5.390. sum_powers5_ctr

DESCRIPTIONLINKS
Origin

Arithmetic constraint.

Constraint

πšœπšžπš–_πš™πš˜πš πšŽπš›πšœ5_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)

Synonyms

πšœπšžπš–_πš™πš˜πš πšŽπš›πšœ5, πšœπšžπš–_𝚘𝚏_πš™πš˜πš πšŽπš›πšœ5, πšœπšžπš–_𝚘𝚏_πš™πš˜πš πšŽπš›πšœ5_πšŒπš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 sum of the power of five of a set of domain variables. More precisely, let πš‚ denote the sum of the power of five of the variables of the πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ collection (when the collection is empty the corresponding sum is equal to 0). Enforce the following constraint to hold: πš‚ π™²πšƒπš πš…π™°πš.

Example
(1,1,2,=,34)

The πšœπšžπš–_πš™πš˜πš πšŽπš›πšœ5_πšŒπšπš› constraint holds since the condition 1 5 +1 5 +2 5 =34 is satisfied.

Typical
|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|>1
πš›πšŠπš—πšπšŽ(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš›)>1
π™²πšƒπšβˆˆ[=,<,β‰₯,>,≀]
Symmetry

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

Arg. properties
  • Contractible wrt. πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ when π™²πšƒπšβˆˆ[<,≀] and πš–πš’πš—πšŸπšŠπš•(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš›)β‰₯0.

  • Contractible wrt. πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ when π™²πšƒπšβˆˆ[β‰₯,>] and πš–πšŠπš‘πšŸπšŠπš•(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš›)≀0.

  • Extensible wrt. πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ when π™²πšƒπšβˆˆ[β‰₯,>] and πš–πš’πš—πšŸπšŠπš•(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš›)β‰₯0.

  • Extensible wrt. πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ when π™²πšƒπšβˆˆ[<,≀] and πš–πšŠπš‘πšŸπšŠπš•(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš›)≀0.

  • Aggregate: πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚(πšžπš—πš’πš˜πš—), π™²πšƒπš(πš’πš), πš…π™°πš(+).

See also

common keyword: πšœπšžπš–_πšŒπšπš›, πšœπšžπš–_πšŒπšžπš‹πšŽπšœ_πšŒπšπš›, πšœπšžπš–_πš™πš˜πš πšŽπš›πšœ4_πšŒπšπš›, πšœπšžπš–_πš™πš˜πš πšŽπš›πšœ6_πšŒπšπš›, πšœπšžπš–_πšœπššπšžπšŠπš›πšŽπšœ_πšŒπšπš›Β (sum).

Keywords

characteristic of a constraint: sum.

constraint type: predefined constraint, arithmetic constraint.