Represent a subquery in relational algebra

Question

How do I represent a subquery in relation algebra? Do I put the new select under the previous select condition?

SELECT number
FROM collection
WHERE number =          


        

Answer 1

According to this pdf, you can convert a sub-query easily to a relational algebric expression.

Firstly, you have to convert the whole query from the form

SELECT Select-list FROM R1 T1, R2 T2, ...
WHERE
some-column = (
    SELECT some-column-from-sub-query from r1 t1, r2 t2, ...
    WHERE extra-where-clause-if-needed)

to

SELECT Select-list FROM R1 T1, R2 T2, ...
WHERE
EXISTS (
    SELECT some-column-from-sub-query from r1 t1, r2 t2, ...
    WHERE extra-where-clause-if-needed and some-column = some-column-from-sub-query)

Then you have to convert the sub-query first into relational algebra. To do this for the sub-query given above:

PI[some-column-from-sub-query](
    SIGMA[extra-where-clause-if-needed 
        ^ some-column = some-column-from-sub-query
        ](RO[T1](R1) x RO[T2](R2) x ... x RO[t1](r1) x RO[t2](r2) x ...)
)

Here R1, R2... are the contextual relations, and r1, r2... are sub-query relations.

As the syntax is pretty disaster in stack overflow, please head over to that pdf to get a broad overview of how to convert sub query to relational algebra.