This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations.(November 2021) (Learn how and when to remove this message)
In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K, it may not be obvious whether there is a smaller field k, and other polynomials defined over k, which still define V.
The issue of field of definition is of concern in diophantine geometry.
and 21 Related for: Field of definition information
In mathematics, the fieldofdefinitionof an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining...
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories:...
used in the theory of lattices in Lie groups, often under the name fieldofdefinition. Fuchsian groups are discrete subgroups of P S L 2 ( R ) {\displaystyle...
The International Astronomical Union's definitionof a planet in the Solar System Object is in orbit around the Sun Object has sufficient mass for its...
computer and information technology fields, other definitions have been used that arose for historical reasons of convenience. A common usage has been...
Artin–Schreier theory of ordered fields and formally real fields. There are two equivalent common definitionsof an ordered field. The definitionof total order...
scholarly or legal, on the definitionof terrorism. Various legal systems and government agencies use different definitionsof terrorism, and governments...
methods in the field that created it. Without a falsifiable operational definition, conceptual definitions assume both knowledge and acceptance of the theories...
grade is referred to as field-grade officers, field officers or officers offield rank. Historically, a regiment or battalion's field officers made up its...
physical activities 3. (mainly British) a competitor in track and field events "Definitionof athlete noun from the Oxford Advanced Learner's Dictionary"....
are three main types of technical definitions.[definition needed] Power definitions Secondary definitions Extended definitions Aniline, a benzene ring...
ordered field. Such a definition does not prove that such a complete ordered field exists, and the existence proof consists of constructing a mathematical...
welfare definitionof economics is an attempt by Alfred Marshall , a pioneer of neoclassical economics, to redefine his fieldof study. This definition expands...
In the context of SQL, data definition or data description language (DDL) is a syntax for creating and modifying database objects such as tables, indices...
expand the definitions to include the idea of abstract algebraic variety over K, and generic point relative to K. Reference to a ground field may be common...
Dedekind-complete ordered field. Other common definitionsof real numbers include equivalence classes of Cauchy sequences (of rational numbers), Dedekind...
Definitionsof education aim to describe the essential features of education. A great variety ofdefinitions has been proposed. There is wide agreement...
Solar System. It has been argued that the definition is problematic because it depends on the location of the body: if a Mars-sized body were discovered...
the fieldofdefinitionof E is a number field K, that is to say, a finite field extension of Q. In particular, the group E(K) of K-rational points of an...
measures the complexity of algebraic structures via their fieldsofdefinition. For example, a quadratic form q : V → K over a field K, where V is a K-vector...
Global Information