Relational Algebra

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Relational algebra is a language to describe relations.

Two categories:

Core:

Abbreviation:

Select operator:

Select operator in RA is like Where syntax in SQL:

It is used to select rows and filter the original relationship:

Project operator:

It is like the select syntax in SQL:

It is used to select columns in a relationship:

Also, it will eliminate the duplicate rows

Cross-product:

Full outer Join in SQL

Can achieve natural join effect by applying one more select operator

Natural Join

Natural Join in SQL

more efficient than cross product

Section 1 summary

Union

full outer join on just one same column

it is euqal to the following SQL:

select student.id from student fuller outer join record on student.id = record.stu.id

Different

left outer join on just one same column and b.key is null

it is equal to the following SQL:

select student.id from student left outer join record on student.id = record.stu.id where record.stu.id = NULL

Intersection

inner join on just one single column,

equal to the following SQL:

select student.id from student join record

intersection just being convenient, does not add new ability. it is equal to natrual join.

Rename Operator

useful in union, different and intersection

useful in self-join

e.g. find pairs in the same table

alternative notation

Two different other ways to write the relational algebra