A function is an equation which shows the relationship between the input x and the output y and where there is exactly one output for each input. Another word. The Graph class represents a Neo4j graph database. Connection . This method will permanently remove all nodes and relationships from the graph and cannot be undone. evaluate Find a single node by label and optional property. Create equations that describe numbers or relationships. • A-CED Create F- IF Compare properties of two functions each represented in a different way. ( algebraically expression, determine which function has the greater rate of change. Analyze functions using . INCLUDED IN THE STUDENT MANUAL. Task #1.
Let's look at the tables required to define this relationship: After finding the matching user IDs, they are used to query the posts table. Now that we have examined the table structure for the relationship, let's define it on the Country model: Typical Eloquent foreign key conventions will be used when performing the relationship's queries. If you would like to customize the keys of the relationship, you may pass them as the third and fourth arguments to the hasManyThrough method.
The third argument is the name of the foreign key on the intermediate model. The fourth argument is the name of the foreign key on the final model. The fifth argument is the local key, while the sixth argument is the local key of the intermediate model: One To One Polymorphic Table Structure A one-to-one polymorphic relation is similar to a simple one-to-one relation; however, the target model can belong to more than one type of model on a single association.
For example, a blog Post and a User may share a polymorphic relation to an Image model. Using a one-to-one polymorphic relation allows you to have a single list of unique images that are used for both blog posts and user accounts.
First, let's examine the table structure: Model Structure Next, let's examine the model definitions needed to build this relationship: For example, to retrieve the image for a post, we can use the image dynamic property: In our case, that is the imageable method on the Image model.
So, we will access that method as a dynamic property: One To Many Polymorphic Table Structure A one-to-many polymorphic relation is similar to a simple one-to-many relation; however, the target model can belong to more than one type of model on a single association. For example, imagine users of your application can "comment" on both posts and videos. Using polymorphic relationships, you may use a single comments table for both of these scenarios. First, let's examine the table structure required to build this relationship: For example, to access all of the comments for a post, we can use the comments dynamic property: In our case, that is the commentable method on the Comment model.
For example, a blog Post and Video model could share a polymorphic relation to a Tag model. Using a many-to-many polymorphic relation allows you to have a single list of unique tags that are shared across blog posts and videos. The Post and Video models will both have a tags method that calls the morphToMany method on the base Eloquent class: So, for this example, we will define a posts method and a videos method: For example, to access all of the tags for a post, you can use the tags dynamic property: In our case, that is the posts or videos methods on the Tag model.
So, you will access those methods as dynamic properties: However, you may wish to decouple your database from your application's internal structure. In that case, you may define a "morph map" to instruct Eloquent to use a custom name for each model instead of the class name: Querying Relations Since all types of Eloquent relationships are defined via methods, you may call those methods to obtain an instance of the relationship without actually executing the relationship queries.
In addition, all types of Eloquent relationships also serve as query buildersallowing you to continue to chain constraints onto the relationship query before finally executing the SQL against your database.
For example, imagine a blog system in which a User model has many associated Post models: Dynamic Properties If you do not need to add additional constraints to an Eloquent relationship query, you may access the relationship as if it were a property.
For example, continuing to use our User and Post example models, we may access all of a user's posts like so: Because of this, developers often use eager loading to pre-load relationships they know will be accessed after loading the model. Eager loading provides a significant reduction in SQL queries that must be executed to load a model's relations.
Representing functions as rules and graphs
Querying Relationship Existence When accessing the records for a model, you may wish to limit your results based on the existence of a relationship. For example, imagine you want to retrieve all blog posts that have at least one comment. To do so, you may pass the name of the relationship to the has and orHas methods: For example, you may retrieve all posts that have at least one comment and vote: These methods allow you to add customized constraints to a relationship constraint, such as checking the content of a comment: For example, imagine you want to retrieve all blog posts that don't have any comments.
To do so, you may pass the name of the relationship to the doesntHave and orDoesntHave methods: These methods allows you to add customized constraints to a relationship constraint, such as checking the content of a comment: For example, the following query will retrieve all posts with comments from authors that are not banned: This means the relationship data is not actually loaded until you first access the property.
However, Eloquent can "eager load" relationships at the time you query the parent model. So, if we have 25 books, this loop would run 26 queries: Thankfully, we can use eager loading to reduce this operation to just 2 queries. When querying, you may specify which relationships should be eager loaded using the with method: Eager Loading Multiple Relationships Sometimes you may need to eager load several different relationships in a single operation.
To do so, just pass additional arguments to the with method: For example, let's eager load all of the book's authors and all of the author's personal contacts in one Eloquent statement: For this reason, Eloquent allows you to specify which columns of the relationship you would like to retrieve: Constraining Eager Loads Sometimes you may wish to eager load a relationship, but also specify additional query constraints for the eager loading query.
Representing Functions and Relations
Of course, you may call other query builder methods to further customize the eager loading operation: For example, this may be useful if you need to dynamically decide whether to load related models: The array values should be Closure instances which receive the query instance: For example, perhaps you need to insert a new Comment for a Post model.
Imagine tossing a ball straight up into the air, watching it rise, stop, and fall back down into your hand. As time passed, the height of the ball changed, creating a relationship between the amount of time the ball was in the air and its height. In mathematics, a relationship between variables that change together such as time and height is called a relation.
Functions Defined There are many kinds of relations. Among the most important algebraic relations are functions. A function is a relation in which one variable specifies a single value of another variable. For example, when you toss a ball, each second that passes has one and only one corresponding height. Time only goes forward, and never repeats itself. The height of the ball depends on how much time has passed since it left your hand.
Eloquent: Relationships - Laravel - The PHP Framework For Web Artisans
This is a one way relationship—although each moment of time is unique, it is possible for the ball to be at a particular height more than once as it goes up and then down. The parts of a function are called inputs and outputs.
An input is the independent, non-repeating quantity. The output quantity is the dependent quantity.
The value of the output depends on the value of the input. For each input, there is a single output. In the case of tossing a ball in the air, time is the input and height is the output. Remember the last time you were in a parking lot? Is this relation a function? Can you use the number of cars to correctly figure out the number of tires?
Every single car has 4 tires, so the number of tires depends on how many cars are in the parking lot. Every input of cars specifies a single possible output of tires.
In this example, the relation of tires to cars is also a function—the number of tires also specifies the number of cars.