Rôle de la monarchie dans le système politique britannique

In the United Kingdom, the constitutional structure balances the role of the Sovereign with the sovereignty of Parliament. If we denote the total legislative influence in the House of Commons as $L_{total} = 100\%$, and the executive authority of the Prime Minister is symbolized as $E_{PM} > 0$, the monarch's direct legislative power is defined as $M_{leg} = 0$. Based on this, explain the role of the monarch in the British political system.