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Relational Algebra Operations
- 1. DDBMS Relational Algebra Operations Assignment Submitted To: Miss Qurat ul Ain Assignment Submitted By: Shefa Idrees # 101631049 Assignment Submission Date: 07-03-2018 Department of Computer Science
- 2. Relational Algebra Operations Query Language A query language is a language in which user requests information from the database. It can either be categorized as procedural or nonprocedural. In a procedural language the user instructs the system to do a sequence of operations on database to compute the desired result. In nonprocedural language the user describes the desired information without giving a specific procedure for obtaining that information. Relational Algebra The relational algebra is a procedural query language. It consists of a set of operations that take one or two relations as input and produces a new relation as output. The relational algebra is a relation-at-a-time (or set) language where all tuples are controlled in one statement without the use of a loop. There are several variations of syntax for relational algebra commands and youuse a common symbolicnotation for the commands and present it informally. Primary Operations of Relational Algebra The primary operations of relational algebra are as follows: Select (σ) Project (∏) Union (∪) Set Difference (−) Cartesian Product (Χ) Rename (ρ) Select Operation Selection operator is used to select tuples from a relation based on some condition. Notation − σp(r)
- 3. Where σ stands for selection predicate and r stands for relation. p is prepositional logic formula which may use connectors like and, or, and not. These terms may use relational operators like − =, ≠, ≥, <, >, ≤. For example − σsubject = "database"(Books) Output − Selects tuples from books where subject is 'database'. Project Operation (∏) Projection operator is used to project particular columns from a relation. The Projection operation works on a single relation R and defines a relation that contains a vertical subset of R, extracting the values of specified attributes and eliminating duplicates. Notation − ∏A1, A2, An (r) Where A1, A2 , An are attribute names of relation r. Duplicate rows are automatically eliminated, as relation is a set. For example − ∏subject, author (Books) Output − Selects and projects columns named as subject and author from the relation Books. Union Operation (∪) For R ∪ S, the union of two relations R and S defines a relation that contains all the tuples of R, or S, or both R and S, duplicate tuples being eliminated. R and S must be union-compatible. For a union operation to be applied, the following rules must hold − R and S must have the same quantity of attributes.
- 4. Attribute domains must be compatible. Duplicate tuples get automatically eliminated. Notation − r U s For example − ∏ author (Books) − ∏ author (Articles) Output − Projects the names of the authors who have either written a book or an article or both. Set Difference Operation (−) For R – S, the Set difference operation defines a relation consisting of the tuples that are in relation R, but not in S. R and S must be union-compatible. Notation − r – s For example − ∏ author (Books) − ∏ author (Articles) Output − Provides the name of authors who have written books but not articles. Cartesian Product (Χ) For R × S, the Cartesian product operation defines a relation that is the concatenation of every tuple of relation R with every tuple of relation S. Notation − r Χ s For example − σauthor= 'tutorialspoint'(Books Χ Articles) Output − Yields a relation, which shows all the books and articles written by tutorialspoint.
- 5. Rename Operation (ρ) The results of relational algebra are also relations but without any name. The rename operation provides database designers to rename the output relation. The rename- operation is denoted using small Greek letter rho (ρ). Notation − ρ x (E)