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 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, 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 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 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 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, 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, 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 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, 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) 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, 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 times of prayer at regular intervals. A book of hours, chiefly a breviary, normally contains a version of, or selection from, such prayers. In ...

, 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 th ...

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