Editing Relational algebra (section)

=== Rename ===

==== Basic rename properties ====

Successive renames of a variable can be collapsed into a single rename.  Rename operations which have no variables in common can be arbitrarily reordered with respect to one another, which can be exploited to make successive renames adjacent so that they can be collapsed.

#<math>\rho_{a / b}(\rho_{b / c}(R)) = \rho_{a / c}(R)\,\!</math>
#<math>\rho_{a / b}(\rho_{c / d}(R)) = \rho_{c / d}(\rho_{a / b}(R))\,\!</math>

==== Rename and set operators ====

Rename is distributive over set difference, union, and intersection.

#<math>\rho_{a / b}(R \setminus P) = \rho_{a / b}(R) \setminus \rho_{a / b}(P)</math>
#<math>\rho_{a / b}(R \cup P) = \rho_{a / b}(R) \cup \rho_{a / b}(P)</math>
#<math>\rho_{a / b}(R \cap P) = \rho_{a / b}(R) \cap \rho_{a / b}(P)</math>