Distance

distance(X::LazySet, Y::LazySet; [p]::Real=2)

Compute the standard distance (induced by the $p$-norm) between two sets.

Input

• X – set
• Y – set
• p – (optional; default: 2) value of the $p$-norm

Output

A real number representing the distance between X and Y.

Notes

The standard distance is zero if the sets intersect, and infinite if one of the sets is empty. Otherwise, it is the $p$-norm of the shortest line segment between any pair of points. Formally,

\[ \inf_{x ∈ X, y ∈ Y} \{ d(x, y) \}.\]