Wikipedia points to the term Canonicalization.
A process for converting data that has more than one possible representation into a "standard" canonical representation. This can be done to compare different representations for equivalence, to count the number of distinct data structures, to improve the efficiency of various algorithms by eliminating repeated calculations, or to make it possible to impose a meaningful sorting order.
The Unicode example made the most sense to me:
Variable-length encodings in the Unicode standard, in particular UTF-8, have more than one possible encoding for most common characters. This makes string validation more complicated, since every possible encoding of each string character must be considered. A software implementation which does not consider all character encodings runs the risk of accepting strings considered invalid in the application design, which could cause bugs or allow attacks. The solution is to allow a single encoding for each character. Canonicalization is then the process of translating every string character to its single allowed encoding. An alternative is for software to determine whether a string is canonicalized, and then reject it if it is not. In this case, in a client/server context, the canonicalization would be the responsibility of the client.
In summary, a standard form of representation for data. From this form you can then convert to any representation you may need.
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.
Canonical form basically holds every variable in its group.
So if you have three variables named A, B and C, your SoM could be A~BC+~ABC+AB~C = Y
Now you can simplify this to reduce the number of variables in the equation. This simplification is easy for us to solve manually. But for a computer, it needs to know the A, B and C values as a group (101+011+110
If you simplify, it just becomes a normal Boolean expression and not a canonical form
The etymology refers to the canon, as a rule or a body of rules, or axiomatic or universal standards. It exists in arts: sculpture, music, script writing, etc. The notion of canon law is also used in the domain of religion: a "set of ordinances and regulations [...] for the government of a Christian organization or church and its members".
In mathematics and engineering, a canonical form is, similarly, a preferred notation, or a somehow unique and natural form, or representation, of an object or a formula. For instance, a canonical basis is one of the many bases of a vector space (or an algebraic structure in general), but a basis that is unique by its simplicity, like the standard basis defined by the Kronecker delta:
In some sources, for linear digital filters, canonical forms refer to sets of structures that are optimal in some sense, with respect to some basic operations (available to a processor, for instance). The most common is the reduction of the number of delays, it is often associated with the name "Direct Form II" (excellent online tutorial by J. O. Smith):
In summary, the DF-II structure has the following properties [...] It is canonical with respect to delay
In theory, one could look for canonical forms with respect to others quantities. In practice, the delay minimization is the most standard, thus the most canonical of the canonical forms. By metonymy, the delay canonical form is thus called "the canonical form".
Other occurences of canonical forms may appear with state-space formulations for filters. In control theory, one may find for instance Observable Canonical Forms and Controllable Canonical Forms.
