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Database Systems: Chapter 6: Relational Algebra Dr. Taysir Hassan Abdel Hamid Lecturer, IS Department Faculty of Computer and Information Assiut University Contact: [email_address] March 30, 2008

Operations in Relational Algebra ,[object Object],[object Object],[object Object],[object Object],[object Object]

Unary Relational Operations SELECT ,[object Object],[object Object],[object Object]

Select Operator ,[object Object],[object Object],1123 John 123 Main stamps 1123 John 123 Main coins 5556 Mary 7 Lake Dr hiking 9876 Bart 5 Pine St stamps 1123 John 123 Main stamps 9876 Bart 5 Pine St stamps Person Id Name Address Hobby ,[object Object]

Selection Condition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],Selection Condition - Examples

[object Object],[object Object]

Projection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Union ,[object Object],[object Object],[object Object],[object Object],[object Object]

Intersection ,[object Object],[object Object],[object Object]

Difference ,[object Object],[object Object],[object Object],[object Object]

Union Compatible Relations ,[object Object],[object Object],[object Object],[object Object],[object Object]

Example Tables: Person (SSN, Name, Address, Hobby) Professor (Id, Name, Office, Phone) are not union compatible. However

Cartesian Product ,[object Object],[object Object],[object Object],[object Object],[object Object],a b c d a b c d x1 x2 y1 y2 x1 x2 y1 y2 x3 x4 y3 y4 x1 x2 y3 y4 x3 x4 y1 y2 R S x3 x4 y3 y4 R  S

Renaming ,[object Object],[object Object],[object Object],[object Object]

Example This is a relation with 4 attributes: StudId, SCrsCode, ProfId, PCrsCode

Derived Operation: Join The expression :  join-condition ´ (R  S) where join-condition ´ is a conjunction of terms: A i oper B i in which A i is an attribute of R, B i is an attribute of S, and oper is one of =, <, >,   ,  , is referred to as the (theta) join of R and S and denoted: R join-condition S Where join-condition and join-condition ´ are (roughly) the same …

Join and Renaming ,[object Object],[object Object],[object Object],[object Object]

Theta Join – Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Equijoin Join - Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Natural Join ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Natural Join (con’t) ,[object Object],R S =  attr-list (  join-cond (R × S) ) where attr-list = attributes (R)  attributes (S) (duplicates are eliminated) and join-cond has the form: A 1 = A 1 AND … AND A n = A n where {A 1 … A n } = attributes(R)  attributes(S)

Natural Join Example ,[object Object], StudId (  CrsCode  CrsCode2 ( Transcript Transcript [StudId, CrsCode2, Sem2, Grade2])) (don’t join on CrsCode, Sem, and Grade attributes)

Division ,[object Object],[object Object],[object Object],[object Object],[object Object]

Division - Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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