1. Relational Algebra 2 Extended-Relational Algebra Adam Nafke CS157A

2. Generalized Projection -Review ● Extends projection operation by allowing arithmetic functions. ● Standard projection – ΠstudentName, grade(classList) ● Generalized projection - ΠstudentName, quizAverage + testAvg(classList) ● Will return a list of names with the sum of the two values.

3. Generalized Projection - continued ● ΠstudentName, quizAverage + testAvg(classList) will return a attribute without a name. ● To name the attribute we use “AS” to cast it to a new attribute for the relation: ΠstudentName, quizAverage + testAvg as testScore(classList)

4. Aggreate Functions - Review ● Aggreate functions are functions on relations which return a single value. However, many values can be retrieved from specific groups within relations. ● e.g. G sum(salary)(professors) would return the total salary of all professors on the relation “professors”.

5. Aggreate functions -continued ● However, we may want to find the total salaries by department. The query department-name G sum(salary) (professors) ● would give us just that.

6. Aggreate functions -continued ● One way to look at the left-hand subscript in any aggreate function is as a for loop. For example: ● department-name G sum(salary)(professors) ● Is just ● for each (department-name){ ● sum all salaries}

7. Aggreate functions -continued Combining aggreate functions with generalized projection we have: department-name G sum(salary) as Total Salary, max(salary) as HighestPaidProfessor(professors) Would perform a “for-each” on the department list and list the sum of the salaries and the amount of the highest paid professor.

8. Aggreate functions - continued It is important to note that if you are trying to find a specific entry in a relation via a aggregate function, do not list a unique name on the left- hand subscript of G. professor-name G max(salary)(professors) Will return the same relation as you started with (provided no two professors are name the same). Find the specific name via a normal query.

9. Modifications to the Database ● Now I will discuss how to add, remove, or change information in the Database. ● We use the assignment operation ( <-) to make modifications to the database.

10. Deletion ● Expressed by r <- r - X (where r is a relation, and X is a query) ● Examples: To remove all of professor Davis's records: professor <- professor – Oprofessor_name = “Davis”(professor) ● Any query which returns a tuple or set of tuples can be used.

11. Insertion ● To insert data into a relation, either a tuple, or a set of tuples must be defined. ● The format of expressing insertion is: ● r <- r U E (r is a relation and E is a expression).

12. Insertion - Example Let's assume there are two relations: Vehicle and Owner. Vehicle has attributes {make, license plate #, color} and Owner maps license plates to owners {license plate #, name}. We add a value to the relations as follows: Vehicle <- Vehicle U {(Corvette, 12345, blue)} Owner <- Owner U {(12345, “John Smith”)}

13. Updating ● Updating is used to change a value in a tuple without changing all values in the tuple. The form is:r <- π F1, F2,...., Fn (r) ● Where each Fi is an expression, involving only constants and the attributes of r, that gives the new value for the attribute.

14. Updating - Example ● Suppose we wanted to halve the tuition for all students in relation (student). We would update this relation as follows: ● student <- п name, id, age, tuition *.5 ( student) ● What if we wanted to do different updates for different tuples?

15. Updating -continued ● An update must cover all tuples in a given relation. So if updating only some tuples is desired, the following format must be used: ● r <- пF1, F2,... (OP(r)) U (r- OP(r)) ● What this says, is that in a update you must union whatever you select with whatever is left in that relation.

16. Updating - example ● Lets say you wanted to double the tuition of all students above the age of 30. ● Пname, age, tution * 2 (O age > 30(students)) selects all students over 30 and doubles the value of tution. ● Пname, age, tution (O age < 30(students)) will select all students under 30. ● Students 30(students)) U Пname, age, tution (O age < 30(students)) Will update all values.