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Given a set S of objects with an equivalence relation R on S, a canonical form is given by designating some objects of S to be "in canonical form", such that every object under consideration is equivalent to exactly one object in canonical form. In other words, the canonical forms in S represent the equivalence classes, once and only once. To test whether two objects are equivalent, it then suffices to test equality on their canonical forms.A canonical form thus provides a classification theorem

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