algebra

# algebra - R el a ti ona l Al gebr a Ch 6.1-6.5 Yi Chen Dept...

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Relational Algebra (Ch 6.1-6.5 ) Yi Chen Dept of Computer Science & Engineering Arizona State University

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CSE 412 2 Query Relational Databases We have discussed SQL, the industry-standard query  language, for relational databases. Now we will discuss two formal query languages Relational algebra is a procedural language, giving the  operations to retrieve the data from the database. Relational calculus is a declarative (nonprocedural)  query language, indicating the properties of the data to  retrieve from the database.
CSE 412 3 Outline Six Fundamental Operators Union Difference cartesian_product Selection Projection Rename Additional Operators Intersection θ -join natural_join division

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CSE 412 4 SIX FUNDAMENTAL OPERATORS Let r and s be relations with schemas R  and S,  respectively union:    s = { t | t   r   t   s }  difference: r - s = { t | t   r   t   s} cartesian_product:                                      r  ×  s = { t | t = t r  t s  where  t r    r   t s    s }  selection: σ   P (r) projection: π   A (r)
CSE 412 5 UNIVERSITY EXAMPLE Schema & Instance eee_majors id name class 2222 Student2 SO 4444 Student4 SR 6666 Student6 SR cse_profs name office Prof1 Office1 Prof2 Office2 cse_courses crsid crstitle CSE412 Database Management CSE513 Rules in Database Systems CSE514 Object Oriented Databases cse_majors id class 1111 Student1 FR Student2 SO 3333 Student3 JR Student4 SR 5555 Student5 GR teaches tname tcrsid Prof1 CSE412 Prof1 CSE513 Prof2 CSE514

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CSE 412 6 UNION r s = { t | t t s } Compatibility Restriction: r and s must be compatible the relations r and s must be of  the same arity (number of  attributes)  the domains of the ith attribute  of r must be the same as the  ith attribute of s Philosophy:  You shouldn't union together  relations that don't belong  together.  EXAMPLE Query: List the student information  for either computer science  or electrical engineering  majors.  Answer: cse_majors   eee_majors Schema: { id, name, class }
CSE 412 7 UNION Example Query Result id name class 1111 Student1 FR 2222 Student2 SO 3333 Student3 JR 4444 Student4 SR 5555 Student5 GR 6666 Student6 SR

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CSE 412 8 DIFFERENCE r - s = { t | t r t s} Restriction:  r and s must be  compatible  EXAMPLE Query : List  the  student  information for computer science majors, who are not double majors in electrical engineering. Answer : cse_majors - eee_majors Schema : { id, name, class }
CSE 412 9 DIFFERENCE Example Query Result id name class 1111 Student1 FR 3333 Student3 JR 5555 Student5 GR

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CSE 412 10 CARTESIAN PRODUCT r × s = { t | t = t r t s where t r t s s } Let  n r  and  n s  denote  the number of tuples in r and s There are n r  * n s
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algebra - R el a ti ona l Al gebr a Ch 6.1-6.5 Yi Chen Dept...

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