## 5.129. distance

Origin

Arithmetic constraint.

Constraint

$\mathrm{𝚍𝚒𝚜𝚝𝚊𝚗𝚌𝚎}\left(𝚇,𝚈,𝚉\right)$

Arguments
 $𝚇$ $\mathrm{𝚍𝚟𝚊𝚛}$ $𝚈$ $\mathrm{𝚍𝚟𝚊𝚛}$ $𝚉$ $\mathrm{𝚍𝚟𝚊𝚛}$
Restriction
$𝚉\ge 0$
Purpose

Enforce the fact that $𝚉$ is equal to $|𝚇-𝚈|$.

Example
$\left(5,7,2\right)$

The $\mathrm{𝚍𝚒𝚜𝚝𝚊𝚗𝚌𝚎}$ constraint holds since $2=|5-7|$.

Typical
$𝚉>0$
Symmetry

Arguments are permutable w.r.t. permutation $\left(𝚇,𝚈\right)$ $\left(𝚉\right)$.

Arg. properties

Functional dependency: $𝚉$ determined by $𝚇$ and $𝚈$.

Systems
related: $\mathrm{𝚊𝚕𝚕}_\mathrm{𝚖𝚒𝚗}_\mathrm{𝚍𝚒𝚜𝚝}$ (fixed minimum distance between all pairs of variables of a collection of variables), $\mathrm{𝚜𝚖𝚘𝚘𝚝𝚑}$.