1. Lecture 3 SQL Relational Algebra Aggregate Operators
GROUP BY and HAVING
Arithmetic, AS in SELECT
DDL
Set theory operators in SQL
Subqueries
Relational Algebra
Join queries
Set queries
Rename operator
Divide operator
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2. Learning Objectives
LO2.1 Write SQL queries involving GROUP BY and HAVING.
LO2.2 Write an SQL query involving set operators.
LO2.3 Write an SQL query involving a subquery.
LO2.4 Tell whether an SQL subquery is correlated.
LO2.5 Write join queries in relational algebra
LO2.6 Write set operator queries in relational algebra
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3. Aggregate Operators Let's return to the cl tables in your handout.
Find the number of donations, the largest, the smallest and the average donation.
SELECT COUNT(*), MAX(amount), MIN(amount), AVG(amount)
FROM indivcl;
round(AVG(amount),2) will get rid of all those significant digits.
count max min avg
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4. Aggregates with DISTINCT*
What is the difference between
SELECT COUNT(street1) FROM commcl;
and
SELECT COUNT(DISTINCT street1) FROM commcl;
The difference is that the first query will retrieve the number of street1 addresses, which is the same as the number of committees. The second will retrieve the number of distinct addresses, which, as you can see, is much less.
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5. Bad SQL*
What are the occupations of donors who gave the highest donations?
This SQL doesn't make sense because the query processor has no way to know which values of occup to list with the MAX value of amount.
What if the aggregate function were AVG?
So if one aggregate operator appears in the SELECT clause, then ALL of the entries in the select clause must be aggregate operators (unless the query includes a GROUP BY clause - covered next).
SELECT occup, MAX(amount)
FROM indivcl;
AVG has the same problem – there may be no one, or more than one donor, who gave the average donation.
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6. French Fries Warmup-1* What is the largest donation for each month?
Month MAX(amount)
STRATEGY: First GROUP the rows by month, then SELECT the month and MAX size
NOTE: “each month”  GROUP BY month
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7. GROUP BY Here is the SQL for that query: SELECT month, MAX(amount)
3 For each month, compute the values in the SELECT clause
FROM indivcl
1 Gather rows from indivgb
GROUP BY month
2 Create groups, one for each GROUP BY value
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8. French Fries Warmup-2*
For each committee that has less than five donations of over $200, what is the total number of donations for that committee?
committeeid SUM(amount) C C
STRATEGY: First keep donations > $500, then GROUP BY commitee, then keep the groups HAVING < 5 distinct donations, then SELECT the committeeid and total donations.
NOTE: Did you include the committeeid in the answer?
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9. SQL for this query: HAVING
SELECT commid, SUM(amount)
5 For each committee, compute the values in the SELECT clause
FROM indivgb
1 Gather rows from indivgb
WHERE amount > 200
2 Keep rows satisfying the WHERE condition
GROUP BY commid
3 Create groups, one for each GROUP BY value
HAVING COUNT(*) > 5;
4 Keep groups satisfying the HAVING condition
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10. Practice Group By/Having*
Back to the indivcl on your handout. What is the SQL for:
For commitees that received at least three donations in March, how many donations did they receive?
SELECT commid, COUNT(*)
FROM indivcl
WHERE month = 3
GROUP BY commid
HAVING COUNT(*) > 2;
Notice that the WHERE clause, keeps rows, whereas the HAVING clause, keeps groups. It is easy to confuse these two clauses, so keep in mind that one keeps rows, the other keeps groups.
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11. 12/7/2018

12. LO2.1: GROUP BY/HAVING
Consider only donations in February and March. For each committee that had at least $2500 in donations, display that committee's range* of donations.
*range = highest - lowest
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13. Arithmetic and AS in SELECT
SELECT commcl.commid, commname,
MAX(amount) - MIN(amount) AS Range
Arbitrary arithmetic is possible in the SELECT clause.
AS is used to label output columns.
FROM commcl JOIN indivcl USING (commid)
WHERE month = 2 OR month = 3
donations in February and March
GROUP BY commcl.commid,
commcl.commname
commname must be here to be in the SELECT clause
HAVING(SUM(amount)>=2500);
any group condition can be in the HAVING clause
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14. NULLs and Aggregates
The value NULL is ignored by all aggregate functions. COUNT, SUM, AVG all ignore it, and it cannot be the MIN or MAX. COUNT(*) is the number of rows but COUNT(att) is the number of rows with non-null att values.
However, if you GROUP BY an attribute, a separate group is created for NULL values of the attribute.
So you don't like NULL and vow never to insert NULL values in your database? Sorry. If you aggregate (except count) over an empty table, you get NULL. There's no way to avoid it.
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15. Return to DDL: Populating a Database
Recall that SQL consists of DDL and DML.
We've been learning DML.
Let's digress for a bit and learn some more DDL, by reviewing the code for populating the PostgreSQL database we're using.
Related to ETL in data warehousing
Populating a database consists of these steps (my files)
0. Format and clean the data (u2uc)
Create the schema (Tables.sql)
Copy the data into the database (cs)
Create structures and other tables (DDL.sql)
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16. 0. Format and clean the data (u2uc)
The first step does not involve DDL
The shell script u2uc prepares files for copying into PostgreSQL.
unzip: decompress
FEC compresses the data for faster data transfer and cheaper storage
dos2unix: remove carriage return
The parameter -437 suppresses an error message
pit: C program to insert delimiter | between fields
split : writes a file into line pieces (xaa,xab,…) so it can be edited
u2uc Document in 
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17. 1. Create the schema (Tables.sql)
The next step is to create schemas for all the FEC tables. This is done in Tables.sql .
Note these DDL statements:
DROP TABLE [IF EXISTS] tablename;
CREATE TABLE tablename (
[ attributename domain [ [NOT] NULL], ….] )
For domains see
CREATE TABLE has many other options, see documentation.
As we have discussed, for efficiency reasons, we don't use any of those other options until after the copy step.
Tables.sql Document in 
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18. Sidebar on DROP DROP TABLE tablename; is not the same as
DELETE FROM tablename;
The former deletes the table's rows and all its structure – it no longer exists. The latter just deletes the rows. There is a shorter way to delete the rows: TRUNCATE tablename;
DROP applies to many objects: databases, schemas, constraints, views, etc, and these depend on each other. So SQL3 requires that you specify either CASCADE or RESTRICT, though no DBMS does.
CASCADE: drop everything that depends on it.
For example, a foreign key dependency
RESTRICT: if anything depends on it, do not execute the command (typically the default).
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19. 2. Copy the data into the database (cs)
There are two COPY commands in PostgreSQL, one in SQL and another in psql.
psql executes in the address space of the DBMS
We use the psql version because CAT's databases are on a remote server.
The COPY commands are invoked from a shell script, cs, which takes as a parameter part of the name of the database, e.g., $ cs 386
Note that blank princomm or assoccand values are changed to NULL.
cs Document in 
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20. 3. Create structures and other tables (DDL.sql): INTO, IN
Now that we have copied data into the database, we use ALTER TABLE to change the database schema, and SELECT … INTO to create new tables.
First we ALTER TABLE tablename DROP column; to get rid of filler columns.
We will discuss the stored procedure next week;
Skip to Oregon versions. Notice INTO…. , which can appear after any SELECT clause.
INTO creates a new table with attributes from the SELECT clause.
An error is raised if a table with that name exists.
Results are not returned to the user.
DDL.sql Document in 
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21. DDL.sql, Ctd.
In the in class versions, notice the use of IN. It can be used in any WHERE clause
IN is true when the left side is contained in the right side
Notice how a primary key constraint is declared
Recall that those columns were declared NOT NULL in the CREATE TABLE statements.
Why do we give a name to the constraints?
Can easily DROP them or ALTER them later.
Notice the foreign key constraints, which we have discussed.
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22. Set Operators in SQL
We now turn to set operators in SQL: UNION, INTERSECT, Difference (in SQL this is called EXCEPT or MINUS).
Suppose A, B are sets. What is the definition of
A UNION B, A∪B?
A INTERSECT B, AB?
A MINUS B, A – B?
You've seen these operators in CS250, but here they operate on multisets. So they come in two versions. UNION, INTERSECT and EXCEPT/MINUS eliminate duplicates. Each of them with ALL preserve duplicates.
Let's see how they work.
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23. UNION Let’s consider the entire FEC data: cand, comm, indiv, pas.
Suppose I have a table indivlast, leftover from the last time I taught the course, representing donations from the 2006 election. I want to combine it with indiv and display all the results. The proper SQL to do that is:
SELECT * FROM indiv
UNION
SELECT * FROM indivlast
The UNION appears between any two SQL statements.
The output of the SQL statements must be UNION-Compatible:
Domains of corresponding attributes must be the same
Names don't need to be the same. The names of the first table are used in the output.
SELECT * from indivcl UNION SELECT * FROM commcl is illegal.
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24. Surprise! (UNION ALL)
Suppose we want to simplify the result by omitting the date:
SELECT fecid,commid,occup,month,amount FROM indivlast
UNION
SELECT fecid,commid,occup,month,amount FROM indiv
We'll be surprised to learn that this time we have fewer donations!
UNION eliminates duplicates.
To avoid duplicate elimination, use UNION ALL.
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25. Subquery in FROM Clause
The previous UNION statements have displayed results on the screen. Suppose I want to place results in indivnew.
SELECT * INTO indivnew
FROM (
(SELECT * FROM indiv)
UNION
(SELECT * FROM indivlast)
) AS indiv_union;
Note the "subquery" in the FROM clause, enclosed in parens.
Any expression, whose result is a table, is legal as a term (comma-separated) in the FROM clause.
SQL requires a range variable after a FROM subquery.
Subquery
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26. INTERSECTION* Is this query legal?
SELECT princomm FROM candcl WHERE party = 'REP'
INTERSECT
SELECT commid FROM indivcl where month = 1;
Identify one row in the answer to this query.
Describe, in nontechnical English, what this query produces:
INTERSECT eliminates duplicates, but INTERSECT ALL will retain them.
It is legal because the SQL statements are union-compatible. Each outputs committee-ids, with the same domains.
The answer to the query is:
princomm C
The principal committees of Republican candidates that received donations in January
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27. EXCEPT (or MINUS)* Identify one row in the answer to this query.
In nontechnical English, what does this query retrieve?
SELECT commid FROM commcl
EXCEPT
SELECT commid FROM indivcl WHERE month=2;
EXCEPT eliminates duplicates, but EXCEPT ALL will retain them
The answer to this query is:
Commid C C C C C C C C C C C C C C
The query retrieves committees that did not receive a donation in February
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28. Example*
In indivcl, which unique committees received donations in January OR in February? Write the answer in three different ways, one with and two without a set operator. Order the results by commid.
SELECT DISTINCT commid FROM indivcl
WHERE month = 1 OR month = 2
order by commid;
WHERE month IN {1,2}
SELECT commid FROM indivcl WHERE month = 1
UNION
SELECT commid FROM indivcl WHERE month = 2
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29. LO2.2: Example*
In indivcl, which unique committees received donations in January AND in February? Write the answer in two different ways, with and without a set operator.
SELECT DISTINCT i1.commid FROM indivcl i1, indivcl i2
WHERE i1.commid = i2.commid AND
I1.month = 1 AND i2.month = 2 ;
SELECT commid FROM indivcl WHERE month = 1
INTERSECT
SELECT commid FROM indivcl WHERE month = 2;
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30. SUBQUERIES (in the WHERE Clause)*
The circled expression, a complete SELECT..FROM..WHERE query, is called an inner block or subquery. The rest is the outer block.
Describe what this query retrieves. Hint: First figure out what the subquery retrieves.
Note that the scope of the range variable in the subquery overrides that of the outer query.
SELECT occup FROM indivcl
WHERE amount =
(SELECT MAX(amount) FROM indivcl)
How would you execute this query?
English: What are the occupations of the donors who gave the highest donations?
Execute: replace subquery with constant, then execute result query.
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31. LO2.3:Practice Subqueries*
Write the SQL to return the occupations of donors who gave donations (at any time) of at least $500 more than the minimum donation given during March.
SELECT occup FROM indivcl
WHERE amount >= 500 +
(SELECT MIN(amount) FROM indivcl where month = 3);
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32. IN and subqueries
You've seen IN, in the definition of the cl tables, e.g.:
SELECT candid, candname, party, street1, princomm
INTO candcl
FROM cand WHERE candid IN ('P ', 'P ' , 'S6OR00094' , 'S8OR00207') ;
IN can also precede a subquery:
SELECT commname FROM commcl m
WHERE m.commid IN ( SELECT i.commid
FROM indivcl i
WHERE amount > 1000);
What does this query return?
How would you execute this query?
NOT IN is also legal in a query
Query returns names of committees that received a donation over $1000.
Execute it by replacing the subquery with a set of commids, then executing the resulting query, which will look like the previous one.
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33. LO2.4:Unnesting/Flattening a Query*
Queries with subqueries are called nested queries.
Often they can be rewritten as flat queries.
This typically makes them much faster to execute
Can you write a flat version of the previous query?
SELECT commname FROM commcl m
WHERE m.commid IN ( SELECT i.commid
FROM indivcl I
WHERE amount > 1000);
Hint: Think of what it returns, then write that query.
Why do you need DISTINCT in the flat version?
Often the nested version is easier to write.
names of committees that received a donation over $1000
SELECT DISTINCT commname
FROM commcl JOIN indivcl USING(commid)
WHERE amount > 1000;
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34. EXISTS* What does this query return? SELECT N.candname FROM candcl N
WHERE EXISTS ( SELECT *
FROM commcl M
WHERE M.assoccand = N.candid AND
M.street1 LIKE '228 S WASHINGTON ST%');
How would you execute this query?
Because of N.candid, you cannot substitute a constant for the subquery
Such a query is called correlated.
Returns names of candidates that have at least one associated committee whose address begins 228 S WASHINGTON ST
You can execute this query using what it called tuple-at-a-time semantics:
For each row N in candcl, execute the subquery, which will return a single value. Then execute the entire query.
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35. Review, Preview
We are working with structured data, modeled with the relational model.
Databasics Anonymous 7-step method:
Organizing structured data into an ER Diagram, Ch. 2
Transforming an ER diagram into a Schema of Tables, Ch. 3
Eliminating anomalies from those tables (normalization), Ch. 21
Structuring those tables efficiently (physical design), Ch. 22
Managing those tables using the intergalactic standard language (SQL), Ch. 5
The DBMS manages the tables internally using Relational Algebra, Ch. 4
Protecting those tables during concurrent use (ACID properties), Ch. 16
Accessing those tables through a web-based interface (some scripting language)
Now we continue step 5 and study Relational Algebra.
Done
Done
Next
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36. (R)DBMS Architecture Security Parser Catalog Optimizer Concurrency
Web Form
Applic. Front end
SQL interface
SQL
Security
Parser
Catalog
Relational Algebra(RA)
Optimizer
Executable Plan (RA+Algorithms)
Concurrency
Plan Executor
Files, Indexes &
Access Methods
Crash
Recovery
Database, Indexes
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37. Relational Algebra: 5 Basic Operations
Select() Selects a subset of rows from a table (horizontal)
Project() Selects a subset of columns from a table (vertical)
Cross-product() Computes all combinations from two tables
Set-difference () Rows in table1, not in table2
Union () Rows in table1 and/or in table2
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38. Algebra Relational Algebra is an algebra of operators on tables
Input is (a) table(s), output is a table
Just as plus, minus, multiply, divide are an algebra of operators on numbers
Since each relational algebra operation produces a table, the relational algebra is closed.
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39. Select ()
Consider the indivcl table in the handout. Suppose we want to find donations of more than $2000.
We construct the answer with the query
amount > 2000 indivcl,
whose output is
fecid commid occup month amount
C PACIFIC CREST/PRINCIPLE
C SELF-EMPLOYED
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40. Examples using the Select Operator*
How many rows are in the output of each query?
amount <= 225 indivcl
(amount > 2000) (commid=‘C ’) indivcl
(commid=‘C ’) (amount > 1000) indivcl
Is there a simple way to calculate this?
(amount > 1000) ( (commid=‘C431445’) indivcl )
The predicate
amount <= 225 indivcl [3]
(amount > 2000) (commid=‘C ’) indivcl [6]
(commid=‘C ’) (amount > 1000) indivcl [0]
Is there a simple way to calculate this?
(amount > 1000) ( (commid=‘C431445’) indivcl ) [0]
An algebraic expression
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41. Project operator () in relational algebra
Which committees received donations from in the period January-April 2008?
commid(indivcl)
This query will produce 21 rows, with many CommIDs repeated – like the Recipient table we saw previously.
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42. The Project operator in the the Relational Model and in DBMSs
The project operator in the relational model operates on relations (sets), so the project operator in the relational algebra eliminates duplicates.
But the project operator in DBMSs, operating on tables/multisets, does not eliminate duplicates.
In this class we will study relational algebra on tables, so project does not eliminate duplicates.
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43. Smart question
At this point some smart person in class will ask: in DBMSs, how do you eliminate duplicates from a multiset of data items?
There is a duplicate elimination operator. It is a terribly important, and expensive, operator, like sorting, but it changes only the presentation properties of the data.
We will introduce these two operators later, when we talk about algorithms for RA operators.
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44. Practice with , *
Show the IDs of our 4 candidates and their principal committees
Show the occupations of donors who donated at least $500
Show the committees that received donations of more than $200.
Show the IDs of our 4 candidates and their principal committees
candid,princommcandcl
Show the occupations of donors who donated at least $500
occup(amount>=500indivcl)
Show the committees that received donations of more than $200.
commid(amount>200indivcl)
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45.  occup(amount < 1000indivcl)
Equivalent Queries*
Describe in English the output of this query
 occup(amount < 1000indivcl)
Which of these queries is equivalent to the above query, i.e. gives the same output for all table instances?
amount < 1000( occup, amountindivcl)
amount < 1000( occupindivcl)
 occup(amount < 1000( occup, amountindivcl))
Describe in English the output of this query
 occup(amount < 1000indivcl)
Occupations of of donors who donated less than $1,000 to some committee.
Which of these queries is equivalent to the first query, i.e. gives the same output for all table instances?
amount < 1000( occup, amountindivcl)
Not equivalent. Has an extra attribute
amount < 1000( occupindivcl)
Not equivalent. Not well formed
 occup(amount < 1000( occup, amountindivcl))
Equivalent
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46. The Cross Product Operator, 
All our previous operators are unary operators, they operate on one table. The cross product operator is our first binary operator and is fundamental to most other binary operators.
T1  T2 is every possible combination of rows from T1 and T2. For example T1 T2
candid candname
P MCCAIN, JOHN S.
P OBAMA, BARACK
S6OR SMITH, GORDON
S8OR MERKLEY, JEFFREY
commid commname
C REPUBLICAN NATIONAL COMMITTEE
C DEMOCRATIC NATIONAL COMMITTEE
T1T2
candid candname commid commname
P MCCAIN, JOHN S. C REPUBLICAN NATIONAL COMMITTEE
P OBAMA, BARACK C REPUBLICAN NATIONAL COMMITTEE
S6OR00094 SMITH, GORDON C REPUBLICAN NATIONAL COMMITTEE
S8OR00207 MERKLEY, JEFFREY C REPUBLICAN NATIONAL COMMITTEE
P MCCAIN, JOHN S. C DEMOCRATIC NATIONAL COMMITTEE
P OBAMA, BARACK C DEMOCRATIC NATIONAL COMMITTEE
S6OR00094 SMITH, GORDON C DEMOCRATIC NATIONAL COMMITTEE
S8OR00207 MERKLEY, JEFFREY C DEMOCRATIC NATIONAL COMMITTEE
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47. The Join Operator, ⋈ Joining condition
Suppose we want to list each candidate’s name along with his/her principal committee’s name.
We want to combine a candidate row n in candcl with a committee row m in commcl if
n.princomm = m.commid
Try it on a few row pairs (n,m).
The notation for the required query is:
candname, commname( candcl ⋈ princomm=commid commcl )
And its output is:
Joining condition
candname commname
MCCAIN, JOHN S. JOHN MCCAIN 2008 INC.
OBAMA, BARACK OBAMA FOR AMERICA
SMITH, GORDON FRIENDS OF GORDON SMITH
MERKLEY, JEFFREY JEFF MERKLEY FOR OREGON
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48. commname, candname(commcl ⋈ assoccand=candidcandcl)
LO2.5 Practice with Join*
Describe in English what this computes:
commname, candname(commcl ⋈ assoccand=candidcandcl)
Write a query describing, for each donor, the occupation of the donor and the name of the candidate to whom he/she donated.
The query computes:
The name of each committee with its associated candidate’s name
The requested query is:
occup, candname((indivcl ⋈commid=commidcommcl) ⋈ assoccand=candidcandcl)
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49. Join as a derived operator
Is it possible to derive the join operator from other operators that we have seen? That is, could you express every join query in terms of previous operators we have seen?
T1 ⋈joincondT2  joincond ( T1 T2)
Note that this is valid for every table T1 and T2 and every join condition “joincond”.
Thus the join operator is not one of the original five operators in the relational algebra.
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50. Foreign Key Joins
Almost every join used in the real world is a foreign key join, in which the join condition is "a foreign key equals the key it refers to".
That is the main reason it helps to draw a picture of a schema with arrows pointing from foreign keys to the keys they refer to; many software tools will do this automatically.
Such a diagram (which looks like but is not the same as an ER diagram) can be very helpful in formulating join queries.
That's why I gave you the file to help you in homework 2.
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51. Seldom used Flavors of Join
The join operators we use are called equijoins since the join conditions are equalities between attributes, typically a foreign key to the key that it references.
There are 2 other kinds of joins that are seldom used.
One is inequalities between attributes, called theta-join or θ-join. Those of you who have used databases: have you ever seen one?
Here’s an example. What does it compute?
commid, commid(indivcl ⋈ amount<amountindivcl)
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52. Natural Join
Another seldom used flavor of join (in practice, though it is important in theory) is the join operator ⋈ without any subscript, called a natural join. To make this work, you give foreign keys the same name as the key they refer to. Here’s an example, with the foreign keys in italics:
newcandcl( candid, candname, party, street1, commid)
newcommcl( commid, commname, address, candid)
newindivcl( fecid, commid, occup, month, amount)
The natural join newindivcl ⋈ newcommcl
will combine each donation with the committee donated to.
There are four reasons the use of natural join is discouraged :
It does not permit the use of meaningful attribute names like candcl(princomm) or commcl(assoccand) .
If you add a new attribute, it may break existing code.
Sometimes a natural join does not give what is intended. For example, what will the query newcandcl ⋈ newcommcl produce?
4. It's hard to distinguish between a natural join and a join without conditions.
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53. Set Operators in Relational Algebra
Set Operators (Union, difference, intersect) in relational algebra are very similar to SQL's set operators.
Their operands must be union-compatible, that is, have the same domains in corresponding attributes, though not necessarily the same names.
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54. The Union Operator 
Suppose indivlast represents donations from 2006, and we want to form the table of 2006 and 2008 donations.
The natural operator is Union:
indivcl  indivlast
The Union operator, in the relational model and in DBMSs, eliminates duplicates.
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55. The Difference Operator  *
Write the RA expression that lists the committees that did not receive donations.
commidcommcl  commidindivcl
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56. The Intersect Operator  *
R intersect S, RS, is the rows that are in R and S.
Like join, intersect adds no computational power to the five basic relational algebra operators, because
R  S = R  (R  S)
What is the meaning of this query?
 princommcandcl   commid(amount>500 indivcl)
Which principal committees have received at least one donation of more than $500?
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57. LO2.6 Practice*
What are the occupations of donors who have given at least one donation of > 500 and at least one donation of <500?
What are the IDs of Committees who have received at least one donation > 1000 and at least one donation < 250 but whose street1 is not ‘228 S WASHINGTON ST’?
occup(amount>500 indivcl)   occup(amount<500 indivcl)
--This is not quite right. Do you see why?
The difficulty arises because occupation is not a key.
So it is possible that there are two different donors with the same occupation. One gives a large donation, the other gives a small donation. But their common occupation still ends up in the answer.
( Commid(amount>1000 indivcl   commid(amount<250 indivcl)) –  commid (street1=‘228 S WASHINGTON ST’ commcl)
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58. ρ(temp,  commID (street1=‘228 S WASHINGTON ST’ commcl))
The Rename Operator ρ
Our relational algebraic expressions will soon get too complex to put on one line, or to formulate in one step.
The rename operator ρ allows us to form temporary tables.
ρ(temp,  commID (street1=‘228 S WASHINGTON ST’ commcl))
This places the result of the  query into the table named temp.
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59. ρ( B,  princomm (party='DEM' candcl))
The Divide Operator 
A(x,y)  B(y) is all values of x such that (x,y) is in A for every value of y in B.
What are the occupations of donors who have given to the principal committee of every democratic candidate?
First form the principal committee of every DEM candidate:
ρ( B,  princomm (party='DEM' candcl))
Now form the occupations and committees of donors:
ρ( A,  commid,occup (indivcl))
and calculate the results
A  B
princomm C C
12/7/2018

60. Divide as a derived operator
Division is another operator that can be derived from the five basic operators, but is useful for logic applications.
Idea: For R(x,y)  S(y), compute all x values that are not “disqualified” by some y value in S.
x value is disqualified if for some y value in S, (x,y) is not in X
Disqualified x values: x((x(R)  S)  R)
R  S = x (R)  disqualified x values
12/7/2018

61. Division in SQL Find account owners who own all types of accounts
SELECT A1. Owner
FROM Account-owner A1
WHERE NOT EXISTS (
SELECT T.Type
FROM Account-types T
SELECT A2.*
FROM Account-owner A2
WHERE A2.Type=T.Type
AND A2.Owner=A1.Owner))
Find owners A1 such that
There is no account type T
That A1 does not possess
12/7/2018