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Unformatted text preview: Relational Algebra Relational Algebra ¡ Procedural language ¡ Six basic operators ¢ select: σ ¢ project: ∏ ¢ union: ∪ ¢ set difference: – ¢ Cartesian product: x ¢ rename: ρ ¡ The operators take one or two relations as inputs and produce a new relation as a result. Select is a Select is a “ “ filtering filtering ” ” operation: operation: ¡ Suppose that we have a relation r: ¡ σ A=B ^ D > 5 (r) A B C D α α β β α β β β 1 5 12 23 7 7 3 10 A B C D α β α β 1 23 7 10 Select Select – – Formal textbook definition: Formal textbook definition: ¡ Notation: σ p ( r ) ¡ p is called the selection predicate ¡ Defined as: σ p ( r ) = { t  t ∈ r and p(t) } Where p is a formula in propositional calculus consisting of terms connected by : ∧ , ∨ , ¬ Each term is one of: <attribute> op <attribute> or <constant> where op is one of: =, ≠ , >, ≥ . <. ≤ ¡ Example of selection (using the textbook’s running example): σ branch_name=“Perryridge” ( account ) And in another scenario And in another scenario  ¡ Suppose that we have the relation boats from the marina example: ¡ What is the result of σ color=“green” (boats) bid name color 1 2 31 4 5 Rosey Jady Sunset Knight Spring green aqua red golden green bid name color 1 5 Rosey Spring green green Project is a Project is a “ “ culling culling ” ” operation: operation: A B C α α β β 10 20 30 40 1 1 1 2 ¡ Suppose that we have a relation r: ¡ ∏ A,C ( r ) A C α α β β 1 1 1 2 = A C α β β 1 1 2 Select Select – – Formal textbook definition: Formal textbook definition: ¡ Notation: ∏ A 1 , A 2 , …, A k (r) where A 1 , A 2 are attribute names and r is a relation name. ¡ The result is defined as the relation of k columns obtained by erasing the columns that are not listed ¡ Duplicate rows removed from result, since relations are sets ¡ Example: To eliminate the branch_name attribute of account ∏ account_number, balance ( account ) And another example from the marina scenario And another example from the marina scenario  ¡ Suppose we are trying to schedule service for boats and we want to know which boats are have reservations for them and when. Consider the reserves relation: ¡ Consider the result of ∏ bid, day (reserves) sid bid day 1 1 21 7 7 31 1 4 31 5 20070301 20070531 20070501 20070321 20070301 bid day 31 1 4 31 5 20070301 20070531 20070501 20070321 20070301 Union is a...
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This note was uploaded on 04/08/2008 for the course EE 468 taught by Professor Conry during the Spring '08 term at Clarkson University .
 Spring '08
 Conry

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