Canonical

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 basis – Basis of a type of algebraic structure

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.