## 5.418. vec_eq_tuple

Origin
Constraint

$\mathrm{\pi \pi \pi }_\mathrm{\pi \pi }_\mathrm{\pi \pi \pi \pi \pi }\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi },\mathrm{\pi \pi \pi Ώ\pi »\pi ΄}\right)$

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

Enforce a vector of domain variables to be equal to a tuple of values.

Example
$\left(β©5,3,3βͺ,β©5,3,3βͺ\right)$

The $\mathrm{\pi \pi \pi }_\mathrm{\pi \pi }_\mathrm{\pi \pi \pi \pi \pi }$ constraint holds since the first, the second and the third items of $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }=\beta ©5,3,3\beta ͺ$ are respectively equal to the first, the second and the third items of $\mathrm{\pi \pi \pi Ώ\pi »\pi ΄}=\beta ©5,3,3\beta ͺ$.

Typical
 $|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|>1$ $\mathrm{\pi \pi \pi \pi \pi }$$\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }.\mathrm{\pi \pi \pi }\right)>1$ $\mathrm{\pi \pi \pi \pi \pi }$$\left(\mathrm{\pi \pi \pi Ώ\pi »\pi ΄}.\mathrm{\pi \pi \pi }\right)>1$
Symmetries
• Arguments are permutable w.r.t. permutation $\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi },\mathrm{\pi \pi \pi Ώ\pi »\pi ΄}\right)$.

• Items of $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ and $\mathrm{\pi \pi \pi Ώ\pi »\pi ΄}$ are permutable (same permutation used).

Arg. properties

Contractible wrt. $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ and $\mathrm{\pi \pi \pi Ώ\pi »\pi ΄}$ (remove items from same position).

Used in

generalisation: $\mathrm{\pi \pi \pi ‘}_\mathrm{\pi \pi \pi \pi \pi }$Β ($\mathrm{\pi \pi \pi \pi \pi \pi \pi }$ replaced by $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$ in second argument).

Keywords
Arc input(s)

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

Arc generator
$\mathrm{\pi \pi  \pi \pi ·\pi \pi Ά\pi }$$\left(=\right)\beta ¦\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi },\mathrm{\pi \pi \pi \pi \pi }\right)$

Arc arity
Arc constraint(s)
$\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi }.\mathrm{\pi \pi \pi }=\mathrm{\pi \pi \pi \pi \pi }.\mathrm{\pi \pi \pi }$
Graph property(ies)
$\mathrm{\pi \pi \pi \pi }$$=|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|$

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.418.1 respectively show the initial and final graph associated with the Example slot. Since we use the $\mathrm{\pi \pi \pi \pi }$ graph property, the arcs of the final graph are stressed in bold.

Signature

Since we use the arc generator $\mathrm{\pi \pi  \pi \pi ·\pi \pi Ά\pi }\left(=\right)$ on the collections $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ and $\mathrm{\pi \pi \pi Ώ\pi »\pi ΄}$, and because of the restriction $|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|=|\mathrm{\pi \pi \pi Ώ\pi »\pi ΄}|$, the maximum number of arcs of the final graph is equal to $|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|$. Therefore we can rewrite the graph property $\mathrm{\pi \pi \pi \pi }=|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|$ to $\mathrm{\pi \pi \pi \pi }\beta ₯|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|$ and simplify $\underset{Μ²}{\stackrel{Β―}{\mathrm{\pi \pi \pi \pi }}}$ to $\stackrel{Β―}{\mathrm{\pi \pi \pi \pi }}$.