# SZU data design and Analysis Chapter 3 relational algebra

Posted by harman on Sat, 08 Jan 2022 09:15:10 +0100

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# Relational algebra

## 1. Union (U)

### 1.1 definition:

Union (\ (\ cup \)
The result of this operation, R  S, is a relationship that contains all tuples in R or S or both. Duplicate tuples do not appear in the output.
Formally: \ (R\) $$\cup$$ $$S$$ $$=$$ $$\{$$ $$t | t$$ $$\in$$ R or t $$\in$$ S \ (\} \)
Joint compatibility: let R and S be two relationships with attributes \ ((A1, A2,..., an) \) and \ ((B1, B2,..., BN) \) respectively. If you want to merge R and S, you should meet the following two rules:

Rule 1: relationships \ (R \) and \ (S \) must have the same degree (attribute).
Rule 2: the domain of attribute \ (i \) of \ (R \) and attribute \ (i \) of S must be the same.
$$dom(A_i) = dom(B_i)$$, where 1 $$\leq$$ i $$\leq$$ n.

## 2. Difference operation

### 2.1 definitions

Like unions, relational difference operators require their operands to be of the same type.
Format: R - S
Formally: R - S = {t | t \ (\ in \) r and t $$\notin$$ S}
Semantics: given two relationships R and s of the same type, the difference between the two relationships R-S is a relationship that contains all tuples in r that do not appear in S.

## 3. Intersection

### 3.1 definitions

The expression r ∩ S returns all tuples that appear in relationships R and S.
Like Union and difference sets, relational intersection operators require their operands to be of the same type.
Formally: R \ (\ cap \) s = {t | t \ (\ in \) r and t $$\in$$ S}
Derive from existing operator:
R $$\cap$$ S = R - (R - S) = S - (S - R)

## 4. Cartesian product (X)

### 4.1 definitions

Cartesian product or cross product is a binary operation used to combine two relationships. Suppose R and s are related to n and m attributes, Cartesian product, R × S can be written as,
R (A1, A2, ..., An) × S (B1, B2, ..., Bm)
The result of the above setting operation is,
Q (A1, A2, ..., An, B1, B2, ..., Bm)
where,
Degree (Q) = n + m
Count (q) = number of tuples in R * number of tuples in S.

## 5. Select \ (\ partial \)

$$\partial_{age=19}(student)=\partial_{selection-condition}(Relation)$$
Multiple choice

## 6. Projection \ (\ pi \)

The projection operation is used to select only a few columns from the relationship.
$$\pi_{attributes}(Relation)$$

## 7.join $$\infty$$

### 7.3 natural connection

When we omit conditions when connecting two relationships, it is called natural connection (*):

Let the relationship R1 have attributes (x1,x2,x3,M) respectively,
R2 has attributes (y1,y2,y3,y4,y5,M) respectively.
That is, the M attribute is common to the two relationships.
Then, the natural connection between R1 and R2 is a relationship with Heading(x1,x2,x3,M, y1,y2,y3,y4,y5) and body. The body is composed of all tuples, and the duplicate attribute M is deleted.

## 8. Division

If B contains all the attributes of A and B \ (common \) at the same time, it can be ignored directly

## 9. SQL statement

### 9.4 create table (primary key + foreign key)

CREATE TABLE rent_Info(
Order_ID int PRIMARY KEY AUTO_INCREMENT,
Date_Rented DATE NOT NULL,
Date_Returned DATE NOT NULL,
Optional_Insurance TINYINT DEFAULT 0,
Customer_ID VARCHAR(10),
Bag_ID int,
reverted TINYINT DEFAULT 0,
CONSTRAINT + (Constraint name) + FOREIGN key(Customer_ID) REFERENCES customers(Customer_ID),
CONSTRAINT FOREIGN key(Bag_ID) REFERENCES bags(Bag_ID)
);

### 9.5 view

create view table_name as + sentence

mysql> ALTER VIEW view_students_info
-> AS SELECT id,name,age
-> FROM tb_students_info;

mysql> DESC view_students_info;
+-------+-------------+------+-----+---------+-------+
| Field | Type        | Null | Key | Default | Extra |
+-------+-------------+------+-----+---------+-------+
| id    | int(11)     | NO   |     | 0       |       |
| name  | varchar(45) | YES  |     | NULL    |       |
| age   | int(11)     | YES  |     | NULL    |       |
+-------+-------------+------+-----+---------+-------+

drop view view_name

### 9.6 Oracle view

1.Primary key constraint
delete:alter table table_name drop primary key
2.Non NULL constraint
add to:alter  table table_name modify Column name data type  not null
delete:alter table table_name modify Column name data type null
3.Unique constraint
delete:alter table table_name drop key Constraint name
4.Automatic growth
add to:alter table table_name  modify Listing int  auto_increment
delete:alter table table_name modify Listing int
5.Foreign key constraint
add to:alter table table_name add constraint Constraint name foreign key(Foreign key column)
references Primary key table (primary key column)
delete:
First step:Delete foreign key
alter table table_name drop foreign key Constraint name
Step 2:Delete index
alter  table table_name drop  index Index name
[^1]:
The constraint name is the same as the index name
6.Default value
add to:alter table table_name alter Listing  set default 'value'
delete:alter table table_name alter Listing  drop default

### 9.9 HAVING

After where and having, there are filter criteria, but there are differences:

1.where before group by, having after group by

2. Aggregate functions (avg, sum, max, min, count) cannot be placed after where as a condition, but can be placed after having

SELECT Websites.name, SUM(access_log.count) AS nums FROM Websites
INNER JOIN access_log
ON Websites.id=access_log.site_id
WHERE Websites.alexa < 200
GROUP BY Websites.name
HAVING SUM(access_log.count) > 200;

### 9.10 DISTINCT

mysql> select DISTINCT(name) from info;
+------+
| name |
+------+
| dcj  |
+------+
3 rows in set (0.00 sec)

### 9.11 INNER JOIN

When using join, the differences between on and where conditions are as follows:

1. The on condition is used when generating temporary tables. It returns the records in the left table regardless of whether the condition in on is true or not.
2. The where condition is the condition for filtering the temporary table after the temporary table is generated. At this time, there is no meaning of left join (the records in the left table must be returned). If the condition is not true, all items will be filtered out.

### 9.12 LEFT /RIGHT JOIN

The left table lists them all

### 9.15 UNOIN / intersect / minus

The UNION operator is used to combine the result sets of two or more SELECT statements.

Note that each SELECT statement inside a UNION must have the same number of columns. Columns must also have similar data types. At the same time, the order of columns in each SELECT statement must be the same.

SELECT column_name(s) FROM table1
UNION ALL(No, ALL) Default de duplication/ instersect/ minus
SELECT column_name(s) FROM table2;