Editing Relational algebra (section)

==== Selection and projection ====

Selection commutes with projection if and only if the fields referenced in the selection condition are a subset of the fields in the projection.  Performing selection before projection may be useful if the operand is a cross product or join.  In other cases, if the selection condition is relatively expensive to compute, moving selection outside the projection may reduce the number of tuples which must be tested (since projection may produce fewer tuples due to the elimination of duplicates resulting from omitted fields).

:<math>\pi_{a_1, \ldots ,a_n}(\sigma_A( R )) = \sigma_A(\pi_{a_1, \ldots,a_n}( R ))\text{ where fields in }A \subseteq \{a_1,\ldots,a_n\}</math>