Extended Relational Algebra

Extended Relational Algebra increases power over basic relational algebra by adding new features and capabilities.

Normal Projection only projects specific columns from a relation.

Generalized Projection

Normal Projection only projects specific columns from a relation.

Generalized Projection extends this by allowing arithmetic operations on the projected columns.

Notation:

⇒ E is any relational-algebra expression.

⇒ Each F1, F2, ..., Fn is an arithmetic expression involving constants and attributes in the schema of E.

Ex:

Ex:

Ex:

Aggregate Functions take a collection of values and return a single value as a result. Common aggregate functions include:

⇒ avg: Average value

⇒ min: Minimum value

⇒ max: Maximum value

⇒ sum: Sum of values

⇒ count: Number of values

⇒ These operations can be applied to the entire relation or to certain groups of tuples. They ignore NULL values, except for count.

Generalized Form (g) of Aggregate Operation:

⇒ E is any relational-algebra expression.

⇒ G1, G2, ..., Gn is a list of attributes on which to group (can be empty).

⇒ Each Fi is an aggregate function.

⇒ Each Ai is an attribute name.

⇒ The result of aggregation does not have a name by default. Use the rename operation to give it a name.

⇒ For convenience, we permit renaming as part of the aggregate operation using the AS keyword.