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a Christian can be a basis for the application of the death penalty?

In the teaching of the church we find the answer:
EV 56: "Both the Church and in civil society and the general public reported to postulate a very limited it [ie, the death penalty - editor. XpK] application, or even total abolition. This problem should be placed in the context of penal justice ever more in line with human dignity and thus - in the final analysis - God's plan for man and society. Indeed, the punishment which society inflicts is primarily intended to "redress the disorder caused by the offense." Public authority must redress the violation of personal and social rights, harming the offender an adequate punishment for the crime, as a condition to regain the exercise of their freedom. In this way authority also fulfills the purpose of defending public order and safety of people, while at the same time offering the offender an incentive and help to improve and to pay for guilt.
It is clear that to achieve all these objectives, the nature and extent of punishment must be carefully considered and evaluated, and ought not go to the highest dimension, ie the offender, in addition to cases of absolute necessity, ie when there are no other ways to defend society. Today, however, by getting better and better organization of the penal system, such cases are very rare, and perhaps not happen at all.
In any event, remains the principle set forth in the new Catechism of the Catholic Church: " If bloodless means are sufficient to defend human lives against an aggressor and to protect public order and safety of persons, public authority should use these measures because they are more consistent with particular contexts common good and are closer to human dignity . "
Pope says clearly that the death penalty is not excluded (the community must be able to effectively defend against an aggressor), but given the development of rehabilitation techniques and methods of isolation in the prison system is usually sufficient to protect the insulation is in jail.
Another issue is the question of why so many people favor the death penalty? Is not this is due to a desire for revenge? If so, it certainly this is not the reason either good or satisfactory.