Editing Implicit function (section)

==In algebraic geometry==
Consider a [[relation (mathematics)|relation]] of the form {{math|1=''R''(''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>) = 0}}, where {{mvar|R}} is a multivariable polynomial. The set of the values of the variables that satisfy this relation is called an [[implicit curve]] if {{math|1=''n'' = 2}} and an '''[[implicit surface]]''' if {{math|1=''n'' = 3}}. The implicit equations are the basis of [[algebraic geometry]], whose basic subjects of study are the simultaneous solutions of several implicit equations whose left-hand sides are polynomials. These sets of simultaneous solutions are called [[affine algebraic set]]s.