finite set of computable invariants"? Computability (whatever this is supposed to mean on a set of functions) is of no help if infinitely many functions must be evaluated or if an uncomputable function must be evaluated.}} (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 provides a distinguished (canonical) element of each class.
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