Relational Algebra. Mr. Prasad Sawant. MACS College. Mr.Prasad Sawant MACS College Pune

Transcription

1 Relational Algebra Mr. Prasad Sawant MACS College Pune MACS College

2 Relational Algebra Tuple - a collection of attributes which describe some real world entity. Attribute - a real world role played by a named domain. Domain - a set of atomic values. Set - a mathematical definition for a collection of objects which contains no duplicates. For example consider following table student The Relational Algebra is used to define the ways in which relations (tables) can be operated to manipulate their data.it is used as the basis of SQL for relational databases, and illustrates the basic operations required of any DML.This Algebra is composed of Unary operations (involving a single table) and Binary operations (involving multiple tables).

3 There are two groups of operations: Mathematical set theory based relations: UNION, INTERSECTION, DIFFERENCE, and CARTESIAN PRODUCT. Special database operations: SELECT (not the same as SQL SELECT), PROJECT, and JOIN. Symbolic Notation Select σ Sigma Selecting certain rows Project Pi Selecting certain columns Join X Cross Compositions of relations Union U Cup -- Intersection Cap -- Differnece - Minus -- Rename ρ Rho Renaming of realtions & attribute Relational SELECT SELECT is used to obtain a subset of the tuples of a relation that satisfy a select condition. R1 := SELECT C (R2) C is a condition (as in if statements) that refers to attributes of R2. R1 is all those tuples of R2 that satisfy C. σ < condition > < tablename >

4 Example: σ course = CM Students Students stud# Course name 100 PH Fred 200 CM Dave 300 CM Bob Answer stud# Course name 200 CM Dave 300 CM Bob Example: Retrieve the Id, Name, Suburb of students who live in Bundoora Figure 11: Select Operation Example - 1 Relational PROJECT The PROJECT operation is used to select a subset of the attributes of a relation by specifying the names of the required attributes. R1 = _L(R2) R1 = project L (R2) where L is a list of attributes from the schema of R2.

5 π < column list > < tablename > Example: π stud#, name Students Students stud# Course name 100 PH Fred 200 CM Dave 300 CM Bob Answer stud# name 100 Fred 200 Dave 300 Bob Example: Retrieve the suburbs that are stored in database Figure 14: Project Operation Example - 1 S ELECT and PROJECT SELECT and PROJECT can be combined together. For example, to get a list of employee numbers for employees in department number 1: π stud#, name (σ course = CM Students)

6 Students stud# Course name 100 PH Fred 200 CM Dave 300 CM Bob Answer stud# name 200 Dave 300 Bob Set Operations Consider two relations R and S. UNION of R and S the union of two relations is a relation that includes all the tuples that are either in R or in S or in both R and S. Duplicate tuples are eliminated. INTERSECTION of R and S the intersection of R and S is a relation that includes all tuples that are both in R and S. Takes the set of rows that are common to each relation Participating relations must be compatible DIFFERENCE of R and S the difference of R and S is the relation that contains all the tuples that are in R but that are not in S. Participating relations must be compatible

7 SET Operations UNION Example Takes the set of rows in each table and combines them, eliminating duplicates Participating relations must be compatible, ie have the same number of columns, and the same column names, domains, and data types INTERSECTION Example Figure : UNION

8 DIFFERENCE Example Figure : Intersection Figure : DIFFERENCE CARTESIAN PRODUCT The Cartesian Product is also an operator which works on two sets. It is sometimes called the CROSS PRODUCT or CROSS JOIN. It combines the tuples of one relation with all the tuples of the other relation.

9 CARTESIAN PRODUCT example Figure : CARTESIAN PRODUCT Students Courses stud# Course name 100 PH Fred 200 CM Dave 300 CM Bob Course# PH CM name Pharmacy Computing Students X Courses = Stud# Student.nam e course Course# Course.nam e 100 Fred PH PH Pharmacy 100 Fred PH CM Computing 200 Dave CM PH Pharmacy 200 Dave CM CM Computing 300 Bob CM PH Pharmacy 300 Bob CM CM Computing

10 Renaming tables and columns This is represented by the lower case greek letter rho (p).the query is written to get required information but it is not possible to get name of the attribute every time. Sometimes we want to add values of two different attribute then the result attribute name is not considered. It display expr in that column. Example: Relation Employee Eid Ename Salary 1 Chayya Surekha Saniya Divya Monica 5000 If we calculate salary with 3% conveyance allowance then the query will be π Eid,Ename,salary,salary+(salary* 3/100) (EMPLOYEE)) Result Eid Ename Salary Expr 1 Chayya Surekha Saniya Divya Monica

11 To change the name of the attribute we use rename operation Syntax = ρ x (E) where x :- attribute name E :- the expression π Eid,Ename,salary, ρ Netsal (salary+(salary* 3/100)(EMPLOYEE)) Eid Ename Salary Netsal 1 Chayya Surekha Saniya Divya Monica DIVISION Operation The Divition Operation is defined on two relation This means that for a tuple t to appear in the result of Division, the values in t must appear in r in combination with every tuple in s.the Division is very useful for a special kind of query such as Retrieve the name of the student who enrolls in all course teach by Professor Ba Example: Retrieve the name of subject that is taught in all courses Figure 22: Division Operation Example

12 JOIN Operator JOIN is used to combine related tuples from two relations: In its simplest form the JOIN operator is just the cross product of the two relations. As the join becomes more complex, tuples are removed within the cross product to make the result of the join more meaningful. JOIN allows you to evaluate a join condition between the attributes of the relations on which the join is undertaken. The notation used is R JOIN join condition S JOIN Example Figure : JOIN Natural Join the JOIN involves an equality test, and thus is often described as an equi-join. Such joins result in two attributes in the resulting relation having exactly the same value. A `natural join' will remove the duplicate attribute(s).

13 If you do use natural joins make sure that the relations do not have two attributes with the same name by accident. OUTER JOINs Notice that much of the data is lost when applying a join to two relations. In some cases this lost data might hold useful information. An outer join retains the information that would have been lost from the tables, replacing missing data with nulls. There are three forms of the outer join, depending on which data is to be kept. LEFT OUTER JOIN - keep data from the left-hand table RIGHT OUTER JOIN - keep data from the right-hand table FULL OUTER JOIN - keep data from both tables OUTER JOIN example 1 Figure : OUTER JOIN (left/right)

14 OUTER JOIN example 2 Left Outer Join: R <R.primary_key = S.foreign_key> S All rows from R are retained and unmatched rows of S are padded with NULL Right Outer Join: R <R.primary_key = S.foreign_key> S All rows from S are retained and unmatched rows of R are padded with NULL Left Outer Join Example Students Courses stud# Course name 100 PH Fred 200 CM Dave 400 EN Peter Course# PH CM CH name Pharmacy Computing Chemistry Students Stud# <course = course#> Courses Student.nam e course Course# Course.nam e

15 100 Fred PH PH Pharmacy 200 Dave CM CM Computing 400 Peter EN NULL NULL Right Outer Join - ExampleStudents Courses stud# Course name 100 PH Fred 200 CM Dave 400 EN Peter Students <course = course#> Courses Course# PH CM CH name Pharmacy Computing Chemistry Stud# Student.nam e course Course# Course.nam e 100 Fred PH PH Pharmacy 200 Dave CM CM Computing NULL NULL NULL CH Chemistry

16