Relational Algebra

Jermaine Rodney

What is an “Algebra”

Mathematical system consisting of:Operands --- Variables or values from which

new values can be constructed.

Operators --- Symbols denoting procedures that construct new values from given values.

What is Relational Algebra? An Operators are mathematical

functions used to retrieve queries by describing a sequence operations on tables or even databases(schema) involved.

Relational algebra received little attention outside of pure mathematics until the publication of E.F. Codd's relational model of data in 1970. Codd proposed algebra as a basis for database query languages.

Core Relational Algebra

The relational algebra uses set union, set difference, and Cartesian product from set theory, but adds additional constraints to these operators.

Constraints

For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes. Because set intersection can be defined in terms of set difference, the two relations involved in set intersection must also be union-compatible.

Constraints cont.

For the Cartesian product to be defined, the two relations involved must have disjoint headers—that is, they must not have a common attribute name.

Core Relational Algebra

Selection: picking certain rows. Projection: picking certain columns. Joins: compositions of relations. Renaming of relations and attributes etc.

Operations

Projection (π) Selection (σ) Rename (ρ) Natural join ( )⋈ Division (÷) Cartesian product (×) Set intersection (∩) Set union ( )∪

Selection Operation

PROFID# NAME DEPT RANK SAL.

1 Adam CS ASST 6000

2 Bob EE ASSO 8000

3 Calvin CS FULL 10000

4 Dorothy EE ASST 5000

5 Emily EE ASSO 8500

6 Frank CS FULL 9000

σSAL. >= 8500(PROF) ∩ σDEPT = CS(PROF)

Selection (σ)

σSAL. >= 8500(PROF) ∩ σdept = CS(PROF)

returns:

ID# NAME DEPT RANK SAL.3 Calvin CS FULL 10000

6 Frank CS FULL 9000

Natural Join

Denoted by T1 T⋈ 2 Where T1 andT2 are tables. The output of the operation is a table T

such that:The schema of T includes all the distinct

columns of T1 andT2 .

TEACH

ID# CID YEAR

1 C1 2011

2 C2 2012

1 C2 2012

PROF TEACH ⋈Returns:

ID# NAME DEPT RANK SAL. CID YEAR

1 Adam CS ASST 6000 C1 2011

2 Bob EE ASSO 8000 C2 2012

1 Adam CS ASST 6000 C2 2012

Natural join ( )⋈

Renaming The ρ operator gives a new schema to a

relation. R1 := ρ R1(A1,...,An) (R2) makes R1 be

a relation with attributes A1,...,An and the same tuples as R2.

Simplified notation: R1(A1,...,An):= R2.

Example: Renaming

Bars( )

R(bar, addr):=Bars

R ( )bar addrJoe’s Maple St.

Sue’s River RD.

Work Cited

http://www.cse.cuhk.edu.hk/~taoyf/course/bmeg3120/notes/rel-algebra2.pdf

http://en.wikipedia.org/wiki/Relational_algebra

http://www.youtube.com/watch?v=3Xu_LWK3SWw