## 5.136. geq

Origin

Arithmetic.

Constraint

$\mathrm{𝚐𝚎𝚚}\left(\mathrm{𝚅𝙰𝚁}\mathtt{1},\mathrm{𝚅𝙰𝚁}\mathtt{2}\right)$

Synonyms

$\mathrm{𝚛𝚎𝚕}$, $\mathrm{𝚡𝚐𝚝𝚎𝚚𝚢}$.

Arguments
 $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ $\mathrm{𝚍𝚟𝚊𝚛}$ $\mathrm{𝚅𝙰𝚁}\mathtt{2}$ $\mathrm{𝚍𝚟𝚊𝚛}$
Purpose

Enforce the fact that the first variable is greater than or equal to the second variable.

Example
$\left(8,1\right)$

The $\mathrm{𝚐𝚎𝚚}$ constraint holds since 8 is greater than or equal to 1.

Typical
$\mathrm{𝚅𝙰𝚁}\mathtt{1}>\mathrm{𝚅𝙰𝚁}\mathtt{2}$
Symmetries
• $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ can be replaced by any value $\ge \mathrm{𝚅𝙰𝚁}\mathtt{2}$.

• $\mathrm{𝚅𝙰𝚁}\mathtt{2}$ can be replaced by any value $\le \mathrm{𝚅𝙰𝚁}\mathtt{1}$.

Systems

geq in Choco, rel in Gecode, xgteqy in JaCoP, #>= in SICStus.

generalisation: $\mathrm{𝚐𝚎𝚚}_\mathrm{𝚌𝚜𝚝}$ ($\mathrm{𝚌𝚘𝚗𝚜𝚝𝚊𝚗𝚝}$ added).