Binary relational operators join and division


The same query can be done in two steps by creating an intermediate table DEPT as follows: The resulting relation is illustrated in Figure 6. If the attributes on which the natural join is specified already have the same names in both relations , renaming is unnecessary.

The resulting relation is shown in Figure 6. There can be a list of join attributes from each relation, and each corresponding pair must have the same name. The lists are used to form equality comparison conditions between pairs of corresponding attributes, and the conditions are then AND ed together.

Notice that if no combination of tuples satisfies the join condition, the result of a JOIN is an empty relation with zero tuples. In general, if R has n R tuples and S has n S. As we can see, a single JOIN operation is used to combine data from two relations so that related information can be presented in a single table. These operations are also known as inner joins , to distinguish them from a different join variation called outer joins see Section 6.

Note that sometimes a join may be specified between a relation and itself, as we will illustrate in Section 6. For example, consider the following three-way join: This combines each project tuple with its controlling department tuple into a single tuple, and then combines that tuple with an employee tuple that is the department manager.

The net result is a consolidated relation in which each tuple contains this project-department-manager combined information. The second way is to use a nested relation, as illustrated by queries Q4A and Q16 in Section 5. The construct of joined tables was added to SQL2 to allow the user to specify explicitly all the various types of joins, because the other methods were more limited. It also allows the user to clearly distinguish join conditions from the selection conditions in the WHERE clause.

Hence, the various JOIN operations are also not strictly necessary for the expressive power of the rela-tional algebra. However, they are important to include as separate operations because they are convenient to use and are very commonly applied in database applications. Other operations have been included in the basic relational algebra for convenience rather than necessity. The preceding operations are shown in Figure 6. Note that in the formulation of the DIVISION operation, the tuples in the denominator relation S restrict the numerator relation R by selecting those tuples in the result that match all values present in the denomina-tor.

Notice that the tuples values b 1 and b 4 appear in R in combination with all three tuples in S ; that is why they appear in the resulting relation T. All other values of B in R do not appear with all the tuples in S and are not selected: SQL has a roundabout way of dealing with the type of query illustrated above see Section 5. In this section we describe a notation typically used in relational systems to represent queries internally. The notation is called a query tree or sometimes it is known as a query evaluation tree or query execution tree.

It includes the relational algebra operations being executed and is used as a possible data structure for the internal representation of the query in an RDBMS. A query tree is a tree data structure that corresponds to a relational algebra expression.

A general join condition is of the form. In that sense, the JOIN operation does not necessarily preserve all of the information in the participating relations, because tuples that do not get combined with matching ones in the other relation do not appear in the result. The most common use of JOIN involves join conditions with equality comparisons only. For example, in Figure 6. If this is not the case, a renaming operation is applied first.

The same query can be done in two steps by creating an intermediate table DEPT as follows: The resulting relation is illustrated in Figure 6. If the attributes on which the natural join is specified already have the same names in both relations , renaming is unnecessary.

The resulting relation is shown in Figure 6. There can be a list of join attributes from each relation, and each corresponding pair must have the same name. The lists are used to form equality comparison conditions between pairs of corresponding attributes, and the conditions are then AND ed together. Notice that if no combination of tuples satisfies the join condition, the result of a JOIN is an empty relation with zero tuples.

In general, if R has n R tuples and S has n S. As we can see, a single JOIN operation is used to combine data from two relations so that related information can be presented in a single table. These operations are also known as inner joins , to distinguish them from a different join variation called outer joins see Section 6.

Note that sometimes a join may be specified between a relation and itself, as we will illustrate in Section 6. For example, consider the following three-way join: This combines each project tuple with its controlling department tuple into a single tuple, and then combines that tuple with an employee tuple that is the department manager. The net result is a consolidated relation in which each tuple contains this project-department-manager combined information.

The second way is to use a nested relation, as illustrated by queries Q4A and Q16 in Section 5. The construct of joined tables was added to SQL2 to allow the user to specify explicitly all the various types of joins, because the other methods were more limited. It also allows the user to clearly distinguish join conditions from the selection conditions in the WHERE clause. Hence, the various JOIN operations are also not strictly necessary for the expressive power of the rela-tional algebra.

However, they are important to include as separate operations because they are convenient to use and are very commonly applied in database applications. Other operations have been included in the basic relational algebra for convenience rather than necessity. The preceding operations are shown in Figure 6. Note that in the formulation of the DIVISION operation, the tuples in the denominator relation S restrict the numerator relation R by selecting those tuples in the result that match all values present in the denomina-tor.

Notice that the tuples values b 1 and b 4 appear in R in combination with all three tuples in S ; that is why they appear in the resulting relation T. All other values of B in R do not appear with all the tuples in S and are not selected: