# Rename (relational algebra)

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In relational algebra, a rename is a unary operation written as ${\displaystyle \rho _{a/b}(R)}$ where:

The result is identical to R except that the b attribute in all tuples is renamed to a. For an example, consider the following invocation of ρ on an Employee relation and the result of that invocation:

${\displaystyle {\text{Employee}}}$ ${\displaystyle \rho _{\text{EmployeeName/Name}}({\text{Employee}})}$
Name EmployeeId
Harry 3415
Sally 2241
EmployeeName EmployeeId
Harry 3415
Sally 2241

Formally, the semantics of the rename operator is defined as follows:

${\displaystyle \rho _{a/b}(R)=\{\ t[a/b]:t\in R\ \}}$

where ${\displaystyle t[a/b]}$ is defined as the tuple t, with the b attribute renamed to a, so that:

${\displaystyle t[a/b]=\{\ (c,v)\ |\ (c,v)\in t,\ c\neq b\ \}\cup \{\ (a,\ t(b))\ \}}$