{"id":1180,"date":"2025-01-13T21:15:03","date_gmt":"2025-01-14T02:15:03","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/nelson\/chapter\/chapter-10-relational-algebra-relational-calculus-and-relational-theory\/"},"modified":"2025-01-13T21:32:04","modified_gmt":"2025-01-14T02:32:04","slug":"chapter10thirdedition","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/nelson\/chapter\/chapter10thirdedition\/","title":{"raw":"Chapter 10 Relational Algebra, Relational Calculus, and Relational Theory","rendered":"Chapter 10 Relational Algebra, Relational Calculus, and Relational Theory"},"content":{"raw":"
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Original Material to the textbook: Fred Strickland<\/p>\r\n\r\n

Learning Outcomes<\/h2>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
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Computing Sub Discipline<\/strong><\/p>\r\n<\/td>\r\n

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Document Code, Reference Code, and Page Number<\/strong><\/p>\r\n<\/td>\r\n

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Text<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n

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Computer Science<\/p>\r\n<\/td>\r\n

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CS2013<\/p>\r\n

IM\/Relational Databases<\/p>\r\n

(Pages 115-116)<\/p>\r\n<\/td>\r\n

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3. Demonstrate use of the relational algebra operations from mathematical set theory (union, intersection, difference, and Cartesian product) and the relational algebra operations developed specifically for relational databases (select (restrict), project, join, and division). [Usage]<\/p>\r\n

4. Write queries in the relational algebra. [Usage]<\/p>\r\n

5. Write queries in the tuple relational calculus. [Usage]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

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CS2023<\/p>\r\n

DM-Querying: Query Construction<\/p>\r\n

(Page 118)<\/p>\r\n<\/td>\r\n

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KA Core 2. Relational Algebra<\/p>\r\n

Non-core 4. Relational Calculus<\/p>\r\n<\/td>\r\n<\/tr>\r\n

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Information Technology<\/p>\r\n<\/td>\r\n

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IT2017<\/p>\r\n

ITE-IMA-05 Database organizational architecture [L3]<\/p>\r\n

(Page 93)<\/p>\r\n<\/td>\r\n

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a. Demonstrate select, project, union, intersection, set difference, and natural join relational operations using simple example relations provided.<\/p>\r\n<\/td>\r\n<\/tr>\r\n

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Introduction to Chapter 10<\/h2>\r\n

We have been looking at relational DBMS from a hands-on or application viewpoint. And we have touched upon the different DBMSs. We have discovered that SQL-92 is not fully implemented by these DBMSs and that there are extensions.<\/p>\r\n

How do the various DBMS groups discuss things? These groups could use relational algebra and relational calculus as the common language.<\/p>\r\n

As textbook authors Thomas Connolly and Caroly Begg wrote:<\/p>\r\n

Both the algebra and the calculus are formal, non-user-friendly languages. They have been used as the basis for other, higher-level Data Manipulation Languages (DML) for relational databases. They are of interest because they illustrate the basic operations required of any DML and because they serve as the standard for comparison for other relational languages.<\/p>\r\n

The relational calculus is used to measure the selective power of relational languages. A language that can be used to produce any relational that can be derived using the relational calculus is said to be relationally complete. Most relational query languages are relatively complete but have more expressive power than the relational algebra or relational calculus because of additional operations such as calculated, summary, and ordering functions.<\/p>\r\n

Now you understand the need for this chapter.<\/p>\r\n\r\n

The Third Edition Style Guide<\/h2>\r\n

This is the style guide that this book will follow for this chapter and for the other chapters.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
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Naming Convention:<\/p>\r\n\r\n

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  • All English names<\/li>\r\n \t
  • Plural table names<\/li>\r\n \t
  • Singular column names<\/li>\r\n \t
  • Capitalized words<\/li>\r\n \t
  • Pascal Case for composite names<\/li>\r\n \t
  • No underscores or special characters<\/li>\r\n \t
  • No unique SQL commands<\/li>\r\n \t
  • No object prefixes<\/li>\r\n<\/ul>\r\n

    Using the IE\u2019s Notation with Crow\u2019s Foot Notation.<\/p>\r\n<\/td>\r\n<\/tr>\r\n

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Figure 10.1 The database style guide. Adapted from https:\/\/vertabelo.com\/blog\/database-schema-naming-conventions\/<\/p>\r\n

The examples will conform to the style guide.<\/p>\r\n\r\n

Regular Algebra and Relational Algebra<\/h2>\r\n

Regular Algebra is a mathematical system that has the following:<\/p>\r\n\r\n