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c# qr code generator Relational Algebra and Relational Calculus in C#.NET
Relational Algebra and Relational Calculus Create QR Code In C#.NET Using Barcode generator for Visual Studio .NET Control to generate, create QR Code image in VS .NET applications. www.OnBarcode.comQuick Response Code Reader In C# Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET applications. www.OnBarcode.comTo manipulate relations (relational variables), you need some operators. Relations and operators on relations form what is called relational algebra. The collection of relational operators is open ended, but some operators are considered basic. Although the basic operators are somewhat intuitive, I ll introduce them for the sake of completeness. Painting Bar Code In Visual C#.NET Using Barcode generator for Visual Studio .NET Control to generate, create barcode image in Visual Studio .NET applications. www.OnBarcode.comReading Bar Code In Visual C#.NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET framework applications. www.OnBarcode.comBasic Operators
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Generate PDF 417 In Visual Studio .NET Using Barcode creator for .NET Control to generate, create PDF417 image in VS .NET applications. www.OnBarcode.comCode39 Reader In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. www.OnBarcode.comThe rst four operators listed here accept two relations as parameters. The fth one checks whether a tuple is a member of a relation in other words, it accepts a tuple as the left parameter and a relation as the right parameter. Finally, the last operator in the list accepts a single relation as a parameter and checks whether it is empty. If you wish, you can de ne additional operators for convenience, such as proper subset of (to mean subset of and not equal to) and proper superset of (superset of and not equal to). I want to mention one other speci c operator that helps greatly with the tabular presentation of a relation the Order By <attribute_1,attribute_2,. . .,attribute_n> operator. The Order By operator does not return an unordered result; thus, it does not return a set or relation, which are unordered. You can think of the return value of the Order By operator as a sorted table. Sorting is not prede ned for relations and tuples, however; therefore, supporting the Order By operator for a particular relation requires that at least one attribute of the relation support ordering and the following operators: Code 39 Generator In None Using Barcode encoder for Font Control to generate, create ANSI/AIM Code 39 image in Font applications. www.OnBarcode.comUPCA Supplement 5 Decoder In Visual Studio .NET Using Barcode scanner for .NET Control to read, scan read, scan image in VS .NET applications. www.OnBarcode.com> (greater than) (greater than or equal to) (less than or equal to) < (less than) QR Code 2d Barcode Drawer In Visual Basic .NET Using Barcode maker for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications. www.OnBarcode.comBar Code Generation In Java Using Barcode creator for Android Control to generate, create barcode image in Android applications. www.OnBarcode.comThe table returned by the Order By operator is sorted according to values of one or more attributes, all of which must be of data types that support the listed type operators. Draw QR Code In None Using Barcode creation for Microsoft Word Control to generate, create QR image in Word applications. www.OnBarcode.comEncoding Denso QR Bar Code In Java Using Barcode generator for Android Control to generate, create QR Code 2d barcode image in Android applications. www.OnBarcode.comRelational Algebra
Relational algebra is a collection of operators that accept relations as input parameters and return relations. The fact that the result of any relational operation is a relation is referred as the relational closure property of the relational algebra. Codd originally de ned eight relational operators four of them are based on traditional set operators, and four of them are special relational operators. These eight are Restrict, Project, Product, Union, Intersect, Minus, Join, and Divide. Relational algebra is not closed; you can de ne additional operators as long as they respect the relational closure property. I ll introduce a handful of useful operators in addition to Codd s original eight. Of course, because the collection of relational operators is open ended, my list is not complete. I deliberately selected the operators that I nd most useful and that are used in the TransactSQL language later in this book. Codd s Eight Original Operators
The Restrict operator lters tuples of a relation. The result of this operator is a relation with fewer tuples than (or the same number as) the original relation. The heading type of the relation returned is the same as the heading type of the original relation. The restriction Inside Microsoft SQL Server 2008: TSQL Querying
is based on a Boolean expression (called the restriction expression) comparing values of attributes to literals, variables, other attributes, or expressions. The Restrict operator s output relation contains exactly those tuples from the original relation for which the restriction expression evaluates to True. The Restrict operator lters a relation horizontally; in contrast, the Project operator lters a relation vertically. The Project operator is much simpler: in addition to a relation, the Project operator takes, as input, a list of attributes needed for the resulting relation. Note that the proper projection should include unique tuples only; otherwise, the result is not a relation. Nevertheless, RDBMS do not enforce this rule because it is more practical to allow a multiset (or a bag) as the result to send it directly to a client application or to store it temporarily. Figure 31 shows the Restrict and the Project operators graphically. Imagine that the right rectangle showing the Project operator represents the relation Employees, with attributes ID, Name, HireDate, DepartmentID, and BirthDate. The Project operator returns a relation with ID, HireDate, and DepartmentID as its attributes, and these attributes are indicated by the darker shading in the gure.

