Field math：Finite field
Finite field
Finitefieldsarefundamentalinanumberofareasofmathematicsandcomputerscience,includingnumbertheory,algebraicgeometry,Galoistheory,finite ...。其他文章還包含有：「abstractalgebra」、「Field(mathematics)」、「Field(mathematics)」、「Field」、「FieldDefinition(expanded)」、「FieldinMathematics」、「Fields」、「MAT240」
查看更多 離開網站Algebraicstructure"Galoisfield"redirectshere.ForGaloisfieldextensions,seeGaloisextension.Inmathematics,afinitefieldorGaloisfield(so-namedinhonorofÉvaristeGalois)isafieldthatcontainsafinitenumberofelements.Aswithanyfield,afinitefieldisasetonwhichtheoperationsofmultiplication,addition,subtractionanddivisionaredefinedandsatisfycertainbasicrules.Themostcommonexamplesoffinitefieldsaretheintegersmodpwhenpisaprimenumber.Theorderofafinitefieldisitsnumberofelements,whichiseitheraprimenumberoraprimepo...
abstract algebra
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So the short answer to your question is: a field is an algebraic structure on a set which allows us to make sense of addition, subtraction, ...
Field (mathematics)
https://en.wikipedia.org
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on ...
Field (mathematics)
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A field is a ring (so it follows the rules above), with these extra rules: Commutativity of multiplication: When multiplication is done, ...
Field
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A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.
Field Definition (expanded)
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Field in Mathematics
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A field is, roughly speaking, a number system in which it makes sense to add, subtract, multiply, divide, and exponentiate numbers. Formally, a ...
Fields
https://brilliant.org
Fields are useful in forming the scalars in a given vector space; for instance, polynomials can draw coefficients from the field of real numbers, but also may ...
MAT 240
https://www.math.toronto.edu
Fields. Definition. A field is a set F, containing at least two elements, on which two operations. + and · (called addition and multiplication, respectively) ...