Rename (Relational Algebra)

relational-algebra

Definition

Rename (Relational Algebra)

The rename operation, denoted by $\rho :\text{Relation}\to \text{Relation}$, modifies the schema of a relation $R$ without altering the data within its tuples. It produces a new relation $R^{\prime }$ with either a new name for the relation itself or new names for its attributes. It is used in two primary forms:

1. Renaming a Relation
   The expression ${\rho }_S(R)$ renames the relation $R$ to $S$. The new relation $S$ has the identical schema and contains the exact same set of tuples as $R$.

   $$S={\rho }_S(R)$$

2. Renaming Attributes
   The expression ${\rho }_{A\leftarrow B}(R)$ produces a new relation $R^{\prime }$ where the attribute $B$ from $R$ is renamed to $A$. This can be extended to rename multiple attributes at once, e.g., ${\rho }_{A_1\leftarrow B_1,A_2\leftarrow B_2}(R)$.

   $$R^{\prime }={\rho }_{A\leftarrow B}(R)$$

The values and the number of tuples remain unchanged, only the attribute names in the schema are modified.