The adjective canonical is applied in many contexts to mean 'according to the

canon Canon or Canons may refer to: Arts and entertainment * Canon (fiction), the material accepted as officially written by an author or an ascribed author * Literary canon, an accepted body of works considered as high culture ** Western canon, th ...

' the

standard Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object ...

, 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 The concept of an archetype ( ) appears in areas relating to behavior, historical psychology, philosophy and literary analysis. An archetype can be any of the following: # a statement, pattern of behavior, prototype, "first" form, or a main mo ...

Science and technology

Canonical form In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an obje ...

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

Mathematics

* *

Canonical coordinates In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of cla ...

, 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 In geometry, the midsphere or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but the uniform polyhedra, including the regular, quasiregular and semiregul ...

, a polyhedron whose edges are all tangent to a common sphere, whose center is the average of its vertices * Canonical ring, a

graded ring In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups R_i such that . The index set is usually the set of nonnegative integers or the set of integers, but ...

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 In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle T^Q of a manifold Q. In physics, it is used to create a correspondence between the velocity of a point in a mechanical system and its momentum, thus pro ...

, a special 1-form defined on the cotangent bundle ''T''*''M'' of a manifold ''M'' *

Canonical symplectic form In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle T^Q of a manifold Q. In physics, it is used to create a correspondence between the velocity of a point in a mechanical system and its momentum, thus p ...

, 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, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. The system can exchange energy with the hea ...

, in statistical mechanics, is a statistical ensemble representing a probability distribution of microscopic states of the system *

Canonical quantum gravity In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity (or canonical gravity). It is a Hamiltonian formulation of Einstein's general theory of relativity. The basic theory was outlined by ...

, an attempt to quantize the canonical formulation of general relativity *

Canonical stress–energy tensor 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 exampl ...

, a conserved current associated with translations through space and time *

Canonical theory Joel E. Keizer (31 August, 1942 - 16 May, 1999) was an American biologist and university professor. He is principally known for his work in non-equilibrium thermodynamics and mathematical modelling of cellular phenomena, in particular human pro ...

, a unified molecular theory of physics, chemistry, and biology *

Canonical conjugate variables Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation— ...

, pairs of variables mathematically defined in such a way that they become Fourier transform duals *

Canonical transformation In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates that preserves the form of Hamilton's equations. This is sometimes known as ''form invariance''. Although Hamilton's equations are preserved, it need not ...

, in Hamiltonian mechanics *

Grand canonical ensemble In statistical mechanics, the grand canonical ensemble (also known as the macrocanonical ensemble) is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that are in thermodynamic equilibri ...

, a probability distribution of microscopic states for an open system, which is being maintained in thermodynamic equilibrium *

Microcanonical ensemble In statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assumed to be isolated in the sense that it canno ...

, a theoretical tool used to analyze an isolated thermodynamic system

Computing

Canonical Huffman code In computer science and information theory, a canonical Huffman code is a particular type of Huffman code with unique properties which allow it to be described in a very compact manner. Rather than storing the structure of the code tree explicitly ...

, a particular type of Huffman code with unique properties which allow it to be described in a very compact manner *

Canonical link element A canonical link element is an HTML element that helps webmasters prevent duplicate content issues in search engine optimization by specifying the " canonical" or "preferred" version of a web page. It is described in RFC 6596, which went live in ...

, an HTML element that helps webmasters prevent duplicate content issues by specifying the “canonical” or “preferred” version *

Canonical model A canonical model is a design pattern used to communicate between different data formats. Essentially: create a data model which is a superset of all the others ("canonical"), and create a "translator" module or layer to/from which all existi ...

, a design pattern used to communicate between different data formats *

Canonical name record A Canonical Name (CNAME) record is a type of resource record in the Domain Name System (DNS) that maps one domain name (an alias) to another (the canonical name). This can prove convenient when running multiple services (like an FTP server '' ...

(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 A MAC address (short for medium access control address or media access control address) is a unique identifier assigned to a network interface controller (NIC) for use as a network address in communications within a network segment. This use i ...

(formerly canonical number), a unique identifier assigned to network interfaces for communications on the physical network segment *

Canonicalization In computer science, canonicalization (sometimes standardization or Normalization (statistics), normalization) is a process for converting data that has more than one possible representation into a "standard", "normal", or canonical form. This ...

, a process for converting data to canonical form

Chemistry

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

Religion

Canonical coronation A canonical coronation () is a pious institutional act of the pope, duly expressed in a formal decree of a papal bull, in which the pope bestows the pontifical right to impose an ornamental crown, a diadem or an aureola, aureole to an image of ...

, an institutional act of the pope to legally crown images venerated by the faithful through a papal bull *

Canonical hours In the practice of Christianity, canonical hours mark the divisions of the day in terms of Fixed prayer times#Christianity, fixed times of prayer at regular intervals. A book of hours, chiefly a breviary, normally contains a version of, or sel ...

, the divisions of the day in terms of periods of fixed prayer at regular intervals. *

Canonical law Canon law (from , , a 'straight measuring rod, ruler') is a set of ordinances and regulations made by ecclesiastical authority (church leadership) for the government of a Christian organization or church and its members. Canon law includes the ...

, a set of ordinances and regulations governing a Christian church or community * Canonical texts or

biblical canon A biblical canon is a set of texts (also called "books") which a particular Jewish or Christian religious community regards as part of the Bible. The English word ''canon'' comes from the Ancient Greek, Greek , meaning 'ruler, rule' or 'measu ...

, the texts accepted as part of the Bible **

Canonical gospel Gospel originally meant the Christian message ("the gospel"), but in the second century AD the term (, from which the English word originated as a calque) came to be used also for the books in which the message was reported. In this sense ...

, the four gospels accepted as part of the New Testament **

Canonical criticism Canonical criticism, sometimes called canon criticism or the canonical approach, is a way of interpreting the Bible that focuses on the text of the biblical canon itself as a finished product. Brevard Childs (1923–2007) popularised this approa ...

, 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