Metraipolis › archive › dc_71bb44ff8683

Lattice reduction — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Lattice_reduction
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T17:40:05.718Z
SHA-256 of the archived text: e269717c042065e85f9a3dd6f31980598e7b822e1e0d549dda297dc85fbce484
Stable URL of this page: https://metraipolis.com/documento/dc_71bb44ff8683

How to cite

Lattice reduction — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Lattice_reduction (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_71bb44ff8683 (Metraipolis archive dc_71bb44ff8683, sha256 e269717c042065e85f9a3dd6f31980598e7b822e1e0d549dda297dc85fbce484)

BibTeX

@misc{dc71bb44ff8683,
  title = {Lattice reduction — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Lattice_reduction},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_71bb44ff8683; sha256 e269717c042065e85f9a3dd6f31980598e7b822e1e0d549dda297dc85fbce484},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Lattice_reduction. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice. Finding a reduced lattice basis is also closely related to the problem in crystallography of finding a unique unit cell. Historically reduction theory was first studied by Lagrange (1773) and independently by Gauss (1801), in order to classify binary quadratic forms, a classic problem in number theory. In a little sidenote to a book review in 1831, Gauss mentions that the reduction theory for certain quadratic forms is equivalent to finding a unit cell for point lattices and he sees the relevance for crystallography. This close relationship in number theory and geometry of point lattices inspired much of the successive work on quadratic forms culminating in Minkowski's important work "Geometry of Numbers" (1896 and 1910).

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Linear algebra»).
Fonte: Wikipedia in inglese, voce «Lattice reduction» — https://en.wikipedia.org/wiki/Lattice_reduction
Wikidata Q6497132 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q6497132
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Lattice_reduction?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1373729309, consultata il 2026-10-15T16:35:25.896Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 1fb4f2a8bb70ab327869f82569333ef6ccaac021902c399b2d87fc5f18e1964f