Editing Third normal form (section)

== Computation ==
A relation can always be decomposed in third normal form, that is, the relation R is rewritten to [[relational projection|projections]] R<sub>1</sub>, ..., R<sub>n</sub> whose [[natural join|join]] is equal to the original relation. Further, this decomposition does not lose any [[functional dependencies|functional dependency]], in the sense that every functional dependency on R can be derived from the functional dependencies that hold on the projections R<sub>1</sub>, ..., R<sub>n</sub>. What is more, such a decomposition can be computed in [[polynomial time]].<ref>[[Serge Abiteboul]], Richard B. Hull, [[Victor Vianu]]: Foundations of Databases. Addison-Wesley, 1995. http://webdam.inria.fr/Alice/ {{ISBN|0201537710}}. Theorem 11.2.14.</ref>

To decompose a relation into 3NF from 2NF, break the table into the [[canonical cover]] functional dependencies, then create a relation for every candidate key of the original relation which was not already a subset of a relation in the decomposition.<ref>{{Cite web |last=Hammo |first=Bassam |title=Decomposition, 3NF, BCNF |url=https://faculty.ksu.edu.sa/sites/default/files/E-%20Decomposition.pdf |archive-url=https://web.archive.org/web/20230315013047/https://faculty.ksu.edu.sa/sites/default/files/E-%20Decomposition.pdf |archive-date=2023-03-15 |url-status=live }}</ref>