Rename (relational algebra)

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

• Template:Mvar is a relation
• Template:Mvar and Template:Mvar are attribute names
• Template:Mvar is an attribute of Template:Mvar

The result is identical to Template:Mvar except that the Template:Mvar attribute in all tuples is renamed to Template:Mvar. For an example, consider the following invocation of Template:Mvar on an Template:Math relation and the result of that invocation:

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

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

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

where $t[a/b]$ is defined as the tuple Template:Mvar, with the Template:Mvar attribute renamed to Template:Mvar, so that:

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