Relational Algebra and Relational Calculus in DBMs

Relational Algebra

Relational Algebra is a fundamental procedural query language embedded within the relational data model. It leverages mathematical set theory operations to manipulate relations (tables). These set operations involve:

1. Union: Merging two relations to create a new relation comprising all distinct rows.
2. Intersection: Identifying common rows between two relations.
3. Set Difference: Finding rows present in one relation but absent in the other.
4. Cartesian Product: Generating all possible row pairs from two relations.

Beyond set operations, Relational Algebra incorporates specific operations tailored for relational databases:

• Selection: Filtering rows based on specified conditions.
• Projection: Choosing particular columns from a relation.
• Join: Merging rows from two relations based on a shared column.

Relational Calculus

Contrarily, Relational Calculus is a declarative query language allowing the specification of desired data using logical expressions without detailing the retrieval method. It encompasses two types:

1. Tuple Relational Calculus: Expressing desired data in terms of tuples (rows) that satisfy given conditions.
2. Domain Relational Calculus: Specifying desired data based on domains (sets of values) that meet specific conditions.

Both Tuple and Domain Relational Calculus utilize logical expressions stemming from predicate calculus, a mathematical logic branch, to delineate the data for retrieval.

Key Differences and Importance

Relational Algebra functions procedurally, employing set and specialized database operations. It emphasizes the execution of operations on relations.

Conversely, Relational Calculus operates declaratively, emphasizing logical expressions to describe desired data without specifying the retrieval mechanism.

These formal languages constitute a robust foundation for database management. They predate SQL and form the basis for SQL and other query languages. Their translation into SQL or other query languages allows for effective manipulation and querying of data within relational databases.