Canonical Explained

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'.

Science and technology

Canonical form, a natural unique representation of an object, or a preferred notation for some object

Mathematics

- Canonical coordinates, sets of coordinates that can be used to describe a physical system at any given point in time
Canonical map, a morphism that is uniquely defined by its main property
Canonical polyhedron, a polyhedron whose edges are all tangent to a common sphere, whose center is the average of its vertices
Canonical ring, a graded ring associated to an algebraic variety
Canonical injection, in set theory
Canonical representative, in set theory a standard member of each element of a set partition

Differential geometry

Canonical one-form, a special 1-form defined on the cotangent bundle T*M of a manifold M
Canonical symplectic form, the exterior derivative of this form
Canonical vector field, the corresponding special vector field defined on the tangent bundle TM of a manifold M

Physics

Canonical ensemble, in statistical mechanics, is a statistical ensemble representing a probability distribution of microscopic states of the system
Canonical quantum gravity, an attempt to quantize the canonical formulation of general relativity
Canonical stress–energy tensor, a conserved current associated with translations through space and time
Canonical theory, a unified molecular theory of physics, chemistry, and biology
Canonical conjugate variables, pairs of variables mathematically defined in such a way that they become Fourier transform duals
Canonical transformation, in Hamiltonian mechanics
Grand canonical ensemble, a probability distribution of microscopic states for an open system, which is being maintained in thermodynamic equilibrium
Microcanonical ensemble, a theoretical tool used to analyze an isolated thermodynamic system

Computing

Canonical Huffman code, a particular type of Huffman code with unique properties which allow it to be described in a very compact manner
Canonical link element, an HTML element that helps webmasters prevent duplicate content issues by specifying the “canonical” or “preferred” version
Canonical model, a design pattern used to communicate between different data formats
Canonical name record (CNAME record), a type of Domain Name System record
Canonical S-expressions, a binary encoding form of a subset of general S-expression
Canonical XML, a normal form of XML, intended to allow relatively simple comparison of pairs of XML documents
MAC address (formerly canonical number), a unique identifier assigned to network interfaces for communications on the physical network segment
Canonicalization, a process for converting data to canonical form

Chemistry

Canonical form, any of a set of representations of the resonance structure of a molecule each of which contributes to the real structure

Religion

Canonical coronation, an institutional act of the pope to legally crown images venerated by the faithful through a papal bull
Canonical hours, the divisions of the day in terms of periods of fixed prayer at regular intervals.
Canonical law, a set of ordinances and regulations governing a Christian church or community
Canonical texts or biblical canon, the texts accepted as part of the Bible
- Canonical gospel, the four gospels accepted as part of the New Testament
- Canonical criticism, a way of interpreting the Bible that focuses on the text of the biblical canon itself as a finished product

Businesses

Canonical Ltd., software company that develops the Ubuntu operating system