Relational Algebra

Jun 28, 2023

Based on Set Theory

• $\sigma_{predicate} (R)$ : (horizontal)
• SELECT * FROM R WHERE a_id = 'a2'

• $\Pi$ : retains only desired columns (vertical)
  Projection takes in a relation and outputs a relation with tuples that contain only specified attributes.
• SELECT b_id-100, a_id FROM R WHERE a_id = 'a2'

• $S1 \cap S2 = S1 - (S1 - S2)$
• (SELECT * FROM R) UNION ALL (SELECT * FROM S)

• (SELECT * FROM R) INTERSECT (SELECT * FROM S)

• (SELECT * FROM R) EXCEPT (SELECT * FROM S)

• (SELECT * FROM R) CROSS JOIN (SELECT * FROM S)
• SELECT * FROM R, S

Get tuples from both $r$ and $s$ and put on restriction $\theta$ on them.
$r \bowtie_{\theta} s = \sigma_{\theta} (r \times s)$

• SELECT * FROM R JOIN S USING (ATTRIBUTE1, ATTRIBUTE2...)

• Natural Join

  • $R \bowtie S = \uppi_{unq} ; \sigma_{cond}(R \times S)$
  • Remove the duplicate column (Natural)