canonical meaning: 1. related to or according to a rule, principle, or law, especially in the Christian Church: 2…. Learn more.
canonical pronunciation. How to say canonical. Listen to the audio pronunciation in English. Learn more.
Suppose we have a mathematical object. There can be many ways of representing an object that are equivalent to this object for the purposes of solving some problem.
Rather than solve a given problem for all possible objects, we often only need to solve the problem for one representative from each equivalence class. Representatives from these equivalence classes can be called canonical; and it is sufficient to solve the problem only for canonical representatives.
We usually choose canonical representatives that are easy for us to work with.
For example, for graphs
We might even allow equivalence classes to have more than one canonical representative. Solving the problem for all canonical representatives nevertheless still amounts to solving the problem for all objects.
As another example, consider Latin squares
However, in the Latin square case, there are usually many ways to permute the rows and columns (and symbols) to get the first row and first column in order. So there would be many reduced (or canonical) representatives from each equivalence class.
When this word is used by programmers, it is a synonym for "authoritative," "standard," or "official." That's meaning number 3 in the definition you quote.
It implies that there is one best, most official, most standard way to represent the string object and this is it.
For example sometimes things can be represented using a relative link or an absolute link. Relative might be something like ../foo.txt\\www.example.com\fileserver\share\foo.txt
The adjective canonical is applied in many contexts to mean "according to the canon" – the standard, rule or primary source that is accepted as authoritative for the body of knowledge or literature in that context. In mathematics, "canonical example" is often used to mean "archetype".
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