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- Canonical_form 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. The distinction between "canonical" and "normal" forms varies by 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 (which can differ from standard notions of equality, for instance by considering different forms of equal objects to be nonequivalent) is defined, a canonical form consists in the choice of a specific object in each class. For example, row echelon form and Jordan normal form are canonical forms for matrices.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. Thus, the equality of two objects can easily be tested by testing the equality of their canonical forms. However canonical forms frequently depend on arbitrary choices (like ordering the variables), and this introduces 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 to test equality by putting the difference of two objects in normal form (see Computer algebra#Equality).Canonical form can also mean a differential form that is defined in a natural (canonical) way; see below.In computer science, data that has more than one possible representation can often be canonicalized into a completely unique representation called its canonical form. Putting something into canonical form is canonicalization.".
- Canonical_form wikiPageID "515096".
- Canonical_form wikiPageRevisionID "597896816".
- Canonical_form hasPhotoCollection Canonical_form.
- Canonical_form subject Category:Algebra.
- Canonical_form subject Category:Concepts_in_logic.
- Canonical_form subject Category:Formalism_(deductive).
- Canonical_form subject Category:Mathematical_terminology.
- Canonical_form 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. The distinction between "canonical" and "normal" forms varies by subfield.".
- Canonical_form label "Canonical form".
- Canonical_form label "Forma canonica".
- Canonical_form label "Forma canónica".
- Canonical_form label "Нормальная форма (математика)".
- Canonical_form sameAs Kanonický_tvar.
- Canonical_form sameAs Forma_canonica.
- Canonical_form sameAs 표준_형식_(수학).
- Canonical_form sameAs Forma_canónica.
- Canonical_form sameAs m.02kftx.
- Canonical_form sameAs Q1152398.
- Canonical_form sameAs Q1152398.
- Canonical_form wasDerivedFrom Canonical_form?oldid=597896816.
- Canonical_form isPrimaryTopicOf Canonical_form.