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3. Relational Algebra and SQL. Example: Let the following relations describe point sets: A(x, y), B(x, y), J(x, y) 2D points in the plane H(x, y, z), I(x, y, z) 3D points in space F(z) line on the z-axis

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## 3. Relational Algebra and SQL

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**3. Relational Algebra and SQL**Example: Let the following relations describe point sets: • A(x, y), B(x, y), J(x, y) 2D points in the plane • H(x, y, z), I(x, y, z) 3D points in space • F(z) line on the z-axis • K(y,z) 2D points in (y, z) plane**3.1 Relation algebra operators**A and B A B A B A \ B**A F**J K** y,z H** x,y H 2x+z = 0 I**Example:**Find the SSN and tax for each person. πSSN,Taxσwages+interest+capital_gain = income Taxrecord × Taxtable Example: Find the area of Lincoln reached by a radio station. ( πX,Y ( σName=“Lincoln” Town ) ) ( πX,Y Broadcast )**3.2 SQL**SELECT a1, ..., an FROM R1, R2, …, Rm WHERE Con1, …,Conk This means: πa1, ..., an( σ Con1( … (σ Conk ( R1× R2 × … ×Rm))…))**Example:**Find the SSN and tax for each person. SELECT SSN, Tax FROM Taxrecord, Taxtable WHERE wages + interest + capital_gain = income**AS – keyword used to rename relations**Two SQL expressions can be combined by: INTERSECT UNION MINUS– set difference**Example:**Find the names of the streets that intersect. SELECT S.NAME, T.NAME FROM Streets AS S, Streets AS T WHERE S.X = T.X and S.Y = T.Y**Example: Assume we have the relations:**Broadcast ( Radio, X , Y ) Town ( Name, X, Y ) Find the parts of Lincoln, NE that can be reached by at least one Radio station. (SELECT X, Y FROM Town WHERE Name = “Lincoln”) INTERSECT (SELECT X, Y FROM Broadcast)**Another way of connecting SQL expressions**is using the IN keyword. SELECT …….. FROM …….. WHERE a IN ( SELECT b FROM ….. WHERE ….. )**SQL with aggregation –**SELECT aggregate_function FROM ……. WHERE …… aggregate_function– Max (c1a1 + ……..+ cnan) where ai are attributes Min (c1a1 + ……..+ cnan) and ci are constants Sum(a) where a is an attribute that is Avg(a) constant in each constraint tuple Count(a)**Example:**Package(Serial_No, From, Destination, Weight) Postage (Weight , Fee) Find the total postage of all packages sent from Omaha. SELECT Sum(Fee) FROM Package, Postage WHERE Package.Weight = Postage.Weight AND Package.From = “ Omaha “**GROUP BY–**SELECT a1, …, an, aggregate_function FROM ….. WHERE …… GROUP BY a1, ..., ak • Evaluates basic SQL query • Groups the tuples according to different values of a1,..,ak • Applies the aggregate function to each group separately • {a1, …, ak} {a1, …, an}**Example:**Find the total postage sent out from each city. SELECT Package.From, Sum(Postage.Fee) FROM Package, Postage WHERE Package.Weight = Postage.Weight GROUP BY Package.From

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