Do Muslims demand the application of Sharia upon Christians in a country whose inhabitants are shared by Muslims and Christians?

Muslims are required to apply Islamic Sharia wherever they have influence, and they apply it among themselves in all aspects of their lives. If they have a state, they are required to apply it to everyone, both Muslims and People of the Book, by obliging the People of the Book to pay Jizya and submit to the banner of Islam, according to the stipulated conditions for Dhimmis. If Christians dispute and resort to Muslims for judgment, Muslims have the option to judge between them or to decline. If they do judge, the judgment must be in accordance with Islamic Sharia. If the dispute is with a Muslim, it is necessary to resort to Muslim judges. Applying Sharia achieves justice and security for all members of society. Fair-minded Christians have acknowledged this, and indeed, they have testified that the rule of Muslims was better than the rule of their own people.