## 5.406. twin

Origin

Pairs of variables related by hiden $\mathrm{\pi \pi \pi \pi \pi \pi \pi }$ constraints sharing the same table.

Constraint

Argument
 $\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }$ $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi ‘}-\mathrm{\pi \pi \pi \pi },\mathrm{\pi ’}-\mathrm{\pi \pi \pi \pi }\right)$
Restrictions
 $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi },\mathrm{\pi ‘}\right)$ $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi },\mathrm{\pi ’}\right)$ $|\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }|>0$
Purpose

Enforce the condition $\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }\left[i\right].\mathrm{\pi ‘}=u\beta §\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }\left[i\right].\mathrm{\pi ’}=v\left(i\beta \left[1,|\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }|\right]\right)\beta \beta j\beta \left[1,|\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }|\right]:\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }\left[j\right].\mathrm{\pi ‘}=u\beta \mathrm{\pi Ώ\pi °\pi Έ\pi \pi }\left[j\right].\mathrm{\pi ’}=v$.

Example
$\left(\begin{array}{c}β©\begin{array}{cc}\mathrm{\pi ‘}-1\hfill & \mathrm{\pi ’}-8,\hfill \\ \mathrm{\pi ‘}-9\hfill & \mathrm{\pi ’}-6,\hfill \\ \mathrm{\pi ‘}-1\hfill & \mathrm{\pi ’}-8,\hfill \\ \mathrm{\pi ‘}-5\hfill & \mathrm{\pi ’}-0,\hfill \\ \mathrm{\pi ‘}-6\hfill & \mathrm{\pi ’}-7,\hfill \\ \mathrm{\pi ‘}-9\hfill & \mathrm{\pi ’}-6\hfill \end{array}βͺ\hfill \end{array}\right)$

The constraint holds since 1 is paired with 8, 9 is paired with 6, 5 is paired with 0, 6 is paired with 7.

Typical
 $|\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }|>1$ $|\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }|>$$\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }.\mathrm{\pi ‘}\right)$ $|\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }|>$$\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }.\mathrm{\pi ’}\right)$ $\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }.\mathrm{\pi ‘}\right)>1$ $\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }.\mathrm{\pi ’}\right)>1$ $\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }.\mathrm{\pi ‘}\right)=$$\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }.\mathrm{\pi ’}\right)$ $\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }.\mathrm{\pi ‘}\right)<|\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }|$ $\mathrm{\pi \pi \pi \pi }$$\left(\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }.\mathrm{\pi ’}\right)<|\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }|$
Arg. properties

Contractible wrt. $\mathrm{\pi Ώ\pi °\pi Έ\pi \pi }$.

related: $\mathrm{\pi \pi \pi \pi \pi \pi \pi }$Β (pairs linked by an element with the same table).