Relational Algebra and Relational Calculus are both approaches to query data from a relational database management system. Both methods represent formal query languages to retrieve and manipulate data, but they differ in syntax, level of abstraction, etc.

This article will discuss the differences between relational algebra and relational calculus.

What is Relational Algebra?

Relational algebra is a procedural query language that retrieves and manipulates data from relations or tables. It uses a set of operations that operate on relations and produce new relations. We use relational algebra to combine data from different relations.

Relational Algebra Operations

The following are basic relational algebra operations:

Selection

This operation selects rows of relations that meet a specific condition. The Greek letter sigma (σ) denotes the selection operation.

For example, σ (Salary > 50000) retrieves all rows from a relation where the salary exceeds 50000.

Projection

This operation selects a subset of attributes from a relation. The Greek letter pi (π) denotes the projection operation.

For example, π (Name, Age) retrieves a relation's name and age attributes.

Union

This operation combines two relations into a new one that contains all the rows from both relations. The ∪ symbol denotes the union operation.

For example, R ∪ S retrieves all rows from relation R and relation S.

Intersection

This operation retrieves all rows common to both relations. The ∩ symbol denotes the intersection operation.

For example, R ∩ S retrieves all rows common to relation R and relation S.

Difference

This operation retrieves all rows present in one relation but not another. The minus symbol (-) denotes the difference operation.

For example, R - S retrieves all rows present in relation R but not in relation S.

Cartesian Product

This operation combines all tuples from one table with all tuples from another. The × symbol denotes the cartesian product operation.

For example, R × S retrieves all combinations of tuples from relation R and relation S.

Join

This operation combines tuples from two different relations based on a common attribute. The ⋈ symbol denotes the join operation. There are different types of joins, including inner join, left outer join, right outer join, and full outer join.

For example, R ⋈ S retrieves all rows from relation R with matching values in relation S.

Division

This operation retrieves all rows from one table with a particular property in common with all rows from another table. The division symbol (÷) denotes the division operation.

For example, R ÷ S retrieves all tuples from relation R with a matching value for every attribute in relation S.

Rename

This operation renames attributes in relations or entire relations. The Greek letter rho (ρ) denotes the rename operation.

For example, ρ (StudentTable)(R) creates a new relation StudentTable equivalent to relation R.

We can combine these operations to create complex queries that retrieve data from one or more tables in a database. We recommend reading this article to understand these operations better using an example.

What is Relational Calculus?

Relational calculus is a non-procedural query language that uses a set of mathematical expressions to retrieve data from a Database. When using relational calculus, we only have to specify what data we want without specifying the procedure to get that data. It is more intuitive than relational algebra, closer to natural language, and easier to understand.

Types of Relational Calculus

There are two types of relational calculus:

Tuple Relational Calculus

Tuple Relational Calculus (TRC) retrieves rows from a table that meets a specific condition. It is similar to the Selection operation of relational algebra. The selection condition consists of variables, predicates and quantifiers.

Domain Relational Calculus

Domain Relational Calculus (DRC) retrieves values from a column that meets a particular requirement. It is similar to the Projection operation of relational algebra.

We perform complex queries using both TRC and DRC together. They allow for a more concise and natural formulation of queries.

Relational Algebra Vs Relational Calculus

The following table shows the differences between Relational Algebra and Relational Calculus:

Based on

Relational Algebra

Relational Calculus

Type of language

Procedural language

Non-procedural language

What it specifies?

We specify the sequence of operations to be performed (prescriptive nature).

We only specify what data we need without specifying what operations are performed (descriptive nature).

Order of execution of operations

Relational algebra defines the order of execution of operations.

Relational calculus does not define the order of execution of operations.

Intuitiveness

It is less intuitive to use than Relational Calculus.

It is more intuitive to use than Relational Algebra.

Use

Used to manipulate and combine relations

Used to retrieve data from a relation

Relation to programming language

Closely related to programming languages as it uses a procedural approach.

More closely associated with a mathematical notation than a programming language.

Domain dependence

Relational algebra queries are domain independent as they are based on mathematical operations that we can apply to tables with the same structure.

Relational calculus queries are domain dependent as they rely on specific attributes of the query table.

Frequently Asked Questions

What are some basic relational algebra operations?

Some basic relational algebra operations include selection, projection, union, intersection, difference, join, division, and rename.

What are some types of relational calculus?

There are two types of relational calculus: Tuple Relational Calculus (TRC) and Domain Relational Calculus (DRC).

What is the difference between TRC and DRC?

TRC retrieves specific tuples from a database based on a condition, while DRC retrieves entire sets of tuples based on a condition.

Which approach is better suited for simpler queries?

Relational algebra is generally better suited for simpler queries involving combining tables or retrieving entire tuples.

Which approach is better suited for complex queries?

Relational calculus is generally better suited for complex queries that involve specific tuples or attributes.

Conclusion

This article discussed the "Difference between Relational Algebra and Relational Calculus". The choice between Relational Algebra and Relational Calculus depends on the requirements of a query.

If you want to learn more about DBMS topics and take your basic knowledge on these topics a notch higher, then you can visit our Guided Path for DBMS on Coding Ninjas Studio. To be more confident in data structures and algorithms, try out our DBMS Course. Until then, All the best for your future endeavours, and Keep Coding.

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