y2 := k*2 + 1
	accum.Add(accum, tmp1.Lsh(numer, 1))
	accum.Mul(accum, tmp1.SetInt64(y2))
	numer.Mul(numer, tmp1.SetInt64(k))
	denom.Mul(denom, tmp1.SetInt64(y2))
}

func eliminateDigit(d int64) {
	accum.Sub(accum, tmp1.Mul(denom, tmp1.SetInt64(d)))
	accum.Mul(accum, ten)
	numer.Mul(numer, ten)
}

func main() {
	i := 0
	k := int64(0)
	for {
		d := int64(-1)
		for d < 0 {
			k++
			nextTerm(k)

				retryInterval := time.Duration(r.Float64() * float64(time.Second))
				logger.Info("Waiting for all MinIO IAM sub-system to be initialized.. possible cause (%v) (retrying in %s)", err, retryInterval)
				time.Sleep(retryInterval)
				continue
			}
			iamLogIf(ctx, fmt.Errorf("IAM sub-system is partially initialized, unable to write the IAM format: %w", err), logger.WarningKind)
			return
		}

		break
	}

///

## Integrando com OpenAPI

Todas as declarações de requisições, validações e requisitos para suas dependências (e sub-dependências) serão integradas em um mesmo esquema OpenAPI.

Então, a documentação interativa também terá toda a informação sobre essas dependências:

<img src="/img/tutorial/dependencies/image01.png">

// Inherit the common kubernetes flags defined in the root package. This is a bit of a hack,
// but it allows us to directly get the final values for each of these flags without needing
// to pass pointers-to-flags through all of the (sub)commands.
func (o *KubeOptions) prepare(ctx cli.Context) {
	o.Namespace = ctx.Namespace()
	if o.Namespace == "" {
		o.Namespace = ctx.IstioNamespace()

		configAccess := clientcmd.NewDefaultPathOptions()

Tudo isso, aninhado arbitrariamente.

### Defina um sub-modelo

Por exemplo, nós podemos definir um modelo `Image`:

```Python hl_lines="9-11"
{!../../docs_src/body_nested_models/tutorial004.py!}
```

### Use o sub-modelo como um tipo

E então podemos usa-lo como o tipo de um atributo:

```Python hl_lines="20"

package mountinfo

import (
	"path/filepath"
	"sync"

	"golang.org/x/sys/windows"
)

// CheckCrossDevice - check if any input path has multiple sub-mounts.
// this is a dummy function and returns nil for now.
func CheckCrossDevice(paths []string) error {
	return nil
}

// mountPointCache contains results of IsLikelyMountPoint
var mountPointCache sync.Map

// error returned in IAM service account
var errIAMServiceAccountNotAllowed = errors.New("Specified service account action is not allowed")

// error returned in IAM subsystem when IAM sub-system is still being initialized.
var errIAMNotInitialized = errors.New("IAM sub-system is being initialized, please try again")

// error returned when upload id not found
var errUploadIDNotFound = errors.New("Specified Upload ID is not found")

$nodeCount }}{{ $endIndex := add $factor $nodeCount }}{{ $beginIndex := mul $i $nodeCount }} {{ $scheme }}://{{ template `minio.fullname` $ }}-{{ `{` }}{{ $beginIndex }}...{{ sub $endIndex 1 }}{{ `}`}}.{{ template `minio.fullname` $ }}-svc.{{ $.Release.Namespace }}.svc{{if (gt $drivesPerNode 1)}}{{ $bucketRoot }}-{{ `{` }}0...{{ sub $drivesPerNode 1 }}{{ `}` }}{{ else }}{{ $bucketRoot }}{{end }}{{- end }} -S {{ .Values.certsPath }} --address :{{ .Values.minioAPIPort }} --console-address :{{ .Values.minioConsolePort...

トークンの有効期限を表す`timedelta`を作成します。

JWTアクセストークンを作成し、それを返します。

```Python hl_lines="115-130"
{!../../docs_src/security/tutorial004.py!}
```

### JWTの"subject" `sub` についての技術的な詳細

JWTの仕様では、トークンのsubjectを表すキー`sub`があるとされています。

使用するかどうかは任意ですが、`sub`はユーザーの識別情報を入れるように規定されているので、ここで使用します。

JWTは、ユーザーを識別して、そのユーザーがAPI上で直接操作を実行できるようにする以外にも、他の用途で使用されることがあります。

例えば、「車」や「ブログ記事」を識別することができます。

```Python hl_lines="3  5"
{!../../docs_src/dependencies/tutorial007.py!}
```

## Sub-dependencies with `yield`

You can have sub-dependencies and "trees" of sub-dependencies of any size and shape, and any or all of them can use `yield`.

**FastAPI** will make sure that the "exit code" in each dependency with `yield` is run in the correct order.