<aside> ℹ️

Relational Algebra:

• The formal language used to describe operations on relations
• relations are essentially “tables in DBs” </aside>

Basic Operations

• Projection ($\pi$): 返回某些列（属性）
• Selection ($\sigma$): 返回某些行
• Set-difference ($-$): finds tuples in X, but not in Y
• Union ($\cup$): finds tuples that belong to table X or Y
• Intersection ($\cap$): finds tuples that belong to table X and Y
• Cartesian Product ($\times$): 相当于 for 两次，两两配对
• Rename ($\rho$): allows us to rename a relation and/or its attributes

Projection $\pi_l(r)$

<aside> 🧑‍💻

SQL: SELECT l FROM r

• Select and return all columns as specified in l
• Remove any duplicated rows </aside>

Python:

def projection (l: List, r: Table) -> Table: 
		cols = r[l, :]
		return cols.drop_duplicate()

Selection $\sigma_c(r)$

<aside> 🧑‍💻

SQL: r WHERE c

• Filters rows from r based on conditions c
• No need to remove duplicates
  • Because $r$ cannot contain duplicates, so neither will its subset </aside>

Python:

def selection (c: Condition, r: Table) -> Table: 
		rows = r[:, c]
		return rows