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Relational Model Part 2 Manipulative part

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2.5 The manipulative part The manipulative part defines the operations you can perform on the relational databases. The manipulative part is expressed in the form relation algebra. Conventional algebra: X+y-(x/20) –Variables, x and y. –A constant number, 20. –Arithmetic operators, +, - and /. the operation is performed on ‘numbers’.

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2.5 The manipulative part relational algebra is defined on a relation: X union (, ). Given X = (, ) then X union (, ) is: (,,, ).

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2.5 The manipulative part Product Prod_NoNameColour P1PantaloonsBlue P2PantaloonsKhaki P3SocksHarebell P4SocksWhite P5PantaloonsWhite Customer Cust_NoNameAddress C1Nippers Ltd25 High St, Leeds C2Tots-Gear5 Low, Oxford C3Super-Brat30 New St Luton C6Tiny-Togs1 Old Rd, Luton Sales_Order Order_NoDateCust_No 011/9/87C1 022/5/87C3 091/9/87C6 0101/9/87C6 Sales_Order_line Order_NoProd_NoQuantity 01P P P P P150 Why need relational algebra? Question: ‘ Extract from the database to know the name of customers who have placed orders on 1/9/87 ’.

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2.5 The manipulative part Extract from the database to know the name of customers who have placed orders on 1/9/87. Order_NoDateCust_No 011/9/87C1 022/5/87C3 091/9/87C6 0101/9/87C6 Step 1: Search through the Sale_Order table - cut out each row where the date is 1/9/87. Order_NoDateCust_No 011/9/87C1 091/9/87C6 0101/9/87C6

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2.5 The manipulative part Step 2: Search through the Customer table the value in the Cust_No column = Cust_No column. Cust_NoNameAddress C1Nippers Ltd25 High St, Leeds C2Tots-Gear5 Low, Oxford C3Super-Brat30 New St Luton C6Tiny-Togs1 Old Rd, Luton Cust_NoNameAddress C1Nippers Ltd25 High St, Leeds C6Tiny-Togs1 Old Rd, Luton C6Tiny-Togs1 Old Rd, Luton Order_NoDateCust_No 011/9/87C1 091/9/87C6 0101/9/87C6

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2.5 The manipulative part Step 2: Search through the Customer table Cut out the Name column in the above table Cut out and throw away any duplicate row. Cust_NoNameAddress C1Nippers Ltd25 High St, Leeds C6Tiny-Togs1 Old Rd, Luton C6Tiny-Togs1 Old Rd, Luton Name Nippers Ltd Tiny-Togs

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2.5 The manipulative part Relational algebra operator and expressions RESTRICTION PROJECT PRODUCT UNION DIFFERENCE Relational algebra includes a set of operators to define new relations (tables). Intersection Division Join unary operator -- operate on one relation binary operator – operate on two relations.

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2.5 The manipulative part RESTRICT RESTRICT is an operator on a single relation (table). RESTRICT is sometimes called ‘SELECT’. RESTRICT SALES_ORDER WHERE CUST_NO=‘C6’ Order_NoDateCust_No 011/9/87C1 022/5/87C3 091/9/87C6 0101/9/87C6 091/9/87C6 0101/9/87C6 Restrict R where C R-- relation, C – condition.

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2.5 The manipulative part RESTRICT – more examples RESTRICT PRODUCT WHERE (COLOUR=‘white’ OR COLOUR=‘blue’) Product Prod_NoNameColour P1PantaloonsBlue P2PantaloonsKhaki P3SocksHarebell P4SocksWhite P5PantaloonsWhite Prod_NoNameColour P1PantaloonsBlue P4SocksWhite P5PantaloonsWhite RESTRICT PRODUCT WHERE NOT(Colour = ‘blue’) AND (Name =’Sock’ OR Name =’Pantaloons’) ??

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2.5 The manipulative part PROJECTION PROJECT is an operator to cut out the attributes. PROJECT Product on Colour PROJECT R ON X R– relation, X – attribute(s). Product Prod_NoNameColour P1PantaloonsBlue P2PantaloonsKhaki P3SocksHarebell P4SocksWhite P5PantaloonsWhite Colour Blue Khaki Harebell White

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2.5 The manipulative part UNION UNION comprise all the tuples from two relations. PRODUCT UNION R UNION S R, S– relations. Product Prod_NoNameColour P1PantaloonsBlue P2PantaloonsKhaki P3SocksHarebell P4SocksWhite P5PantaloonsWhite P7SocksBlue

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2.5 The manipulative part DIFFERENCE DIFFERENCE - take the tuples of R according to S. SALES_ORDER MINUS R MINUS S R, S– relations. Sales_Order Order_NoDateCust_No 011/9/87C1 022/5/87C3 091/9/87C6 0101/9/87C6 Order_NoDateCust_No 011/9/87C1 091/9/87C6 0101/9/87C6

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2.5 The manipulative part Cartesian Product R TIMES S R, S– relations. Product_Name Name Pantaloons Socks Colour Blue Harebell Product_Colour TIMES NameColour PantaloonsBlue PantaloonsHarebell SocksBlue SocksHarebell

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2.5 The manipulative part INTERSECT Include the tuples that exist in two relations. R INTERSECT S R, S– relations. Product_in_Stock Prod_No P1 P3 Prod_No P3 P5 Product_On_Order INSTERSECT Prod_No P3

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2.5 The manipulative part DIVIDE DIVIDE R BY S R, S– relations. Language English French Langs DIVIDE Employ_No E3 E4 Salesman_Lang Employee_NoLanguage E1French E3English E3French E4English E4French E4German E5English E5German E5Swedish

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2.5 The manipulative part JOIN Natural JOIN EQUI-JOIN THETA-JOIN SEMI-JOIN OUTER-JOIN To construct a new relation according to the specific similarity between the different relations of a database. JOINs may be of the following types:

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2.5 The manipulative part JOIN Example Product Prod_NoNameColour P1PantaloonsBlue P2PantaloonsKhaki P3SocksHarebell P4SocksWhite P5PantaloonsWhite Customer Cust_NoNameAddress C1Nippers Ltd25 High St, Leeds C2Tots-Gear5 Low, Oxford C3Super-Brat30 New St Luton C6Tiny-Togs1 Old Rd, Luton Sales_Order Order_NoDateCust_No 011/9/87C1 022/5/87C3 091/9/87C6 0101/9/87C6 Sales_Order_line Order_NoProd_NoQuantity 01P P P P P150

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2.5 The manipulative part NATURAL JOIN NATURAL JOIN is to combine two relations on the basis of all the attributes which occur in both of them. JOIN Sales_Order AND Customer Order_NoDateCust_NoNameAddress 011/9/87C1Nippers Ltd25 High St, Leeds 022/5/87C3Tots-Gear5 Low, Oxford 091/9/87C6Tiny-Togs1 Old Rd, Luton 0101/9/87C6Tiny-Togs1 Old Rd, Luton

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2.5 The manipulative part EQUI-JOIN EQUI-JOIN combines tuples from two relations, with the specified attributes have the same value for the associating tuples. JOIN R AND S WHERE R.A=S.B It combines tuples in R and S where the values of attributes (A in R and B in S) are equal.

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2.5 The manipulative part EQUI-JOIN Dept _Employee DepartmentEmployee_NoGrade D1E1II D1E2IB D1E3IA D1E4III D2E5III D2E9II Management ManagerSubordinate E1E2 E1E3 E2E4 E5E9 DepartmentEmployee_NoGradeManagerSubordinate D1E1IIE1E2 D1E1IIE1E3 D1E2IBE2E4 D2E5IIIE5E9 JOIN Dept_Employee AND Management WHERE Dept_Employee.Employee_No = Management.Manager

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2.5 The manipulative part THETA-JOIN In a THETA-JOIN, the condition is not restricted to equality. Any comparison operator may be used. In EQUI-JOIN, tuples are joined where the values of specified attributes are equal. e.g. >, =, and so on…

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2.5 The manipulative part THETA-JOIN Example JOIN Payment AND Invoice WHERE Payment.Date > Invoice.Date. Payment. Invoice_No Payment. Date Invoice. Invoice_No Invoice. Date Invoice. Amount I I I I I I Invoice_NoData I I Invoice_NoDateAmount I I I Payment Invoice

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2.5 The manipulative part THETA-JOIN Example JOINT Payment AND Invoice WHERE ((Payment.Date>= Invoice.Date) AND (Payment.Invoice_No = Invoice.Invoice_No)) Payment. Invoice_No Payment. Date Invoice. Invoice_No Invoice. Date Invoice. Amount I I Payment. Invoice_No Payment. Date Invoice. Invoice_No Invoice. Date Invoice. Amount I I I I I I

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2.5 The manipulative part SEMI-JOIN SEMI-JOIN of two relations is the set of all the tuples of the first, which will join with tuple of the second. Customer Cust_NoNameAddress C1Nippers Ltd25 High St, Leeds C2Tots-Gear5 Low, Oxford C3Super-Brat30 New St Luton C6Tiny-Togs1 Old Rd, Luton Sales_Order Order_NoDateCust_No 011/9/87C1 022/5/87C3 091/9/87C6 0101/9/87C6 SJOIN Customer AND Sales_Order

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2.5 The manipulative part SEMI-JOIN Customer Cust_NoNameAddress C1Nippers Ltd25 High St, Leeds C2Tots-Gear5 Low, Oxford C3Super-Brat30 New St Luton C6Tiny-Togs1 Old Rd, Luton Sales_Order Order_NoDateCust_No 011/9/87C1 022/5/87C3 091/9/87C6 0101/9/87C6 SJOIN Customer AND Sales_Order Cust_NoNameAddress C1Nippers Ltd25 High St, Leeds C3Tots-Gear5 Low, Oxford C6Tiny-Togs1 Old Rd, Luton SEMI-NATURAL JOIN SEMI-EQUI JOIN SEMI-THETA JOIN SJOIN R AND S WHERE C

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2.5 The manipulative part OUTER-JOIN OUTER-JOIN is an information-preserving version of the join. OJOIN Sales_Order AND Customer Order_NoDateCust_NoNameAddress 011/9/87C1Nippers Ltd25 High St, Leeds Null C2Tots-Gear5 Low, Oxford 022/5/87C3Tots-Gear5 Low, Oxford 091/9/87C6Tiny-Togs1 Old Rd, Luton 0101/9/87C6Tiny-Togs1 Old Rd, Luton

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2.5 The manipulative part Complex Expression Have a close read pp

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2.5 The manipulative part Summary Section Reading: Section 2.4 Exercise: 2.5

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