Canonical form

[1] The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero.

Despite this advantage, canonical forms frequently depend on arbitrary choices (like ordering the variables), which introduce difficulties for testing the equality of two objects resulting on independent computations.

Formally, a canonicalization with respect to an equivalence relation R on a set S is a mapping c:S→S such that for all s, s1, s2 ∈ S: Property 3 is redundant; it follows by applying 2 to 1.

For example, in modular arithmetic, the canonical form for a residue class is usually taken as the least non-negative integer in it.

Operations on classes are carried out by combining these representatives, and then reducing the result to its least non-negative residue.

[3] The German term kanonische Form is attested in a 1846 paper by Eisenstein,[4] later the same year Richelot uses the term Normalform in a paper,[5] and in 1851 Sylvester writes:[6] "I now proceed to [...] the mode of reducing Algebraical Functions to their simplest and most symmetrical, or as my admirable friend M. Hermite well proposes to call them, their Canonical forms.

Standard form is used by many mathematicians and scientists to write extremely large numbers in a more concise and understandable way, the most prominent of which being the scientific notation.

[13] In the field of software security, a common vulnerability is unchecked malicious input (see Code injection).

Other forms of data, typically associated with signal processing (including audio and imaging) or machine learning, can be normalized in order to provide a limited range of values.

In content management, the concept of a single source of truth (SSOT) is applicable, just as it is in database normalization generally and in software development.

Competent content management systems provide logical ways of obtaining it, such as transclusion.