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Unformatted text preview: Remember from Friday Remember from Friday – – the Relational Algebra the Relational Algebra ¡ Procedural language ¡ Six basic operators ¢ select: σ ¢ project: ∏ ¢ union: ∪ ¢ set difference: – ¢ Cartesian product: x ¢ rename: ρ ¡ All of these operators except renaming ( ρ ) take two relations as inputs and produce a new relation as a result. The renaming operator takes an expression in the relational algebra as an operand and returns the result of the expression under a new name and perhaps with attributes renamed as well. ¡ Composition of relational algebra operations is common! Formal Definition (from the text) Formal Definition (from the text) ¡ A basic expression in the relational algebra consists of either one of the following: ¢ A relation in the database ¢ A constant relation ¡ Let E 1 and E 2 be relationalalgebra expressions; the following are all relationalalgebra expressions: ¢ E 1 ∪ E 2 ¢ E 1 – E 2 ¢ E 1 x E 2 ¢ σ p ( E 1 ), P is a predicate on attributes in E 1 ¢ ∏ s ( E 1 ), S is a list consisting of some of the attributes in E 1 ¢ ρ x ( E 1 ), x is the new name for the result of E 1 Additional Operations Additional Operations ¡ Some operations built using the basic six are very convenient. They represent “intuitively appealing” operations that are often useful. ¡ So … We define additional operations that do not add any power to the relational algebra, but that simplify common queries. ¢ Set intersection ¢ Natural join ¢ Division ¢ Assignment Set Set Intersection Operation Intersection Operation ¡ Notation: r ∩ s ¡ Defined as: ¡ r ∩ s = { t  t ∈ r and t ∈ s } ¡ Assume: ¢ r , s have the same arity ¢ attributes of r and s are compatible ¡ Note: r ∩ s = r – ( r – s ) Set Set Intersection Operation Intersection Operation – – Example Example ¡ Relation r, s : ¡ r ∩ s A B α β 2 3 s r A B α α β 1 2 1 r  s A B α β 1 1 A B α 2 It’s easy to see that r – (r – s) is the same as r ∩ s In the marina scenario: In the marina scenario: ¡ Suppose that we want the names of all sailors who reserved a green boat and also reserved a red boat ¢ strategy: find all sailors who reserved a green boat ¡ find the boat numbers for all green boats ¡ pick sid’s from reservations records for these boats ¡ find the names of the sailors with these sid’s Π sname ( σ boat.color=“green” ∧ boat.bid=reserves.bidboat....
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 Spring '08
 Conry
 Algebra, Relational model, relation, Sam Sam

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