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Relational Algebra 2 Extended-Relational Algebra

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Adam Nafke

CS157A

- 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.

- 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)

- 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”.

- However, we may want to find the total salaries by department. The querydepartment-name G sum(salary) (professors)
- would give us just that.

- 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}

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.

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.

- 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.

- 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.

- 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).

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”)}

- 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.

- 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?

- 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.

- 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 <- Пname, age, tution * 2 (O age > 30(students)) U Пname, age, tution (O age < 30(students)) Will update all values.