Relational Algebra for LaTeX Cheat Sheet

Relational algebra is a mathematical language used to describe and manipulate data stored in relational databases. It is a set of operations that can be used to query and manipulate data in a database. The operations in relational algebra are based on set theory and logic, and they provide a way to express complex queries in a concise and precise manner.

Relational algebra is an important tool for database designers and developers, as it provides a way to express complex queries in a concise and precise manner. It is also used in the development of query languages such as SQL, which is used to interact with relational databases. Understanding relational algebra is essential for anyone working with relational databases, as it provides a foundation for understanding how data is stored and manipulated in these systems.

This cheat sheet lists operators for relational algebra queries for LaTeX.

Basic Operators

Operator	Description
$\sigma_{condition}(R)$	Selects tuples from relation R that satisfy the given condition
$\pi_{attribute_1, attribute_2, …, attribute_n}(R)$	Projects the specified attributes from relation R
$R \times S$	Cartesian product of relations R and S
$R \cup S$	Union of relations R and S
$R – S$	Difference of relations R and S
$R \bowtie_{condition} S$	Natural join of relations R and S that satisfy the given condition
$R \Join_{condition} S$	Join of relations R and S that satisfy the given condition

Additional Operators

Operator	Description
$\rho_{new_name}(R)$	Renames relation R to new_name
$\delta(R)$	Removes duplicate tuples from relation R
$\gamma_{attribute_1, attribute_2, …, attribute_n}(F)$	Aggregates the specified attributes from relation F
$\leftarrow$	Assignment operator
$\cup_{attribute}(R)$	Returns the distinct values of the specified attribute from relation R
$\cap_{attribute}(R)$	Returns the common values of the specified attribute from relation R
$\div$	Division operator

Examples

Select

Query	Result
$\sigma_{age > 25}(Employees)$	Selects all employees with age greater than 25
$\sigma_{name = ‘John’ \land age > 25}(Employees)$	Selects all employees named John with age greater than 25

Project

Query	Result
$\pi_{name, age}(Employees)$	Projects the name and age attributes from Employees
$\pi_{name}(Employees \bowtie_{department_id = 1} Departments)$	Projects the name attribute from the join of Employees and Departments on department_id

Cartesian Product

Query	Result
$Employees \times Departments$	Returns the Cartesian product of Employees and Departments

Union

Query	Result
$R \cup S$	Returns the union of relations R and S

Difference

Query	Result
$R – S$	Returns the difference of relations R and S

Natural Join

Query	Result
$Employees \bowtie_{department_id = id} Departments$	Returns the natural join of Employees and Departments on department_id and id

Join

Query	Result
$Employees \Join_{department_id = id} Departments$	Returns the join of Employees and Departments on department_id and id

Rename

Query	Result
$\rho_{NewEmployees}(Employees)$	Renames Employees to NewEmployees

Duplicate Removal

Query	Result
$\delta(Employees)$	Removes duplicate tuples from Employees

Aggregation

Query	Result
$\gamma_{department_id, COUNT(*)}(Employees)$	Counts the number of employees in each department
$\gamma_{department_id, AVG(salary)}(Employees)$	Calculates the average salary for each department

Assignment

Query	Result
$NewEmployees \leftarrow \sigma_{age > 25}(Employees)$	Assigns the result of the select query to NewEmployees

Distinct Values

Query	Result
$\cup_{department_id}(Employees)$	Returns the distinct department_id values from Employees

Common Values

Query	Result
$\cap_{department_id}(Employees)$	Returns the common department_id values from Employees

Division

Query	Result
$R \div S$	Returns the division of relations R and S

Reference

Relational Algebra – Wikipedia