Algebraic Equation
An algebraic equation in n variables is an polynomial equation of the form
where the coefficients c_(e_1,e_2,...,e_n) are integers (where the exponents e_i are nonnegative integers and the sum is finite).
Examples of algebraic equations are given in the following table.
curve equation
Cayley's sextic 4(x^2+y^2-x)^3-27(x^2+y^2)^2=0
eight curve x^4-(x^2-y^2)=0
line through (1,0) and (0,1) x+y-1=0
plane
through (1,0,0), x+y+z-1=0
(0,1,0), and (0,0,1)
unit circle x^2+y^2-1=0
unit
sphere x^2+y^2+z^2-1=0
The roots of an algebraic equation in one variable are known as algebraic numbers.
See also
Algebraic Expression, Algebraic Function, Algebraic Number, Conjugate Elements, Equation, Gröbner Basis, Integer Polynomial, Irreducible Polynomial, Polynomial, Polynomial Roots, Transcendental EquationPortions of this entry contributed by David Terr
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Cite this as:
Terr, David and Weisstein, Eric W. "Algebraic Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlgebraicEquation.html