Special Relational Operations.
Written by VR Saturday, 02 April 2011 19:08
Projection: The projection operator yield a “vertical” subset of a given relation that is that subset obtained by selecting specified attributes and that eliminating redundant duplicate tuples within the attribute selected
Join: The theta-join of relation A on attribute X with relation B on attribute Y is the set of all tuples t such that t is the concatenation of a tuple a belonging to A and tuple b belonging to B and the condition “a.X theta b.Y” evaluates to true. If theta is equality the join is called an equijoin. It follows from the definition that the result of an equijoin must include two identical attributes. If one of those two attributes is eliminated the result is called the natural join. The unqualified term “join” is usually taken to mean the natural join specifically.
Division: In its simplest form the division operator divides a relation of degree two by a relation of degree one and produces a result relation of degree one. Let the dividend(A) have attributes X and Y and let the divisor(B) have attribute Y.Attribute A.Y and B.Y should be defined on the same domain. The result of dividing A by B is the relation C with sole attribute X such that every value x of C.X appears as a value of A.X and the a pair of values(x,y) appears in A for all values y appearing in B.
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