algebraic equation

The equation

$$f(x_1,x_2,\mathrm{\dots },x_m)=0,$$

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  $x^3+x^{2}y+x{y}^2+y^3=0$  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