Global Constraint Catalog: Cabs

5.1. abs_value

DESCRIPTION

LINKS

Origin

Arithmetic.

Constraint

$𝚊𝚋𝚜_𝚟𝚊𝚕𝚞𝚎 (𝚈, 𝚇)$

Usual name

$𝚊𝚋𝚜$

Synonym

$𝚊𝚋𝚜𝚘𝚕𝚞𝚝𝚎_𝚟𝚊𝚕𝚞𝚎$ .

Arguments

$𝚈$	$𝚍𝚟𝚊𝚛$
$𝚇$	$𝚍𝚟𝚊𝚛$

Restriction

𝚈 \geq 0

Purpose

Enforce the fact that the first variable is equal to the absolute value of the second variable.

Example

(8, - 8)

The $𝚊𝚋𝚜_𝚟𝚊𝚕𝚞𝚎$ constraint holds since 8 is equal to $| - 8 |$ .

All solutions

Figure 5.1.1 gives all solutions to the following non ground instance of the $𝚊𝚋𝚜_𝚟𝚊𝚕𝚞𝚎$ constraint: $𝚈 \in [1, 6],$ $𝚇 \in [- 2, 3],$ $𝚊𝚋𝚜_𝚟𝚊𝚕𝚞𝚎$ $(𝚈, 𝚇)$ .

Figure 5.1.1. All solutions corresponding to the non ground example of the $𝚊𝚋𝚜_𝚟𝚊𝚕𝚞𝚎$ constraint of the All solutions slot

Arg. properties

Functional dependency: $𝚈$ determined by $𝚇$ .

Systems

abs in Choco, abs in Gecode.

See also

implied by: $𝚎𝚚$ .

implies: $𝚐𝚎𝚚$ , $𝚣𝚎𝚛𝚘_𝚘𝚛_𝚗𝚘𝚝_𝚣𝚎𝚛𝚘$ .

implies (if swap arguments): $𝚘𝚙𝚙𝚘𝚜𝚒𝚝𝚎_𝚜𝚒𝚐𝚗$ , $𝚣𝚎𝚛𝚘_𝚘𝚛_𝚗𝚘𝚝_𝚣𝚎𝚛𝚘$ .

Keywords

constraint arguments: binary constraint, pure functional dependency.

constraint type: predefined constraint, arithmetic constraint.

filtering: arc-consistency.

modelling: functional dependency.

Global Constraint Catalog

5. Global Constraint Catalogue

5.1. abs_value

Figure 5.1.1. All solutions corresponding to the non ground example of the 𝚊𝚋𝚜_𝚟𝚊𝚕𝚞𝚎 constraint of the All solutions slot

Figure 5.1.1. All solutions corresponding to the non ground example of the $𝚊𝚋𝚜_𝚟𝚊𝚕𝚞𝚎$ constraint of the All solutions slot