Expansion of the relational algebra

Traditionally, the relational algebra uses four groups of operations as follows: the set operations, the selection and projection, the different kinds of the joins, and the rename. There are several operational identities which are very useable in the query optimization processes of database systems. The experience of practical usage of databases has showed that the expansion of the classical relational algebra is required. The new operations are: sorting, grouping, aggregations, extension of the projection, and extension of the join. Several operational identities have been introduced in the expanded relational algebra. Based on this knowledge we are able to growing the effectiveness of the database systems. This is a remarkable retroactivity from the practice to the development of the theory. The paper is devoted to demonstrate the development of the relational algebra springing from the practice.