Transcript Chapter 8: Foundations of Relational Implementation

Relational Algebra
MBAD 613
R. Nakatsu
Relational Data Manipulation
Language
•
•
•
•
Query-by-Example; Query-by-Form
Transform-Oriented Languages
Relational Algebra
Relational Calculus
DML Interfaces
• Forms
• Query Language Interface
SELECT Name, Age
FROM PATIENT
WHERE Physician = ‘Levy’
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Domain Definitions
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Domain Compatibility
Two domains are domain compatible if
1) they have the same number of attributes and
2) each corresponding attribute has the same domain.
Page 204
Attribute Domains
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Relational Operators
1.
2.
3.
4.
5.
6.
7.
8.
Union (A U B or A + B)
Difference (A – B)
Intersection (A ∩ B)
Projection
Selection
Product (A X B)
Join (equijoiin, outer join)
Division (A / B)
1. Union
Adding 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
AB
a
a1
a1
a2
a3
a3
a3
B
b
b1
b2
b2
b1
b2
b3
What is AB / B?
b
b1
b2
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