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The database schema, a set of related tables and other database objects, is a fundamental concept in relational databases, and it is part of the logical database structure of an Oracle database. A schema

is always associated with a user, and it can be defined as a named collection of objects owned by a user. That is why the terms user and schema are used almost synonymously in Oracle databases. A relational database schema consists of the definition of all relations with their specific attribute names, as well as a primary key. The schema further includes the definition of all the domains, which are the ranges of values the attributes can take. All work on a relational database is essentially performed through the use of a database language called Structured Query Language (SQL).

Relational databases are founded on basic mathematical principles (set theory). The very first line of E. F. Codd s seminal paper that outlined the relational database model makes this clear: This paper is concerned with the application of elementary relation theory to systems which provide shared access to large banks of formatted data.1 Relational algebra consists of a set of operations for manipulating one or more relations without changing the originals. The following are the basic operations that you can perform on a relational database using relational algebra; these are called unary operations, because they involve the manipulation of tuples in a single relation. Selection: A selection operation extracts (or eliminates) a set of tuples from a relation based on the values of the attributes of the relation. Projection: A projection operation extracts (or eliminates) a specified set of columns of a relation. Besides these unary operations, relational algebra supports binary or set operations to manipulate the relations themselves. (Remember that a relation is a set of tuples.) Binary operations merge elements from two relations into a new relation. The set operations are as follows: Union: A union combines two relations to produce a new, larger relation. Intersection: Intersection creates a new relation that has only the common tuples in two relations. Difference: Difference creates a new relation that has only the noncommon tuples in two relations. Cartesian product: The Cartesian product creates a new relation that concatenates every tuple in relation A with every tuple in relation B. The Cartesian product is just one example of a join operation.

Join operations combine two or more relations to derive a new relation based on identical values in the columns (join columns) on the basis they are joined. The resulting relation would be a Cartesian product if you include all the tuples in both relations. However, you usually need only a part of this Cartesian product, based on all tuples in both relations that share a common value for the join column. A natural join is where you combine tuples from two relations, A and B, by combining all rows in A and B that have identical values for all common attributes. A theta-join, on the other hand, pairs tuples in two relations, based on an arbitrary condition.

1. E. F. Codd, A Relational Model of Data for Large Shared Data Banks, Communications of the ACM, vol. 13, no. 6 (June 1970): 377 87.

It looks as if relational algebra, which is based on set theory principles, should be sufficient to retrieve information from relational databases, which are also based on set theory. The problem with relational algebra is that though it s based on correct mathematical principles, it relies on a mathematical procedural language. So if you want to use it for anything but the simplest database queries, you re apt to run into quite complex, messy mathematical operations. Only highly skilled professional programmers can use such a database. To avoid the complexity of relational algebra and to focus on the queries without worrying about the procedural techniques, you use relational calculus.