Relational Algebra

MBAD 613R. Nakatsu

Relational Data Manipulation Language

• Query-by-Example; Query-by-Form• Transform-Oriented Languages• Relational Algebra• Relational Calculus

DML Interfaces

• Forms

• Query Language InterfaceSELECT Name, AgeFROM PATIENTWHERE Physician = ‘Levy’

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Domain Definitions

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Domain Compatibility

Page 204

Two domains are domain compatible if

1) they have the same number of attributes and

2) each corresponding attribute has the same domain.

Attribute Domains

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Relational Operators

1. Union (A U B or A + B)2. Difference (A – B)3. Intersection (A ∩ B)4. Projection5. Selection6. Product (A X B)7. Join (equijoiin, outer join)8. Division (A / B)

1. UnionAdding tuples from one relation A to those of

a second B. Denoted A + B or A U B. A and B must be domain compatible.

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2. Difference

Includes tuples that occur in the first relation A but not the second B. Denoted A - B. A and B must be domain compatible.

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3. Intersection

Includes tuples that are in both the first relation A and the second relation B. Denoted A ∩ B. A and B must be domain compatible.

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4. Projection

Selects specified attributes (columns) from a relation”

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5. Selection

Selects tuples (rows) from a relation.

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6. Product

The product of two relations (sometimes called the Cartesian Product) is the concatenation of every tuple of one relation A with every tuple of a second relation B.

Denoted A X B

7. Join

The join operator allows us to combine information from two or more tables.

It is a combination of the product, selection, and (possibly) projection operations.

Two basic types: - equijoin: includes only matched pairs– outer join: the unmatched pairs

are retained, and the values are left null.

Equijoin, Natural, Left Outer

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8. Division

Find those values in the first relation A that are related to all of the values in the second relation B.

Denoted A / B

Example: Division

aa1a1a2a3a3a3

bb1b2b2b1b2b3

bb1b2

ABAB BB

What is AB / B?

Example Data

StudentStudent EnrollEnroll

CourseCourse