algebraic equation

The equation

 $f(x_{1},\,x_{2},\,...,\,x_{m})=0,$

where the left hand 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  $x^{3}+x^{2}y+xy^{2}+y^{3}=0$  are algebraic equations over the field $\mathbb{Q}$, the degrees of which are 2 and 3.

 Title algebraic equation Canonical name AlgebraicEquation Date of creation 2013-03-22 15:14:07 Last modified on 2013-03-22 15:14:07 Owner PrimeFan (13766) Last modified by PrimeFan (13766) Numerical id 7 Author PrimeFan (13766) Entry type Definition Classification msc 13P05 Classification msc 11C08 Classification msc 12E05 Related topic Equation Related topic PolynomialEquationOfOddDegree Related topic SymmetricQuarticEquation Defines degree of equation
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