cover {relations}

Covering Relations

Description

Compute the covering relation of an endorelation.

Usage

relation_cover(x)

Arguments

x

an endorelation.

Details

Let R be an endorelation with domain (X, X) and P be the asymmetric part of R for which x P y iff x R y and not y R x. (If R is a \le order relation, P is the associated strict order.) We say that x is covered by y if x P y and there is no z such that x P z and z P y. One also says that y covers x, or that it is a successor of x.

The covering relation of R consists of all pairs (x, y) for which x is covered by y.