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The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
In relational algebra, a rename is a unary operation written as / where: . R is a relation; a and b are attribute names; b is an attribute of R; The result is identical to R except that the b attribute in all tuples is renamed to a. [1]
A relation algebra (L, ∧, ∨, −, 0, 1, •, I, ˘) is an algebraic structure equipped with the Boolean operations of conjunction x∧y, disjunction x∨y, and negation x −, the Boolean constants 0 and 1, the relational operations of composition x•y and converse x˘, and the relational constant I, such that these operations and constants satisfy certain equations constituting an ...
The operator distributes over if it both left distributes and right distributes over . In the definitions above, to transform one side to the other, the innermost operator (the operator inside the parentheses) becomes the outermost operator and the outermost operator becomes the innermost operator.
The most common numerical relational operators used in programming languages are shown below. Standard SQL uses the same operators as BASIC, while many databases allow != in addition to <> from the standard. SQL follows strict boolean algebra, i.e. doesn't use short-circuit evaluation, which is common to most languages below. E.g.
In relational algebra, a selection (sometimes called a restriction in reference to E.F. Codd's 1970 paper [1] and not, contrary to a popular belief, to avoid confusion with SQL's use of SELECT, since Codd's article predates the existence of SQL) is a unary operation that denotes a subset of a relation.
Queries made against the relational database, and the derived relvars in the database are expressed in a relational calculus or a relational algebra. In his original relational algebra, Codd introduced eight relational operators in two groups of four operators each. The first four operators were based on the traditional mathematical set operations:
In relational algebra, a projection is a unary operation written as ,..., (), where is a relation and ,..., are attribute names. Its result is defined as the set obtained when the components of the tuples in are restricted to the set {,...,} – it discards (or excludes) the other attributes.