5.174. ith_pos_different_from_0

Origin

N.Β Beldiceanu

Constraint

$\mathrm{\pi \pi \pi }_\mathrm{\pi \pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi }_\mathrm{\pi \pi \pi \pi }_\mathtt{0}\left(\mathrm{\pi Έ\pi \pi ·},\mathrm{\pi Ώ\pi Ύ\pi },\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }\right)$

Arguments
 $\mathrm{\pi Έ\pi \pi ·}$ $\mathrm{\pi \pi \pi }$ $\mathrm{\pi Ώ\pi Ύ\pi }$ $\mathrm{\pi \pi \pi \pi }$ $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi }-\mathrm{\pi \pi \pi \pi }\right)$
Restrictions
 $\mathrm{\pi Έ\pi \pi ·}\beta ₯1$ $\mathrm{\pi Έ\pi \pi ·}\beta €|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|$ $\mathrm{\pi Ώ\pi Ύ\pi }\beta ₯\mathrm{\pi Έ\pi \pi ·}$ $\mathrm{\pi Ώ\pi Ύ\pi }\beta €|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|$ $\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

$\mathrm{\pi Ώ\pi Ύ\pi }$ is the position of the ${\mathrm{\pi Έ\pi \pi ·}}^{th}$ non-zero item of the sequence of variables $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$.

Example
$\left(2,4,β©3,0,0,8,6βͺ\right)$

The $\mathrm{\pi \pi \pi }_\mathrm{\pi \pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi }_\mathrm{\pi \pi \pi \pi }_\mathtt{0}$ constraint holds since 4 corresponds to the position of the 2th non-zero item of the sequence $30086$.

Typical
 $|\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }|>1$ $\mathrm{\pi \pi \pi \pi \pi }$$\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }.\mathrm{\pi \pi \pi }\right)>1$ $\mathrm{\pi \pi \pi \pi \pi \pi \pi }$$\left(1,\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi },0\right)$
Symmetry

An occurrence of a value of $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }.\mathrm{\pi \pi \pi }$ that is different from 0 can be replaced by any other value that is also different from 0.

Keywords
Automaton

FigureΒ 5.174.1 depicts the automaton associated with the $\mathrm{\pi \pi \pi }_\mathrm{\pi \pi \pi }_\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi }_\mathrm{\pi \pi \pi \pi }_\mathtt{0}$ constraint. To each variable ${\mathrm{\pi  \pi °\pi }}_{i}$ of the collection $\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ corresponds a 0-1 signature variable ${\mathrm{\pi }}_{i}$. The following signature constraint links ${\mathrm{\pi  \pi °\pi }}_{i}$ and ${\mathrm{\pi }}_{i}$: ${\mathrm{\pi  \pi °\pi }}_{i}=0\beta {\mathrm{\pi }}_{i}$.