Android actionbar

Este codigo es de la actividad principal donde pongo la Toolbar
<!-- /res/layout/activity_main.xml -->
<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context="com.techcomputerworld.tcw.test_menu.MainActivity">


    <android.support.v7.widget.Toolbar
        android:id="@+id/toolbar"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:background="?attr/colorPrimary"
        android:minHeight="?attr/actionBarSize"
        android:elevation="4dp"
        android:theme="?attr/actionBarTheme"
        android:layout_alignParentTop="true"
        android:layout_alignParentStart="true"
        app:popupTheme="@style/ThemeOverlay.AppCompat.Light"
        />
</RelativeLayout>
/*
 * otra layout que define el menu que solo he puesto uno
 */
<!-- /res/menu/actionmenu.xml -->
<?xml version="1.0" encoding="utf-8"?>
<menu xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto">
    <!-- "Mark Favorite", should appear as action button if possible -->
    <item
        android:id="@+id/action_favorite"
        android:icon="@drawable/ic_favorite_black"
        android:title="@string/action_favorite"
        app:showAsAction="ifRoom"/>

    <!-- Settings, should always be in the overflow -->
    <item android:id="@+id/action_settings"
        android:title="@string/action_settings"
        app:showAsAction="never"/>

</menu>
/*
 * Aqui ya pongo codigo en Java para que lo veais y tambien pondre el manifiesto de la aplicacion que es importante añadir la linea que           hay que añadir
mainactivity.java
 */
package com.techcomputerworld.tcw.test_menu;

import android.support.v7.app.ActionBar;
import android.support.v7.app.AppCompatActivity;


import android.os.Bundle;
import android.support.v7.widget.Toolbar;
import android.view.MenuItem;

public class MainActivity extends AppCompatActivity {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        Toolbar maintoolbar = (Toolbar)findViewById(R.id.toolbar);
        setSupportActionBar(maintoolbar);

        //obtener el soporte correspondiente a la toolbar
        ActionBar ab = getSupportActionBar();

        //Enable the Up Button
        ab.setDisplayHomeAsUpEnabled(true);

    }
    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        switch (item.getItemId()) {
            case R.id.action_settings:
                // User chose the "Settings" item, show the app settings UI...
                return true;

            case R.id.action_favorite:
                // User chose the "Favorite" action, mark the current item
                // as a favorite...
                return true;

            default:
                // If we got here, the user's action was not recognized.
                // Invoke the superclass to handle it.
                return super.onOptionsItemSelected(item);

        }
    }
}
/*
aqui pongo otro fichero xml
androidmanifest.xml
*/
<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="com.techcomputerworld.tcw.test_menu">

    <application
        android:allowBackup="true"
        android:icon="@mipmap/ic_launcher"
        android:label="@string/app_name"
        android:roundIcon="@mipmap/ic_launcher_round"
        android:supportsRtl="true"
        android:theme="@style/Theme.AppCompat.Light.NoActionBar">
        <!--android:theme="@style/Theme.AppCompat.DayNight.NoActionBar"-->

        <activity android:name=".MainActivity"
            android:parentActivityName=".MainActivity">

            <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
    </application>

</manifest>
Esta claro que en algun sitio esta el error, si pudierais revisarlo porque fijo que es un error tonto de novato.