1. Session 3 Welcome: To session 3-the sixth learning sequence
“ Relational algebra “
Recap : In the previous learning sequences, we discussed the eight operators of relational algebra.
Present learning: We shall explore the following topic:
- Generalized Projection & Group Functions

2. Relational Algebra

3. Relational Algebra More Relational Algebra operators
Generalized Projection
Group Functions
The operators take one or more relations as inputs and give a new relation as a result.

4. Generalized Projection
Extends the projection operation by allowing arithmetic functions to be used in the projection list.  F1, F2, …, Fn(E)
E is any relational-algebra expression
Each of F1, F2, …, Fn are are arithmetic expressions involving constants and attributes in the schema of E.

5. Generalized Projection
Given relation credit-info(customer-name, limit, credit-balance).
find how much more each person can spend:
customer-name, limit – credit-balance, limit*2 (credit-info)

6. Generalized Projection
Credit-info
customer-name
Limit
credit-balance
Ali
1500
380
Ahmed
2000
1400
Rana
1000
500
Kasim
3500

7. Generalized Projection
The result relation is:
customer-name
Limit-credit-balance
Ali
1120
Ahmed
600
Rana
500
Kasim
2100

8. Group Functions
A type of request that cannot be expressed in the basic relational algebra is to specify mathematical group functions on collections of values from the database.
Examples of such functions include retrieving the average or total salary of all employees or the total number of employee tuples. These functions are used in simple statistical queries that summarize information from the database tuples.
Common functions applied to collections of numeric values include SUM, AVERAGE, MAXIMUM, and MINIMUM. The COUNT function is used for counting tuples or values.

9. Group Functions (Cont.)
Group functions take a collection of values and return a single value as a result.
avg: average value min: minimum value max: maximum value sum: sum of values count: number of values

10. Group Functions G1, G2, …, Gn g F1(A1), F2(A2),…, Fn(An) (E)
E is any relational-algebra expression
G1, G2 …, Gn is a list of attributes on which to group (can be empty)
Each Fi is an group function
Each Ai is an attribute name

11. Group Functions – ExampleB C
Relation r:     7 3 10
sum-C
g sum(c) (r) 27

12. Group Functions – Example
account
branch-name
account-number
balance
Perryridge
Brighton
Redwood
A-102
A-201
A-217
A-215
A-222
400
900
750
700
branch-name g sum(balance) (account)
branch-name
balance
Perryridge
Brighton
Redwood
1300
1500
700

13. Group Functions (Cont.)
Result of aggregation does not have a name
Can use rename operation to give it a name
For convenience, we permit renaming as part of group operation
branch-name g sum(balance) as sum-balance (account)
Branch-name
Sum-balance
Perryridge
1300
Brighton
1500
Redwood
700

14. Relational Algebra
Summary: In this learning sequence, we discussed another basic operators of the topic relational algebra.

15. END