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 conceptual material accepted as official in a fictional universe by its fan base * Literary canon, an accepted body of works considered as high culture ** Western ca ...

" 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 th ...

, 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 ot ...

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 ...

, 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 ch ...

, 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 po ...

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

Canonical ring In mathematics, the pluricanonical ring of an algebraic variety ''V'' (which is non-singular), or of a complex manifold, is the graded ring :R(V,K)=R(V,K_V) \, of sections of powers of the canonical bundle ''K''. Its ''n''th graded component (for ...

, 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 R_i R_j \subseteq R_. The index set is usually the set of nonnegative integers or the ...

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 \iot ...

, 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 pr ...

, 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 heat b ...

, 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 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 example ...

, 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. Canoni ...

, 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 equilibrium ...

, 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 t ...

, 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 (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, 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