## 5.273. product_ctr

 DESCRIPTION LINKS GRAPH
Origin

Arithmetic constraint.

Constraint

$\mathrm{\pi \pi \pi \pi \pi \pi \pi }_\mathrm{\pi \pi \pi }\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi },\mathrm{\pi ²\pi \pi },\mathrm{\pi  \pi °\pi }\right)$

Arguments
 $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi }-\mathrm{\pi \pi \pi \pi }\right)$ $\mathrm{\pi ²\pi \pi }$ $\mathrm{\pi \pi \pi \pi }$ $\mathrm{\pi  \pi °\pi }$ $\mathrm{\pi \pi \pi \pi }$
Restrictions
 $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$$\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi },\mathrm{\pi \pi \pi }\right)$
Purpose

Constraint the product of a set of domain variables. More precisely, let $\mathrm{\pi Ώ}$ denote the product of the variables of the $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ collection. Enforce the following constraint to hold: $\mathrm{\pi Ώ}\mathrm{\pi ²\pi \pi }\mathrm{\pi  \pi °\pi }$.

Example
$\left(β©2,1,4βͺ,=,8\right)$

The $\mathrm{\pi \pi \pi \pi \pi \pi \pi }_\mathrm{\pi \pi \pi }$ constraint holds since its last argument $\mathrm{\pi  \pi °\pi }=8$ is equal (i.e.,Β $\mathrm{\pi ²\pi \pi }$ is set to $=$) to $2Β·1Β·4$.

Symmetry

Items of $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ are permutable.

Used in
See also
Keywords
Arc input(s)

$\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$

Arc generator
$\mathrm{\pi \pi Έ\pi Ώ\pi Ή}$$\beta ¦\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi }\right)$

Arc arity
Arc constraint(s)
$\mathrm{\pi \pi \pi \pi ΄}$
Graph property(ies)
$\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi },\mathrm{\pi \pi \pi }\right)\mathrm{\pi ²\pi \pi }\mathrm{\pi  \pi °\pi }$

Graph model

Since we want to keep all the vertices of the initial graph we use the $\mathrm{\pi \pi Έ\pi Ώ\pi Ή}$ arc generator together with the $\mathrm{\pi \pi \pi \pi ΄}$ arc constraint. This predefined arc constraint always holds.

PartsΒ (A) andΒ (B) of FigureΒ 5.273.1 respectively show the initial and final graph associated with the Example slot. Since we use the $\mathrm{\pi \pi \pi \pi ΄}$ arc constraint both graphs are identical.