relational algebra

the basic set of operations for the formal relational model is the relational algebra. these operations enable a user to specify basic retrieval requests as relational algebra expressions. the result of a retrieval query is a new relation. the algebra operations thus produce new relations, which can be further manipulated using operations of the same algebra. a sequence of relational algebra operations forms a relational algebra expression, whose result will also be a relation that represents the result of a database query (or retrieval request).
[cite:@elmasri_db_2015 chapter 8 the relational algebra and relational calculus]

the operations of relational algebra include:

• set operations
• select operation
• project operation
• rename operation
• division operation
• join operation
  • [[blk:1704909500][semi join]]
  • [[blk:1704910986][outer join]]
  • [[blk:1704911074][inner join]]
  • [[blk:1704810819][natural join]]
• outer union
• insert operation
• delete operation
• update operation

the set of relational algebra operations is a complete set; that is, any of the other original relational algebra operations can be expressed as a sequence of operations from this set.
[cite:@elmasri_db_2015 chapter 8.3.3 a complete set of relational algebra operations]