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单词 AlgebraicEquation
释义

algebraic equation


The equation

f(x1,x2,,xm)=0,

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.

Titlealgebraic equation
Canonical nameAlgebraicEquation
Date of creation2013-03-22 15:14:07
Last modified on2013-03-22 15:14:07
OwnerPrimeFan (13766)
Last modified byPrimeFan (13766)
Numerical id7
AuthorPrimeFan (13766)
Entry typeDefinition
Classificationmsc 13P05
Classificationmsc 11C08
Classificationmsc 12E05
Related topicEquation
Related topicPolynomialEquationOfOddDegree
Related topicSymmetricQuarticEquation
Definesdegree of equation
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更新时间:2025/5/4 11:32:23