The materials are from Internet search not sourced. Our work is considered to be improvement, criticism and evaluation of a method or a theory. In relational algebra, a simple example is to list students that completed all the required courses. We use MySQL as the scripting language.

First, we create the tables and fill the data. CREATE TABLE IF NOT exists completed ( student varchar (255), task varchar(255)); CREATE TABLE IF NOT exists dbproject( task varchar(255)); /* CREATE TABLE completed ( student varchar (255), task varchar(255));*/ insert into completed (student, task) VALUES ('Fred','Database1'), ('Fred','Database2'), ('Fred','Compiler1'), ('Eugene','Database1'), ('Eugene','Compiler1'), ('Sarah','Database1'), ('Sarah','Database2'); select * from relational_division.completed; insert into dbproject (task) VALUES ('Database1'), ('Database2');

Basically, we can formalize the process with the algebraic notation.

/* R div T 1. select unique R as UR 2. UR X T as URXT 3. URXT - R ( URXT left join R on RHS row = LHS row, select rows having null) as RnotT 4. R - RnotT is the rows in R that have columns that are T. */

The concrete steps implemented.

select * from dbproject; select * from completed left join dbproject on 1=1; select distinct student from completed; /* compute student X task in dbproject 2. UR X T as URXT*/ select student, task from (select distinct student from completed) as student_names left join dbproject on 1=1; /* 3. URXT - R ( URXT left join R on RHS row = LHS row, select rows having null) as RnotT */ select * from ( select student_names.stu1, dbproject.task as task1 from (select distinct student as stu1 from completed) as student_names left join dbproject on 1=1 ) as full_table left join completed on 1=1 AND full_table.stu1 = completed.student AND full_table.task1 = completed.task; /* 4. R - RnotT is the rows in R that have columns that are T. */ SELECT stu1 FROM ( select * from ( select * from ( select student_names.stu1, dbproject.task as task1 from (select distinct student as stu1 from completed) as student_names left join dbproject on 1=1 ) as full_table left join completed on 1=1 AND full_table.stu1 = completed.student AND full_table.task1 = completed.task ) as withnull where withnull.student IS NULL ) as minus_result ;

We can add more data. When we run step 4 in the above section, we should get 't' in addition.

insert into completed (student, task) VALUES ('t','Database1'), ('t','Database2'), ('z','Compiler1'), ('h','Database1'), ('h','Compiler1'), ('m','Database1'), ('a','Database2');