* Validate **complex structures**:
    * Use of hierarchical Pydantic models, Python `typing`’s `List` and `Dict`, etc.
    * And validators allow complex data schemas to be clearly and easily defined, checked and documented as JSON Schema.

The most common is the implicit flow.

The most secure is the code flow, but it's more complex to implement as it requires more steps. As it is more complex, many providers end up suggesting the implicit flow.

/// note

It's common that each authentication provider names their flows in a different way, to make it part of their brand.

real(complexT) floatT
imag(complexT) floatT
</pre>

<p>
The type of the arguments and return value correspond.
For <code>complex</code>, the two arguments must be of the same
<a href="#Numeric_types">floating-point type</a> and the return type is the
<a href="#Numeric_types">complex type</a>
with the corresponding floating-point constituents:

## Recap { #recap }

With what you have seen up to now, you can set up a secure **FastAPI** application using standards like OAuth2 and JWT.

In almost any framework handling the security becomes a rather complex subject quite quickly.

 * <p>
 * This annotation can be used on static methods to programmatically create and configure
 * beans that will be managed by the dependency injection container. It's particularly
 * useful when the bean creation requires complex logic or when the bean needs to be
 * configured based on runtime conditions.
 * <p>
 * Example usage:
 * <pre>
 * public class Providers {
 *     {@literal @}Provides
 *     {@literal @}Singleton

        }
    }

    @Nested
    class AttributeAndStateTests {

        @Test
        public void testGetTypeForFile() throws Exception {
            // Mocking underlying connection and info retrieval is complex.
            // This test focuses on the logic based on the URL structure.
            SmbFile file = new SmbFile("smb1://server/share/file.txt");
            // Without a real connection, getType relies on path parsing.

        assertNotNull(e.getMessage());
    }

    @Test
    void testMockedSuccessfulParsing() throws PACDecodingException, IOException {
        // Test with mocked PacMac to avoid complex signature calculation
        try (MockedStatic<PacMac> pacMacMock = mockStatic(PacMac.class)) {
            // Mock the calculateMac method to return a valid checksum
            byte[] mockChecksum = new byte[16];

 *   <li>network/transfer errors</li>
 *   <li>file system errors: permissions</li>
 * </ul>
 *
 * TODO carlos: all these possible has*Exceptions and get*Exceptions methods make the clients too
 *       complex requiring a long list of checks, need to create a parent/interface/encapsulation
 *       for the types of exceptions
 */
@Deprecated
public class ArtifactResolutionResult {

            // Verify overwrite
            assertEquals(concreteImplementation, cacheMap.get(key));
            assertNotEquals(oldEntry, cacheMap.get(key));
        }
    }

    @Nested
    @DisplayName("Complex Scenarios Tests")
    class ComplexScenariosTests {

        @Test
        @DisplayName("Should handle multiple fixup operations")
        void testMultipleFixupOperations() {

    String SELF_COMBINATION_REMOVE = XmlService.SELF_COMBINATION_REMOVE;

    /**
     * In case of complex XML structures, combining can be done based on id.
     */
    @Deprecated(since = "4.0.0", forRemoval = true)
    String ID_COMBINATION_MODE_ATTRIBUTE = XmlService.ID_COMBINATION_MODE_ATTRIBUTE;

    /**
     * In case of complex XML structures, combining can be done based on keys.
     * This is a comma separated list of attribute names.