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3. Relational Algebra and SQL3. Relational Algebra and SQLExample:

Let the following relations describe point sets:

A(x, y), B(x, y), J(x, y) 2D points in the plane

H(x, y, z), I(x, y, z) 3D points in space

F(z) line on the z-axis

K(y,z) 2D points in (y, z)

plane

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3.1 Relation algebra operators3.1 Relation algebra operators

A B

A B A \ B

A and B

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A v F J K

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T x,y H

T y,z H

W 2x+z = 0 I

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Example:

Find the SSN and tax for each person.

SSN,Tax wages+interest+capital_gain = income Taxrecord Taxtable

Example:

Find the area of Lincoln reached by a

radio station.( X,Y ( Name=Lincoln Town ) ) ( X,Y Broadcast )

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3.2 SQL

SELECT a1, ..., an

FROM R1, R2, , Rm

WHERE Con1, ,Conk

This means:

a1, ..., an( Con1( ( Conk ( R1

R2

Rm))))

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Example:

Find the SSN and tax for each person.

SELECT SSN, Tax

FROM Taxrecord, Taxtable

WHERE wages + interest + capital_gain = income

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AS keyword used to rename relations

Two SQL expressions can be combined by:

INTERSECTUNION

MINUS set difference

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Example:

Find the names of the streets that intersect.

SELECT S.NAME, T.NAME

FROM Streets AS S, Streets AS TWHERE S.X = T.X and

S.Y = T.Y

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Example:Assume we have the relations:

Broadcast ( Radio, X , Y )

Town ( Name, X, Y )

Find the parts of Lincoln, NE that can

be reached by at least one Radio station.

(SELECT X, Y

FROM Town

WHERE Name = Lincoln)

INTERSECT(SELECT X, Y

FROM Broadcast)

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Another way of connecting SQL expressions

is using the IN keyword.

SELECT ..

FROM ..WHERE a IN ( SELECT b

FROM ..

WHERE .. )

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SQL with aggregation

SELECT aggregate_function

FROM .WHERE

aggregate_function

Max (c1a1 + ..+ cnan) where ai are attributes

Min (c1a1 + ..+ cnan) and ci are constants

Sum(a) where a is an attribute that is

Avg(a) constant in each constraint tuple

Count(a)

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Example:

Package(Serial_No, From, Destination, Weight)

Postage (Weight , Fee)

Find the total postage of all packages sent

from Omaha.

SELECT Sum(Fee)

FROM Package, Postage

WHERE Package.Weight = Postage.Weight AND

Package.From = Omaha

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GROUP BY

SELECT a1, , an, aggregate_functionFROM ..

WHERE

GROUP BY a1, ..., ak

Evaluates basic SQL query

Groups the tuples according to different values ofa1,..,ak

Applies the aggregate function to each groupseparately

{a1, , ak} {a1, , an}

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Example:

Find the total postage sent out from each city.

SELECT Package.From, Sum(Postage.Fee)

FROM Package, PostageWHERE Package.Weight = Postage.Weight

GROUP BY Package.From