Important Alg Rela

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Relational Algebra & SQL

Lecture 5


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Relational Algebra

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).


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SQL

Structured Query Language (SQL)Standardised by ANSI

Supported by modern RDBMSs

Commands fall into three groups

Data Definition Language (DLL)

Create tables, etc

Data Manipulation Language (DML)

Retrieve and modify data Data Control Language

Control what users can dogrant and revoke privileges


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Unary Operations

Selection

Projection


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Selection

The selection or operation selects rows from a tablethat satisfy a condition:

< condition > < tablename >

Example:course = CMStudents

Students

stud# name course

100 Fred PH stud# name course

200 Dave CM 200 Dave CM

300 Bob CM 300 Bob CM


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Projection

The projection or operation selects a list ofcolumns from a table.

< column list> < tablename >

Example: stud#, nameStudents

Students

stud# name course stud# name

100 Fred PH 100 Fred

200 Dave CM 200 Dave

300 Bob CM 300 Bob


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Binary Operations

Cartesian ProductTheta Join

Inner Join

Natural Join

Outer Joins

Semi Joins


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Cartesian Product

Concatenation of every row in the first

relation (R) with every row in the second

relation (S):

R X S


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Cartesian Product - Example

Students Coursesstud# name course course# name

100 Fred PH PH Pharmacy

200 Dave CM CM Computing

300 Bob CM

Students XCourses =

stud# Students.name course course# Courses.name


100 Fred PH CM Computing

200 Dave CM PH Pharmacy


300 Bob CM PH Pharmacy

300 Bob CM CM Computing


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Theta Join

A Cartesian product with a condition applied:

R S


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Inner Join (Equijoin)

A Theta join where the is the

match (=) of the primary and foreign keys.

R S


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Inner Join - Example

Students Courses

stud# name course course# name



300 Bob CM

Students course = course# Courses

stud# Students.name course course# Courses.name100 Fred PH PH Pharmacy


300 Bob CM CM Computing


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Natural Join - Example

Students Coursesstud# name course course# name



300 Bob CM

R1=Students CoursesR2= R1

stud# Students.name course Courses.name100 Fred PH Pharmacy

200 Dave CM Computing

300 Bob CM Computing


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Outer Joins

Inner join + rows of one table which do not satisfythe .

Left Outer Join: R SAll rows from R are retained and unmatched rows of S are

padded with NULL

Right Outer Join: R SAll rows from S are retained and unmatched rows of R are

padded with NULL


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Left Outer Join - Example

Students Courses




400 Peter EN CH Chemistry

Students Courses


100 Fred PH PH Pharmacy200 Dave CM CM Computing

400 Peter EN NULL NULL


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Right Outer Join - Example

Students Courses




400 Peter EN CH Chemistry

Students Courses




NULL NULL NULL CH Chemistry


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Combination of Unary and Join Operations

Students Courses

stud# name address course course# name

100 Fred Aberdeen PH PH Pharmacy

200 Dave Dundee CM CM Computing

300 Bob Aberdeen CM

Show the names of students (from Aberdeen) and the names of their courses

R1= Students CoursesR2= R1

R3=

R2 Students.name Courses.nameFred Pharmacy

Bob Computing


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Set Operations

Union

IntersectionDifference


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Intersection

Takes the set of rows that are common to eachrelation

Participating relations must be compatible

R S R S

A B

a1 b1

a2 b2

A B

a2 b2

a3 b3

A B

a2 b2


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Difference

Takes the set of rows in the first relation but notthe second

Participating relations must be compatible

R S R - S

A B

a1 b1

a2 b2

A B

a2 b2

a3 b3

A B

a1 b1


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Unary Operations

Selection

course = ComputingStudents

In SQL:

Select *

From StudentsWhere course = Computing;

Projectionstud#, nameStudents

In SQL:

Select stud#, name

From Students;

Selection & Projection

stud#, name(course = ComputingStudents)In SQL:

Select stud#, name

From students

Where course = Computing;


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Outer Joins

Left Outer Join

Students Courses

In SQL:

Select *

From Students, Courses

Where course = course#(+)

Right Outer Join

Students Courses

In SQL:Select *


Where course(+) = course#


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Combination of Unary and Join Operations

R1= Students

CoursesR2= R1

R3= R2

In SQL:

Select Students.name, Courses.name


Where course=course#

AND address=Aberdeen;


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Set Operations

Union: RSIn SQL:

Select * From R

UnionSelect * From S;

Intersection: R SIn SQL:

Select * From R

IntersectSelect * From S;

Difference: R- S

In SQL:

Select * From R

Minus

Select * From S;


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SQL Operators

SELECT Catno

FROM Loan

WHERE Date-Returned IS NULL;

SELECT Catno

FROM Loan

WHERE Date-Returned IS NOT NULL;


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SQL Operators

SELECT Name

FROM Member

WHERE memno IN (100, 200, 300, 400);

SELECT Name

FROM MemberWHERE memnoNOTIN (100, 200, 300, 400);


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Important Alg Rela

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