07.03 cartesian product

1. DBMS Relational Algebra Cartesian Product Bishal Ghimire [email protected]

2. The rename operation It is denoted as  ρ E  :  relational algebra expression ρ x (E):  returns the result of expression E under the name x. ρ x (A1, A2, A3… An) (E):  returns the result of expression E under the name x with attributes renamed to A1, A2, A3… An.

3. Rename Operator The rename operator returns an existing relation under a new name. ρ A (B) is the relation B with its name changed to A. Name EmployeeId Harry 3415 Sally 2241 EmployeeName EmployeeId Harry 3415 Sally 2241 Employee

4. Cartesian Product If R and S are two relations, R  S is the set of all concatenated tuples < x,y >, where x is a tuple in R and y is a tuple in S R and S need not be union compatible. But R and S must have distinct attribute names. Each row of R is paired with each row of S. Result schema has one field per field of S and R, with field names `inherited’ if possible.

5. Cartesian Product A B a1 b1 a2 b2 C D c1 d1 c2 d2 A B C D a1 b1 c1 d1 a1 b1 c2 d2 a2 b2 c1 d1 a2 b2 c2 d2 R S R x S

6. sID sName GPA HS sID sName major dec Student Apply Q : Names and GPAs of students with HS >1000 who applied to CS and were rejected   π sName , GPA ( σ Student.sID = Apply.sID ^ HS > 1000 ^ Major =‘ cs ’ ^ dec = ‘R’ ( Student x Apply ) )