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[parent] algebraic equation (Definition)

The equation

$\displaystyle f(x_1,\,x_2,\,...,\,x_m) = 0,$
where the left hand side is a polynomial in $ x_1$, $ x_2$, ..., $ x_m$ with coefficients in a certain field, is called an algebraic equation over that field. Often the field in question is $ \mathbb{Q}$; then the coefficients may be assumed to be integers.

By the degree of an algebraic equation is meant the degree of the polynomial.

E.g. $ 3x^2-1 = 0$ and $ x^3+x^2y+xy^2+y^3 = 0$ are algebraic equations over the field $ \mathbb{Q}$, the degrees of which are 2 and 3.



"algebraic equation" is owned by PrimeFan. [ owner history (3) ]
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See Also: equation, polynomial equation of odd degree


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binomial equation (Definition) by pahio
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Cross-references: degree, integers, field, coefficients, polynomial, equation
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This is version 3 of algebraic equation, born on 2005-05-04, modified 2008-01-29.
Object id is 7006, canonical name is AlgebraicEquation.
Accessed 3718 times total.

Classification:
AMS MSC12E05 (Field theory and polynomials :: General field theory :: Polynomials )
 11C08 (Number theory :: Polynomials and matrices :: Polynomials)
 13P05 (Commutative rings and algebras :: Computational aspects of commutative algebra :: Polynomials, factorization)

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