Canonical is an adjective derived from canon. In Grammar, an adjective is a word whose main syntactic role is to modify a Noun or Pronoun, giving more information about the Canon comes from the Greek word kanon "rule" (perhaps originally from kanna "reed", cognate to cane) is used in various meanings. A cane is a long straight wooden stick generally of Bamboo, Malacca ( Rattan) or some similar plant mainly used as a support such as a Walking stick

basic, canonic, canonical: reduced to the simplest and most significant form possible without loss of generality, e. g. "a basic story line"; "a canonical syllable pattern"

Contents 1 Religion 2 Literature and art 3 Mathematics 4 Computer science 5 Physics 6 See also 7 References

Religion

This word is used by theologians and canon lawyers to refer to the canons of the Roman Catholic, Eastern Orthodox and Anglican Churches adopted by ecumenical councils. Canon law is internal ecclesiastical law governing the Roman Catholic Church, the Eastern Orthodox churches and the Anglican Communion of churches Canon law is internal ecclesiastical law governing the Roman Catholic Church, the Eastern Orthodox churches and the Anglican Communion of churches This is a general introduction to ecumenical councils For the Roman Catholic councils, see Catholic Ecumenical Councils. It also refers to later law developed by local churches and dioceses of these churches. The function of this collection of various "canons" is somewhat analogous to the precedents established in common law by case law. Common law refers to law and the corresponding legal system developed through decisions of courts and similar tribunals rather than through legislative statutes or executive Case law' (also known as decisional law or judicial precedent) is that body of reported Judicial opinions in countries that have Common law

In the 20th century, the Roman Catholic Church revised its canon law in 1917 and then again 1981 into the modern Code of Canon Law. Canon Law, the Ecclesiastical law of the Catholic Church, is a fully developed legal system with all the necessary elements courts lawyers judges a fully articulated This code is no longer merely a compilation of papal decrees and conciliar legislation, but a more completely developed body of international church law. It is analogous to the English system of Statute law. A statute is a formal written enactment of a Legislative authority that governs a Country, State, City, or County.

Canonical can also mean "part of the canon", i. e. , one of the books comprising a biblical canon, as opposed to apocryphal books. A Biblical canon or canon of scripture is a list or Set of Biblical books considered to be authoritative as Scripture by a particular religious

The term is also applied by Westerners to other religions, but in inconsistent ways: for example, in the case of Buddhism one authority^[1] refers to "scriptures and other canonical texts", while another^[2] says that scriptures can be categorized into canonical, commentarial and pseudo-canonical.

Canonization is the process by which a person is recognized as a saint. A saint (from the Latin sanctus) is a human being to whom has been attributed (and who has generally demonstrated a high level of Holiness and Sanctity

Literature and art

The word is also often used when describing bodies of literature or art: those books that all educated people have supposedly read, or are advised to read, make up the "canon", for example the Western canon. The Western canon is a term used to denote a canon of books and more widely music and art, that has been the most influential in (See also canon (fiction)). This article is not about Literary canons of influential works of fiction but about the concept of a canon which defines the world of a particular fictional series

Mathematics

Mathematicians have for perhaps a century or more used the word canonical to refer to concepts that have a kind of uniqueness or naturalness, and are (up to trivial aspects) "independent of coordinates. In Mathematics, the phrase " up to xxxx" indicates that members of an Equivalence class are to be regarded as a single entity for some purpose " Examples include the canonical prime factorization of positive integers, the Jordan canonical form of matrices (which is built out of the irreducible factors of the characteristic polynomial of the matrix), and the canonical decomposition of a permutation into a product of disjoint cycles. In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 In Mathematics, factorization ( also factorisation in British English) or factoring is the decomposition of an object (for The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French In Linear algebra, Jordan normal form (often called Jordan canonical form)shows that a given square matrix M over a field K In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally In Linear algebra, one associates a Polynomial to every Square matrix, its characteristic polynomial. In several fields of Mathematics the term permutation is used with different but closely related meanings Various functions in mathematics are also canonical, like the canonical homomorphism of a group onto any of its quotient groups, or the canonical isomorphism between a finite-dimensional vector space and its double dual. In Abstract algebra, a homomorphism is a structure-preserving map between two Algebraic structures (such as groups rings or Vector In Mathematics, a group is a set of elements together with an operation that combines any two of its elements to form a third element In Abstract algebra, an isomorphism ( Greek: ἴσος isos "equal" and μορφή morphe "shape" is a bijective In Mathematics, a vector space (or linear space) is a collection of objects (called vectors) that informally speaking may be scaled and added Although a finite-dimensional vector space and its dual space are isomorphic, there is no canonical isomorphism. This lack of a canonical isomorphism can be made precise in terms of category theory, but one could say at a simpler level that "any isomorphism you can think of here depends on choosing a basis. In Mathematics, category theory deals in an abstract way with mathematical Structures and relationships between them it abstracts from sets " As stated by Goguen, "To any canonical construction from one species of structure to another corresponds an adjunction between the corresponding categories. " ^[3]

Being canonical in mathematics is stronger than being a conventional choice. For instance, the vector space Rⁿ has a standard basis which is canonical in the sense that it is not just a choice which makes certain calculations easy; in fact most linear operators on Euclidean space take on a simpler form when written as a matrix relative to some basis other than the standard one (see Jordan form). In Mathematics, a vector space (or linear space) is a collection of objects (called vectors) that informally speaking may be scaled and added In Mathematics, the standard basis (also called natural basis or canonical basis) of the n- dimensional Euclidean space In Mathematics, a linear map (also called a linear transformation, or linear operator) is a function between two Vector spaces that In Linear algebra, Jordan normal form (often called Jordan canonical form)shows that a given square matrix M over a field K In contrast, an abstract n-dimensional real vector space V would not have a canonical basis; it is isomorphic to Rⁿ of course, but the choice of isomorphism is not canonical.

The word canonical is also used for a preferred way of writing something, see the main article canonical form. Generally in Mathematics, a canonical form (often called normal form or standard form) of an object is a standard way of presenting that object

In set theory, the term "canonical" identifies an element as representative of a set. If a set is partitioned into equivalence classes, then one member can be chosen from each equivalence class to represent that class. In Mathematics, a partition of a set X is a division of X into non-overlapping " parts " or " blocks " In Mathematics, given a set X and an Equivalence relation ~ on X, the equivalence class of an element a in X That representative member is the canonical member. If you have a canonicalizing function, f(x), that maps x to the canonical member of the equivalence class which contains it, then testing whether two items, a and b, are equivalent is the same as testing whether f(a) is identical to f(b).

Computer science

Some circles in the field of computer science have borrowed this usage from mathematicians. Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their It has come to mean "the usual or standard state or manner of something"; for example, "the canonical way to organize a file system is as a hierarchy, with extensions to make it a directed graph". In Computing, a file system (often also written as filesystem) is a method for storing and organizing Computer files and the data they contain to make @@@ main@@@ - title Hierarchy@@@ keywords structure; sociology; information@@@ review@@@ - In Mathematics and Computer science, a graph is the basic object of study in Graph theory. XML Signature defines canonicalization as the process of converting XML content to a canonical form, to take into account changes that can invalidate a signature over that data (from JWSDP 1. XML Signature (also called XMLDsig, XML-DSig, XML-Sig) is a W3C recommendation that defines an XML syntax for Digital signatures Don't change "Extensible" The Java Web Services Development Pack ( JWSDP) is a free Software development kit (SDK for developing Web Services, Web applications and 6).

In enterprise application integration, the "canonical data model" is a design pattern used to communicate between different data formats. Enterprise Application Integration (EAI is defined as the uses of Software and computer systems architectural principles to integrate a set of enterprise computer applications It introduces an additional format, called the "canonical format", "canonical document type" or "canonical data model". Instead of writing translators between each and every format (with potential for a combinatorial explosion), it is sufficient just to write a translator between each format and the canonical format. In Mathematics a combinatorial explosion describes the effect of functions that grow very rapidly as a result of Combinatorial considerations The Open Applications Group Integration Specification (OAGIS) is an example of an integration architecture that is based on a canonical data model.

For an illuminating story about the word's use among computer scientists, see the Jargon File's entry for the word[1]. The Jargon File is a Glossary of hacker Slang. The original Jargon File was a collection of hacker slang from technical cultures such as the MIT AI

Some people have been known to use the noun canonicality; others use canonicity. In fields other than computer science, canonicity is this word's canonical form.

In computer science, a canonical name record (or CNAME) is a type of DNS record. The Domain Name System (DNS is a hierarchical naming system for computers services or any resource participating in the Internet.

In computer science, a canonical number is the old designation for a MAC code on routers and servers.

Physics

In theoretical physics, the concept of canonical (or conjugate, or canonically conjugate) variables is of major importance. Theoretical physics employs Mathematical models and Abstractions of Physics in an attempt to explain experimental data taken of the natural world Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. They always occur in complementary pairs, such as spatial location x and linear momentum p, angle φ and angular momentum L, and energy E and time t. In Geometry, Topology and related branches of mathematics a spatial point describes a specific point within a given space that consists of neither Volume In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of They can be defined as any coordinates whose Poisson brackets give a Kronecker delta (or a Dirac delta in the case of continuous variables). In Mathematics and Classical mechanics, the Poisson bracket is an important operator in Hamiltonian mechanics, playing a central role in the definition In Mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker ( 1823 - 1891) is a function of two The Dirac delta or Dirac's delta is a mathematical construct introduced by the British theoretical physicist Paul Dirac. Continuity may refer to In mathematics: Continuous probability distribution or random variable in probability and statistics For The existence of such coordinates is guaranteed under broad circumstances as a consequence of Darboux's theorem. Darboux's theorem is a Theorem in the mathematical field of Differential geometry and more specifically Differential forms, partially generalizing Canonical variables are essential in the Hamiltonian formulation of physics, which is particularly important in quantum mechanics. Hamiltonian mechanics is a re-formulation of Classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons For instance, the Schrödinger equation and the Heisenberg uncertainty relation always incorporate canonical variables. In Physics, especially Quantum mechanics, the Schrödinger equation is an equation that describes how the Quantum state of a Physical system In Quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the Momentum of the particle uncertain Canonical variables in physics are based on the aforementioned mathematical structure and therefore bear a deeper meaning than being just convenient variables. One facet of this underlying structure is expressed by Noether's theorem, which states that a (continuous) symmetry in a variable implies an invariance of the conjugate variable, and vice versa; for instance symmetry under spatial displacement leads to conservation of momentum, and time-independence implies energy conservation. Noether's theorem (also known as Noether's first theorem) states that any differentiable symmetry of the action of a physical system has Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or In Mathematics and Theoretical physics, an invariant is a property of a system which remains unchanged under some transformation. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may

In statistical mechanics, the canonical ensemble, the grand canonical ensemble, and the microcanonical ensemble are archetypal probability distributions for the (unknown) microscopic state of a thermal system, applying respectively in the physical cases of:- a closed system at fixed temperature (able to exchange energy with its environment); an open system at fixed temperature (able to exchange both energy and particles); and a closed thermally isolated system (able to exchange neither). Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics A canonical ensemble in Statistical mechanics is a Statistical ensemble representing a Probability distribution of microscopic states of the system In Statistical mechanics, the grand canonical ensemble is a Statistical ensemble (a large collection of identically prepared systems where each system is in The microcanonical ensemble is the simplest of the ensembles of Statistical mechanics. In Probability theory and Statistics, a probability distribution identifies either the probability of each value of an unidentified Random variable In Statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system that the system visits in the course of its thermal fluctuations These probability distributions can be applied directly to practical problems in thermodynamics. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning "

See also

• Literary canons and Canon (fiction)
• Canonicalization is a transformation to get the canonical form. The Western canon is a term used to denote a canon of books and more widely music and art, that has been the most influential in This article is not about Literary canons of influential works of fiction but about the concept of a canon which defines the world of a particular fictional series Not to be confused with Canonization. In Computer science, canonicalization (abbreviated c14n, where 14 represents the

References

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