Relational Algebra Join - necessary to rename? - join

Let's assume i have some 2 simple tables:
IMPORTANT: This is about relational algebra, not SQL.
Band table:
band_name founded
Gambo 1975
John. 1342
Album table:
album_name band_name
Celsius. Gambo
Trambo Gambo
Now, since the Band and the Album table share the same column name "band_name", would it be necessary to rename it when i would join them?
As far as i know, the join eliminates the duplicate entry that is shared amongst the join. This example, where i simply pick all Bands that are existing in the Album table (obviously just 'Gambo' in this giving example)
Πfounded, band_name(Band ⋈ Album)
should therefore work fine, right? Can somebody confirm?

(Have to enter a caveat that there are many variants of Relational Algebra; that they differ in semantics; and they differ in syntax. Assuming you intend a variant similar to that in wikipedia ...)
Yes that expression should work fine. The natural join operator ⋈ matches same-named attributes between its two operands. So the subexpression Band ⋈ Album produces a result with attributes {band_name, founded, album_name}. Your expression projects two of those.
Note the attributes for a relation value are a set not a sequence; therefore any operation over relation operands with same-named attributes must match attributes.
In contrast, Cartesian Product × requires its operands to have disjoint attribute names. Then Band × Album is ill-formed and would be rejected. (So you'd need to Rename band_name in one of them, to get relations that could be operands.)
I'm not all that happy with your way of putting it "the join eliminates the duplicate entry that is shared amongst the join." Because only in SQL do you get a duplicate (from SELECT * FROM Band, Album ... -- which results in a table with four columns, of which two are named band_name). SQL FROM list of tables is a botch-up: neither join nor Cartesian Product, but something trying to be both, and succeeding only in being neither. RA's ⋈ never produces a "duplicate" so never does it "eliminate" anything.
Particularly if there's Keys declared and a Foreign Key constraint (from Album's band_name to Band's) I see those as identifying the same band, then the natural operation is to bring together that which has been taken apart, so the name 'Natural Join'.

Related

Why does `has_one` in rails require a foreign key?

Consider two tables Foo and Bar and consider models based on them. Now consider a one-to-one relationship between them.
Foo contains has_one :bar in it's declaration so that we're able to access Bar from Foo's objects. But then what I don't understand is why Bar needs a foreign key referencing Foo?
Shouldn't it be easier if they just compare both the ids to get the result?
I'm assuming that there will be problems with comparing both ids and I want to know what the problems are.
The problem with ids is that they store auto-incremented values. Let's consider 2 tables students and projects.
Let's assume a student can have at most 1 project. Which means he can either have a project or not.
Now consider 2 students A & B.
students table
id name
1 A
2 B
now projects table
id name
1 P1
2 NULL
in this case A has a project named as P1 but B doesn't and we're creating a null entry just to maintain and match the id of records present in projects with the students but this is not feasible in the long term. If in a school there are 1000 students then we'll have may be 500 empty rows for 500 students who are not working on a project.
That's why adding a column in projects table is a feasible solution to reduce the size of the table and maintain relationships as well and also if you're going to delete a record then the new id won't be same as the previous one as id's are auto-incremented.
now projects table
id name student_id
1 P1 1
is more feasible and flexible as well. You can make it has_many as well because a student can work on multiple projects as well.
I hope this helps you.
You can't assume that the DB engine will add the same IDs to rows in different tables. You can (I would not recommend) make an app with such behavior and implement it with triggers and constraints, but this would be a very creative (in a negative sense) approach to relational databases.

ER Model representing entities not stored in DB and user choice

I'm trying to create a ER diagram of a simple retail chain type database model. You have your customer, the various stores, inventory etc.
My first question is, how to represent a customer placing an order in a store. If the customer is a discount card holder, the company has their name, address etc, so I can have a cardHolder entity connect to item and store with an order relationship. But how do I represent an order being placed by a customer who is not really an entity in the database?
Secondly, how are conditional... stuff represented in ER diagrams, e.g. in a car dealership, a customer may choose one or more optional extra when buying a car. I would think that there is a Car entity with the relevant attributes and the options as a multi-valued attribute, but how do you represent a user picking those options (I.e. order table shows the car ordered, extras chosen and the added cost of extras) in the order relationship?
First, do you really need to model customers as distinct entities, or do you just need order, payment and delivery details? Many retail systems don't track individual customers. If you need to, you can have a customer table with a surrogate key and unique constraints on identifying attributes like SSN or discount card number (even if those attributes are optional). It's generally hard to prevent duplication in customer tables since there's no ideal natural key for people, so consider whether this is really required.
How to model optional extras depends on what they depends on. Some extras might be make or model-specific, e.g. the choice of certain colors or manual/automatic transmission. Extended warranties might be available across the board.
Here's an example of car-specific optional extras:
car (car_id PK, make, model, color, vin, price, ...)
car_extras (extra_id PK, car_id FK, option_name, price)
order (order_id PK, date_time, car_id FK, customer_id FK, payment_id FK, discount)
order_extras (order_id PK/FK, car_id FK, extra_id PK/FK)
I excluded price totals since those can be calculated via aggregate queries.
In my example, order_extras.car_id is redundant, but supports better integrity via the use of composite FK constraints (i.e. (order_id, car_id) references the corresponding columns in order, and (car_id, extra_id) references the corresponding columns in car_optional_extras to prevent invalid extras from being linked to an order).
Here's an ER diagram for the tables above:
First, as per your thought you can definitely have two kinds of customers. Discount card holders whose details are present with the company and new customers whose details aren't available with the company.
There are three possible ways to achieve what you are trying,
1) Have two different order table in the system(which I personally wouldn't suggest)
2) Have a single Order table in the system and getting the details of those who are a discount card holder.
3) Insert a row in the discount card holder table for new/unregistered customers having only one order table in the system.
Having a single order table would make the system standardized and would be more convenient while performing many other operations.
Secondly, to solve your concern, you need to follow normalization. It will reduce the current problem faced and will also make the system redundant free and will make the entities light weighted which will directly impact on the performance when you grow large.
The extra chosen items can be listed in the order against the customer by adding it at the time of generating a bill using foreign key. Dealing with keys will result in fast and robust results instead of storing redundant/repeating details at various places.
By following normalization, the problem can be handled by applying foreign keys wherever you want to refer data to avoid problems or errors.
Preferably NF 4 would be better. Have a look at the following link for getting started with normalization.
http://www.w3schools.in/dbms/database-normalization/

Select rows with "one of each" in relational algebra

Say I have a Personstable with attributes {name, pet}. How do I select the names of people where they have one of each kind of pet (dog, cat, bird), but a person only has one of each kind of pet if they pet is in the table.
Example: Bob, Dog and Bob, Cat are the only rows in the table. Therefore, Bob has one of each kind of pet. But the moment Lynda, Bird are added, Bob doesn't have one of each type of pet anymore.
I think the first step to this is to π(pet). You get a list of all kinds of pets since relational algebra removes duplicates. Not sure what to do after this, but I have think I need to join π(pet) and Persons.
I've tried a few things like Natural Join and Cross products but I haven't arrived at a result yet and I'm out of ideas.
The answer to the question can be found with the Division operator:
Persons ÷ πpet(Persons)
This relational algebra expression returns a relation with only the column name, containing all the names of the persons that have all the different kind of pets currently present in the Persons table itself.
The division is an operator that, in some sense, is the inverse of the product operator (the name is derived exactly from this fact). It is a derived operator that can be defined in terms of projection, set difference and product (see for instance this answer).

Entity Relationship Diagram: How to create a Yelp-kind of app with not just one price-range?

Im new to Rails and I'm in the middle of sketching up an ERD for my new app. A Yelp-sort of app, where a Client is sorted by price.
So I want one Client to have many priceranges - One Client can both have pricerange $ and Pricerange $$$$ for example. The priceranges are:
$ - $$ - $$$ - $$$$ - $$$$$
How would this look in a table? Would I create a table called PriceRange with Range1, Range2, Range3, Range4, Range5 to be booleans?
Doesn't the PriceRange-table need any foreign/primary keys?
PriceRange
Range1 (Boolean)
Range2 (Boolean)
Range3 (Boolean)
Range4 (Boolean)
Range5 (Boolean)
Look, I'm Brazilian and I'm not very knowledgeable about yelp applications. I do not quite know what it is, but from what I saw, they are systems to assess/measure/evaluate (perhaps the translation is wrong here for you) things, in this case, companies, right?
Following this logic, let's think...
By the description of your problem (context), you have clients (companies), and they can have price ranges, correct? If:
A price interval is represented by textual names, such as "$", "$$",
and so on,
and the same price range may have (numeric) values for different companies,
And the same price range (type) can be (or not) assigned to different
companies,
Then here is what we have:
By decomposing this conceptual model, you would end up with three tables:
Companies
Price Ranges
Price Ranges from Companies
The primary keys of Company and Price Ranges will be passed to Price Ranges from Companies as foreign keys. You can use them as a composite primary key, or use a surrogate key. If using a surrogate key, you will permit/allow a company to have the same kind of price range more than once, which I believe is not the case.
Let's look at another situation, if things are simpler as:
If there is no need to store prices,
and an company may have or not one or more price ranges represented by "$", "$$", and so on,
Then here is what we have:
Similarly, we'll have the same 3 tables. Likewise, you still must pass the primary keys of Companies and Price Ranges to Price Ranges from Companies as foreign keys.
So I want one Client to have many priceranges - One Client can both
have pricerange $ and Pricerange $$$$ for example
Notice how N-N relationships allow us to create optional relationships between entities. This will allow a company to have zero, one, two, (etc.) or all price ranges defined. Again, so that is not allowed a company to have a price range more than once, set the foreign keys as composite primary key in Price Ranges from Companies.
If you have any questions or anything I explained has nothing to do with your context, please do not hesitate to comment.
EDIT
Is the Price ranges from companies what is called a Joint table?
Yes. There are also other terms used, some in different areas of computer science, such as Link Table, or Intermediate Table.
Actually we do not have a table here in the diagram, but an entity. In the Conceptual Model there are no tables, but entities and relationships. Be careful with this terminology when developing the Conceptual Model, or else you may get confused (I say this from experience).
However, yes, once decomposed, we will have a table from this relationship. When decomposed, N-N relationships will always become tables, no exception. Differently, 1-1 and 1-N (or N-1) relationships do not become tables. These tables with these special names (Join/Link/Intermediate Tables) serves to associate records from different tables, hence the name.
And is it necessary to have a column called Price Range Id? I mean
what is it there for?
At where? If you say at the Price Ranges entity, it is rather necessary. Must We not identify records in a table in some way? Here I set what is called a Surrogate Key. If on the other hand, you have a column with unique values for each record in the table, you can also use this column. I highly recommend that you consider the use of surrogate keys. Read the link I gave you.
In the Conceptual Model, we have to define the properties and also the primary keys. During the phase of the conceptual model, natural attributes of entities can become primary keys if you so desire. In this case, we have what is called a Natural Key.
If on the other hand you refer to Price Ranges from Companies entity, so the question is another ("And is it necessary to have a column called Price Range Id?"). Here we have a table with two columns, as I told you. The two are foreign keys. You need it so you can relate rows from the two tables... I think you were not referring to that, is not it? If so, no problem, you can comment and ask more questions. I do not care to answer. To be honest, I did not quite understand your question.
EDIT 2
So that Company 28 can be identified in the Price Ranges (for instance
ID 40) Which would make it easier to call out the price ranges it has?
Maybe my English is not very good, but it seems to me that you have a beginner's doubt/question in relation to the concept of tables and relationships between them. If not that, I apologize because maybe I did not understand. But let's see...
The tables in a database have rows / records. Each line has its own data. Even with this, each line / record needs to be differentiated and identified somehow. That is why we attach to each line an identifier, known as the primary key (this, and this). In summary, the primary key is how we identify, differentiate, separate and organize different records.
Even if all records have different values, you must select a field (column) that represents the primary key of the table. By obligation, every record MUST have a primary key. Although you can choose which field is a primary key, you are allowed to choose one or more fields to serve as the primary key. When this happens, that is, when more than one field participates/serves as the primary key, we have a table with something called Composite Primary Key. Similarly, it has the ability to identify records. Note that, because of that, primary key values must be unique, otherwise you may have 2 identical records.
This is the basic concept so that we can relate tables to each other, in case, records/rows of tables together. If we have a Company identified by the ID 28 (a line/record), and we want to relate it to a Price Range identified by the ID 40, then we need to store somewhere that relationship (28 <--> 40). This is where the role of intermediate/link/join tables comes in (but only to relationships N-N! For 1-N or N-1 relationships it works similarly, but not identical).
My original question was whether it was necessary, and why a company
ID had to link up with a price range ID at all.
With this table storing records which relates to other records (for their primary keys), we can perform a SQL join operation (If you have questions about this, see this image). Depending on how you perform this operation, you'll get:
All companies that have Price Ranges.
All companies that do not have Price Ranges.
All the Price Ranges of a given company.
All companies that have or not a X Price Range.
All price ranges that are given or not to companies.
...
Anyway, you get all this because of the established relationship.
If it could just be taken out and then the table of price ranges would
only involve Pricerange1-5.
This sentence I did not understand. What should be taken out? Could you please explain this sentence better?

What do I miss in understanding 1NF

I have a nooby question regarding 1NF.
As I read from different sources a table is in the 1NF if it contains no repeating groups.
I understand this with the examples given online (usually with customers and contact names etc) but when it comes to my specific data I face difficulties.
I have the following fields:
ID TOW RECEIVER Phi01_L1 Phi01_L2 Phi01_L3
1 4353 gpo1 0.007 0.006 0.4
2 4353 gpo1 0.9 0.34 0.3
So, this table here is not in 1NF? How should it be in order to become?
What is Fist normal form (1NF)?
1NF- Disallows:
composite attributes
multivalued attributes
and nested relations; attributes whose values for an individual tuple are non-atomic
How to convert a relation into 1NF?
Two ways to convert into 1 NF:
Expand relation:
Increase number of colons in relation (as you did)
Increase rows and change Primary key value. (PK will include non-atomic attribute)
Hence your relation looks in 1-NF in present relation-state. and solution you made is expansion.
Break Relation:
Break relation into two relations -e.g. remove non-atomic col from base relation and create a new relation and add to new with PK.
Normal forms are best explain in Elmasri/Navath book

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