5.273. product_ctr

DESCRIPTIONLINKSGRAPH
Origin

Arithmetic constraint.

Constraint

πš™πš›πš˜πšπšžπšŒπš_πšŒπšπš›(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,π™²πšƒπš,πš…π™°πš)

Arguments
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšŸπšŠπš›-πšπšŸπšŠπš›)
π™²πšƒπšπšŠπšπš˜πš–
πš…π™°πšπšπšŸπšŠπš›
Restrictions
πš›πšŽπššπšžπš’πš›πšŽπš(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšŸπšŠπš›)
π™²πšƒπšβˆˆ[=,β‰ ,<,β‰₯,>,≀]
Purpose

Constraint the product of a set of domain variables. More precisely, let 𝙿 denote the product of the variables of the πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ collection. Enforce the following constraint to hold: 𝙿 π™²πšƒπš πš…π™°πš.

Example
(2,1,4,=,8)

The πš™πš›πš˜πšπšžπšŒπš_πšŒπšπš› constraint holds since its last argument πš…π™°πš=8 is equal (i.e.,Β π™²πšƒπš is set to =) to 2Β·1Β·4.

Symmetry

Items of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ are permutable.

Used in

πšŒπšžπš–πšžπš•πšŠπšπš’πšŸπšŽ_πš™πš›πš˜πšπšžπšŒπš.

See also

common keyword: πš›πšŠπš—πšπšŽ_πšŒπšπš›, πšœπšžπš–_πšŒπšπš›Β (arithmetic constraint).

Keywords

characteristic of a constraint: product.

constraint type: arithmetic constraint.

Arc input(s)

πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚

Arc generator
π‘†πΈπΏπΉβ†¦πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšŸπšŠπš›πš’πšŠπš‹πš•πšŽπšœ)

Arc arity
Arc constraint(s)
πšƒπšπš„π™΄
Graph property(ies)
ππ‘πŽπƒ(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšŸπšŠπš›) π™²πšƒπš πš…π™°πš

Graph model

Since we want to keep all the vertices of the initial graph we use the 𝑆𝐸𝐿𝐹 arc generator together with the πšƒπšπš„π™΄ arc constraint. This predefined arc constraint always holds.

PartsΒ (A) andΒ (B) of FigureΒ 5.273.1 respectively show the initial and final graph associated with the Example slot. Since we use the πšƒπšπš„π™΄ arc constraint both graphs are identical.

Figure 5.273.1. Initial and final graph of the πš™πš›πš˜πšπšžπšŒπš_πšŒπšπš› constraint
ctrs/product_ctrActrs/product_ctrB
(a) (b)