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The cost of the cartesian product in the third statement of this de nition makes a direct implementation of division desirable Without division, sequences of boolean operations and counting operations are required to provide the power of universal quanti ers when sets of subsets are needed

1

Solution to Exercise 20-2. We ll try something slightly more complicated now. Write a program to display the name and ID of products with fewer than 10 units in stock. This is another rather simple exercise, again focusing on the command string. This time, you need to include a where clause in your string. From the Products table, you want to retrieve the ProductID and ProductName columns, if the UnitsInStock column is less than 10. Note that you don t actually retrieve the UnitsInStock column; you only use it to determine which records to retrieve. The command string looks like this:

An industrial implementation, REGIS, solves the problem of constructing sets which summarize subsets with a special statement:

string commandString = "Select ProductID, ProductName from Products where UnitsInStock < 10";

Example 9-13

The full listing for this exercise is shown in Example A-60.

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The query to determine which Possible suppliers id can deliver all parts for which (assembly, type), applied to: Possible supplier: RELATION s id, p id : ; Parts skill required : RELATION assembly, type, p id : no req, ;

Example A-60. One solution to Exercise 20-2

can now be constructed as follows: To nd the suppliers who can supply all the parts create a relation by joining Parts skill required and Possible supplier which contains all types to be supplied The natural join of the two summaries over two domains provides the result Supplier explosion = JOIN (PROJECT Parts skill required BY type, p id) ON p id WITH Possible supplier ON p id; Supplier capability = SUMMARY Supplier explosion ONKEY(type,s id) COUNT p id; Type needs = SUMMARY (PROJECT Parts skill required BY type, p id) ONKEY type COUNT p id; Result = JOIN Supplier capability ON type WITH Type needs ON type

using using using using using using System; System.Collections.Generic; System.Linq; System.Text; System.Data; System.Data.SqlClient;

DBMS code is organized into several modules: the disk space manager, the bu er manager, a layer that supports the abstractions of les and index structures, a layer that implements relational operators, and a layer that optimizes queries and produces an execution plan in terms of relational operators (Section 18) A database administrator (DBA) manages a DBMS for an enterprise The DBA designs schemas, provide security, restores the system after a failure, and periodically tunes the database to meet changing user needs Application programmers develop applications that use DBMS functionality to access and manipulate data, and end users invoke these applications (Section 19)

Sec 9-3

namespace Exercise_20_2 { class Program { static void Main(string[] args) { // create the data connection string connectionString = "server=.\\sqlexpress; " + "Trusted_Connection=yes;database=Northwind"; // create the string to hold the SQL command // to get records from the Customers table string commandString = "Select ProductID, " + "ProductName from Products " + "where UnitsInStock < 10"; // create the data adapter with the // connection string and command SqlDataAdapter myDataAdapter = new SqlDataAdapter(commandString, connectionString); // Create and fill the DataSet object DataSet myDataSet = new DataSet( ); myDataAdapter.Fill(myDataSet); // Retrieve the Orders table DataTable myDataTable = myDataSet.Tables[0]; // iterate over the rows collection // and output the fields Console.WriteLine( "Products with less than 10 units in stock:"); foreach (DataRow dataRow in myDataTable.Rows) { Console.WriteLine("ProductID: {0} \tProduct Name: {1}", dataRow["ProductID"], dataRow["ProductName"]); } } } }

The relation Sub rel will have one tuple for each value type in quot attr There will be as many domains in Sub rel as there were in Rel, and all domains other than quot attr will contain the totals of the matching source domains, except for one arbitrary domain speci ed by count attr, which will be replaced with an attribute column containing the number of value-tokens for each type-token which de ned a subset tuple in Sub rel In the example we will name the new domain with a pre x # This count can be used for testing or for the computation of averages, and for operations on subsets, as Example 9-13 shows Supplier explosion: type, p id, s id;

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The output looks like this, if you want to check your results:

Body Body Body Body Body Fender Fender Fender Fender Fender Fender P1 P2 P2 P4 P4 P1 P3 P3 P3 P3 P3 S1 S1 S2 S2 S4 S1 S1 S2 S3 S4 S5

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