algebraic equation

The equation


where the left hand is a polynomialPlanetmathPlanetmath in x1, x2, …, xm with coefficients in a certain field, is called an algebraic equation over that field.  Often the field in question is ; 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.  3x2-1=0  and  x3+x2y+xy2+y3=0  are algebraic equations over the field , 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