<img src="/img/tutorial/bigger-applications/image01.png">

## Include the same router multiple times with different `prefix` { #include-the-same-router-multiple-times-with-different-prefix }

You can also use `.include_router()` multiple times with the *same* router using different prefixes.

This could be useful, for example, to expose the same API under different prefixes, e.g. `/api/v1` and `/api/latest`.

/// tip

    for (int i = 0; i < keyBits; i++) {
      int same = 0x0; // bitset for output bits with same values
      int diff = 0x0; // bitset for output bits with different values
      int count = 0;
      // originally was 2 * Math.log(...), making it try more times to avoid flakiness issues
      int maxCount = (int) (4 * Math.log(2 * keyBits * hashBits) + 1);
      while (same != 0xffffffff || diff != 0xffffffff) {

And these same full-stack generators were the base of the [**FastAPI** Project Generators](project-generation.md){.internal-link target=_blank}.

/// info

Flask-apispec was created by the same Marshmallow developers.

///

/// check | Inspired **FastAPI** to

Generate the OpenAPI schema automatically, from the same code that defines serialization and validation.

///

///

And we are using this model to declare our input and the same model to declare our output:

{* ../../docs_src/response_model/tutorial002_py310.py hl[16] *}

Now, whenever a browser is creating a user with a password, the API will return the same password in the response.

In this case, it might not be a problem, because it's the same user sending the password.

* Each application that you have running on your computer has some process behind it, each running program, each window, etc. And there are normally many processes running **at the same time** while a computer is on.
* There can be **multiple processes** of the **same program** running at the same time.

The parameter `name` is defined as `Optional[str]`, but it is **not optional**, you cannot call the function without the parameter:

```Python
say_hi()  # Oh, no, this throws an error! 😱
```

The `name` parameter is **still required** (not *optional*) because it doesn't have a default value. Still, `name` accepts `None` as the value:

```Python
say_hi(name=None)  # This works, None is valid 🎉
```

* **Machine Learning**: it normally requires lots of "matrix" and "vector" multiplications. Think of a huge spreadsheet with numbers and multiplying all of them together at the same time.

This is the same mechanism used when you give permissions while logging in with Facebook, Google, GitHub, etc:

<img src="/img/tutorial/security/image11.png">

## JWT token with scopes { #jwt-token-with-scopes }

Now, modify the token *path operation* to return the scopes requested.

   *       (<i>symmetric</i> property)
   *   <li>If {@code equivalent(x, y)} and {@code equivalent(y, z)} are both true, then {@code
   *       equivalent(x, z)} is also true (<i>transitive</i> property)
   * </ul>
   *
   * <p>Note that all calls to {@code equivalent(x, y)} are expected to return the same result as
   * long as neither {@code x} nor {@code y} is modified.