Editing Relational algebra (section)

==== Aggregation ====
Furthermore, computing various functions on a column, like the summing up of its elements, is also not possible using the relational algebra introduced so far. There are five [[aggregate function]]s that are included with most relational database systems. These operations are Sum, Count, Average, Maximum and Minimum. In relational algebra the aggregation operation over a schema (''A''<sub>1</sub>, ''A''<sub>2</sub>, ... ''A''<sub>''n''</sub>) is written as follows:

:<math>G_1, G_2, \ldots, G_m\ g_{f_1({A_1}'), f_2({A_2}'), \ldots, f_k({A_k}')}\ (r)</math>

where each ''A''<sub>''j''</sub>', 1 ≤ ''j'' ≤ ''k'', is one of the original attributes ''A''<sub>''i''</sub>, 1 ≤ ''i'' ≤ ''n''.

The attributes preceding the ''g'' are grouping attributes, which function like a "group by" clause in SQL. Then there are an arbitrary number of aggregation functions applied to individual attributes. The operation is applied to an arbitrary relation ''r''. The grouping attributes are optional, and if they are not supplied, the aggregation functions are applied across the entire relation to which the operation is applied.

Let's assume that we have a table named {{mono|Account}} with three columns, namely {{mono|Account_Number, Branch_Name}} and {{mono|Balance}}. We wish to find the maximum balance of each branch. This is accomplished by <sub>{{mono|Branch_Name}}</sub>''G''<sub>Max({{mono|Balance}})</sub>({{mono|Account}}). To find the highest balance of all accounts regardless of branch, we could simply write ''G''<sub>Max({{mono|Balance}})</sub>({{mono|Account}}).

Grouping is often written as <sub>{{mono|Branch_Name}}</sub>''ɣ''<sub>Max({{mono|Balance}})</sub>({{mono|Account}}) instead.<ref name="Garcia-MolinaUllman2009" />