This HTML5 document contains 132 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dcthttp://purl.org/dc/terms/
yago-reshttp://yago-knowledge.org/resource/
dbohttp://dbpedia.org/ontology/
n17http://dbpedia.org/resource/File:
foafhttp://xmlns.com/foaf/0.1/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
freebasehttp://rdf.freebase.com/ns/
n10http://commons.wikimedia.org/wiki/Special:FilePath/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
n14http://en.wikipedia.org/wiki/
dbchttp://dbpedia.org/resource/Category:
dbphttp://dbpedia.org/property/
provhttp://www.w3.org/ns/prov#
xsdhhttp://www.w3.org/2001/XMLSchema#
goldhttp://purl.org/linguistics/gold/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Canonical_form
rdfs:label
Canonical form
rdfs:comment
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 object and which allows it to be identified in a unique way. The distinction between "canonical" and "normal" forms varies from subfield to subfield. In most fields, a canonical form specifies a unique representation for every object, while a normal form simply specifies its form, without the requirement of uniqueness.
owl:sameAs
freebase:m.0nb1nzb yago-res:Canonical_form freebase:m.02kftx
dbp:wikiPageUsesTemplate
dbt:For dbt:Refimprove dbt:Citation dbt:Main dbt:Main_article
dct:subject
dbc:Formalism_(deductive) dbc:Algebra dbc:Mathematical_terminology dbc:Concepts_in_logic
dbo:thumbnail
n10:Anagram_canonical_svg.svg?width=300
foaf:depiction
n10:Anagram_canonical_svg.svg
gold:hypernym
dbr:Way
prov:wasDerivedFrom
n14:Canonical_form?oldid=1072264276&ns=0
dbo:wikiPageID
515096
dbo:wikiPageLength
15590
dbo:wikiPageRevisionID
1072264276
dbo:wikiPageWikiLink
dbr:Normal_form_(natural_deduction) dbr:Cotangent_bundle dbr:Software_development dbr:Inverse_element dbr:Normal_form_(dynamical_systems) dbr:Graph_theory dbr:Classification_theorem dbr:Ordinal_arithmetic dbr:Equivalence_class dbr:Data_validation dbr:Large_numbers dbr:Hermite_normal_form dbr:Computing dbc:Mathematical_terminology dbr:Single_source_of_truth dbr:Frobenius_normal_form dbr:Symplectic_manifold dbr:Lambda_calculus dbr:Table_(database) dbr:Graph_labeling dbr:Howell_normal_form dbr:Normal_matrix dbr:Convex_polytope dbr:Normal-form_game dbr:Beta_normal_form dbr:Skolem_normal_form dbr:Graph_isomorphism dbr:Canonicalization dbr:Manifold dbr:Diagonal_matrix dbr:Vector_space dbr:Character_encoding dbr:Unimodular_matrix dbr:Midsphere dbr:Homeomorphism dbr:Standardization dbr:Content_management dbr:Third_fundamental_form dbr:Prenex_normal_form dbr:Content_management_system dbc:Formalism_(deductive) dbr:Continued_fraction dbr:Normalization dbr:Database_normalization dbr:Code_injection dbr:Character_encodings_in_HTML dbr:Analytic_geometry dbr:Abstract_rewriting_system dbr:Up_to dbr:Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain dbr:Audio_signal_processing dbr:Negation_normal_form dbr:Mathematics dbr:Spectral_theorem dbr:Smith_normal_form dbr:Modular_arithmetic dbr:Unitary_matrix dbr:Euler–Lagrange_equation dbr:Tautological_one-form dbr:Invertible_matrix dbr:Weyr_canonical_form dbr:First_fundamental_form dbr:Transclusion dbr:Integrable_system dbr:Machine_learning dbr:Decimal_representation dbr:Complex_number dbr:Singular_value_decomposition dbr:Computer_algebra dbr:Disjunctive_normal_form dbc:Algebra n17:Anagram_canonical_svg.svg dbr:Second_fundamental_form dbr:Dynamical_system dbr:Cardinality dbr:Row_echelon_form dbr:Ordinal_number dbr:Signal_processing dbr:Computer_science dbr:Scientific_notation dbr:Compact_space dbr:Algebraically_closed_field dbr:Computer_security dbr:Canonical_basis dbr:Canonical_bundle dbr:Data_redundancy dbr:Hamiltonian_mechanics dbr:Matrix_similarity dbr:Jordan_normal_form dbr:Equivalence_relation dbr:Differential_form dbr:Hausdorff_space dbr:Hilbert_space dbr:Differential_equation dbc:Concepts_in_logic dbr:Mathematical_object dbr:Idempotence dbr:Algebraic_normal_form dbr:Vulnerability_(computing) dbr:Expression_(mathematics) dbr:Relational_database dbr:Digital_image_processing dbr:Blake_canonical_form dbr:Fundamental_theorem_of_arithmetic dbr:Field_(computer_science) dbr:Natural_number dbr:Conjunctive_normal_form dbr:Linear_equation dbr:Principal_ideal_domain
dbo:abstract
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 object and which allows it to be identified in a unique way. The distinction between "canonical" and "normal" forms varies from subfield to subfield. In most fields, a canonical form specifies a unique representation for every object, while a normal form simply specifies its form, without the requirement of uniqueness. The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero. More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific object in each class. For example: * Jordan normal form is a canonical form for matrix similarity. * The row echelon form is a canonical form, when one considers as equivalent a matrix and its left product by an invertible matrix. In computer science, and more specifically in computer algebra, when representing mathematical objects in a computer, there are usually many different ways to represent the same object. In this context, a canonical form is a representation such that every object has a unique representation (with canonicalization being the process through which a representation is put into its canonical form). Thus, the equality of two objects can easily be tested by testing the equality of their canonical forms. Despite this advantage, canonical forms frequently depend on arbitrary choices (like ordering the variables), which introduce difficulties for testing the equality of two objects resulting on independent computations. Therefore, in computer algebra, normal form is a weaker notion: A normal form is a representation such that zero is uniquely represented. This allows testing for equality by putting the difference of two objects in normal form. Canonical form can also mean a differential form that is defined in a natural (canonical) way.
foaf:isPrimaryTopicOf
n14:Canonical_form