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The Relational Algebra and Calculus

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The basic set of operations for the relational model is known as the relational algebra. These operations enable a user to specify basic retrieval requests. The result of a retrieval is a new relation, which may have been formed from one or more relations. The algebra operations thus produce new relations, which can be further manipulated using operations of the same algebra. | The Relational Algebra and Calculus Chapter Outline Example Database Application (COMPANY) Relational Algebra Unary Relational Operations Relational Algebra Operations From Set Theory Binary Relational Operations Additional Relational Operations Examples of Queries in Relational Algebra Relational Calculus Tuple Relational Calculus Domain Relational Calculus Overview of the QBE language (appendix D) Database State for COMPANY All examples discussed below refer to the COMPANY database shown here. Relational Algebra The basic set of operations for the relational model is known as the relational algebra. These operations enable a user to specify basic retrieval requests. The result of a retrieval is a new relation, which may have been formed from one or more relations. The algebra operations thus produce new relations, which can be further manipulated using operations of the same algebra. A sequence of relational algebra operations forms a relational algebra expression, whose result will also be a relation that represents the result of a database query (or retrieval request). Unary Relational Operations SELECT Operation SELECT operation is used to select a subset of the tuples from a relation that satisfy a selection condition. It is a filter that keeps only those tuples that satisfy a qualifying condition – those satisfying the condition are selected while others are discarded. Example: To select the EMPLOYEE tuples whose department number is four or those whose salary is greater than $30,000 the following notation is used: DNO = 4 (EMPLOYEE) SALARY > 30,000 (EMPLOYEE) In general, the select operation is denoted by (R) where the symbol (sigma) is used to denote the select operator, and the selection condition is a Boolean expression specified on the attributes of relation R Unary Relational Operations SELECT Operation Properties The SELECT operation (R) produces a relation S that has the same schema as R The SELECT | The Relational Algebra and Calculus Chapter Outline Example Database Application (COMPANY) Relational Algebra Unary Relational Operations Relational Algebra Operations From Set Theory Binary Relational Operations Additional Relational Operations Examples of Queries in Relational Algebra Relational Calculus Tuple Relational Calculus Domain Relational Calculus Overview of the QBE language (appendix D) Database State for COMPANY All examples discussed below refer to the COMPANY database shown here. Relational Algebra The basic set of operations for the relational model is known as the relational algebra. These operations enable a user to specify basic retrieval requests. The result of a retrieval is a new relation, which may have been formed from one or more relations. The algebra operations thus produce new relations, which can be further manipulated using operations of the same algebra. A sequence of relational algebra operations forms a relational algebra expression, whose result .

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