Editing Equation (section)

===Algebraic geometry===
{{main|Algebraic geometry}}
[[Algebraic geometry]] is a branch of [[mathematics]], classically studying solutions of [[polynomial equations]]. Modern algebraic geometry is based on more abstract techniques of [[abstract algebra]], especially [[commutative algebra]], with the language and the problems of [[geometry]].

The fundamental objects of study in algebraic geometry are [[algebraic variety|algebraic varieties]], which are geometric manifestations of [[solution set|solutions]] of [[systems of polynomial equations]]. Examples of the most studied classes of algebraic varieties are: [[plane algebraic curve]]s, which include [[line (geometry)|lines]], [[circle]]s, [[parabola]]s, [[ellipse]]s, [[hyperbola]]s, [[cubic curve]]s like [[elliptic curve]]s and quartic curves like [[lemniscate of Bernoulli|lemniscates]], and [[Cassini oval]]s. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the [[singular point of a curve|singular points]], the [[inflection point]]s and the [[point at infinity|points at infinity]]. More advanced questions involve the [[topology]] of the curve and relations between the curves given by different equations.