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A canonical form is an element of a set of representatives of equivalence classes of forms such that there is a function or procedure which projects every element of each equivalence class onto that one element, the canonical form of that equivalence class. The canonical form is expected to be simpler than the rest of the forms in some way. For example, for cubic polynomials acted upon by the group of translations along the abscissa, the canonical forms are cubic polynomials without a quadratic term.
And while I listed long, Day rose, and still he sang, And all his stanchless song, As something falling unaware, Fell out of the tall trees he sang among,
Stowed away in the plane Jack had a signal pistol and several red and green cartridges, but until a search plane appeared the flares would be useless.
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