Editing General position (section)

{{Use American English|date = January 2019}}
{{Short description|Concept in algebraic geometry}}
{{refimprove|date=May 2014}}

In [[algebraic geometry]] and [[computational geometry]], '''general position''' is a notion of [[generic property|genericity]] for a set of points, or other geometric objects. It means the ''general case'' situation, as opposed to some more special or coincidental cases that are possible, which is referred to as '''special position'''. Its precise meaning differs in different settings.

For example, generically, two lines in the plane intersect in a single point (they are not parallel or coincident). One also says "two generic lines intersect in a point", which is formalized by the notion of a ''[[generic point]]''. Similarly, three generic points in the plane are not [[Line (geometry)|collinear]]; if three points are collinear (even stronger, if two coincide), this is a [[degeneracy (mathematics)|degenerate case]].

This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating general [[theorem]]s or giving precise statements thereof, and when writing [[computer program]]s (see ''[[Generic-case complexity|generic complexity]]'').