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

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 ob ...

, 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 c ...

, sets of coordinates that can be used to describe a physical system at any given point in time *

Canonical map In mathematics, a canonical map, also called a natural map, is a map or morphism between objects that arises naturally from the definition or the construction of the objects. Often, it is a map which preserves the widest amount of structure. A c ...

, a morphism that is uniquely defined by its main property *

Canonical polyhedron In geometry, the midsphere or intersphere of a polyhedron is a sphere which is tangent to every edge of the polyhedron. That is to say, it touches any given edge at exactly one point. Not every polyhedron has a midsphere, but for every convex ...

, 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 mathematics, if A is a subset of B, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \iota that sends each element x of A to x, treated as an element of B: \iota : A\rightarrow B, \qquad \iota ...

, in set theory * Canonical representative, in set theory a standard member of each element of a

set partition In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a set defines a partition of this set, and every parti ...

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, the exterior derivative of this form *

Canonical vector field In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M . As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points and of ...

, 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 b ...

, 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 examp ...

, 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 prod ...

, 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. It need not preserve the form of the Hamiltonian itself. Canon ...

, 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. Data compressors generally work in one of two ways. Either ...

, 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 Ap ...

, 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 existing ...

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

Canonical name record A Canonical Name record (abbreviated as 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 (li ...

(CNAME record), a type of Domain Name System record *

Canonical S-expressions A Canonical S-expression (or csexp) is a binary encoding form of a subset of general S-expression (or sexp). It was designed for use in SPKI to retain the power of S-expressions and ensure canonical form for applications such as digital signatures ...

, a binary encoding form of a subset of general S-expression *

Canonical XML Canonical XML is a normal form of XML, intended to allow relatively simple comparison of pairs of XML documents for equivalence; for this purpose, the Canonical XML transformation removes non-meaningful differences between the documents. Any XML do ...

, a normal form of XML, intended to allow relatively simple comparison of pairs of XML documents *

MAC address A media access control address (MAC 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 is common in most IEEE 802 networking tec ...

(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 (chemistry) In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or polyatomic ions by the combination of several contributing structures (or ''forms'', also variously known as ''resonance structures'' or '' ...

, 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 ( la, Coronatio Canonica) is a pious institutional act of the pope, duly expressed in a bull, in which the pope bestows the right to impose an ornamental crown, a diadem or an aureole to an image of Christ, Mary or Jo ...

, 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 Canon law (from grc, κανών, , 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. It is 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 Greek , meaning "rule" or " measuring stick". The us ...

, the texts accepted as part of the Bible **

Canonical gospel Gospel originally meant the Christian message ("the gospel"), but in the 2nd century it came to be used also for the books in which the message was set out. In this sense a gospel can be defined as a loose-knit, episodic narrative of the words an ...

, 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 approach ...

, a way of interpreting the Bible that focuses on the text of the biblical canon itself as a finished product