## 5.325. power

Origin
Constraint

Synonym

$\mathrm{\pi ‘\pi \pi ‘\pi \pi ’\pi \pi \pi £}$.

Arguments
 $\mathrm{\pi }$ $\mathrm{\pi \pi \pi \pi }$ $\mathrm{\pi ½}$ $\mathrm{\pi \pi \pi \pi }$ $\mathrm{\pi }$ $\mathrm{\pi \pi \pi \pi }$
Restrictions
 $\mathrm{\pi }\beta ₯0$ $\mathrm{\pi ½}\beta ₯0$ $\mathrm{\pi }\beta ₯0$
Purpose

Enforce the fact that $\mathrm{\pi }$ is equal to ${\mathrm{\pi }}^{\mathrm{\pi ½}}$.

Example
$\left(2,3,8\right)$

The constraint holds since 8 is equal to ${2}^{3}$.

Typical
 $\mathrm{\pi }>1$ $\mathrm{\pi ½}>1$ $\mathrm{\pi ½}<5$ $\mathrm{\pi }>1$
Arg. properties

Functional dependency: $\mathrm{\pi }$ determined by $\mathrm{\pi }$ and $\mathrm{\pi ½}$.

Algorithm

InΒ [DenmatGotliebDucasse07] a filtering algorithm for the constraint was automatically derived from the algorithm that multiplies $\mathrm{\pi }$ by itself $\mathrm{\pi ½}$ times by using constructive disjunction and abstract interpretation in order to approximate the behaviour of the while loop of that algorithm.

Systems