Decomp --- Introduction ---

This is a mathematical exercise with a very simple principle: given a function (real of one variable x) φ(x)=f(g(x)) which is composed of two functions f et g, and eventually one of the composing functions, the exercise asks you to find the other composing function.

In practice, this exercise may call for knowledges in various fields: linear algebra, factorization of integers, derivatives, roots right up to knowledges in algebraic geometry.:

This exercise accepts several option parameters which change the style and the level of difficulty. This level of difficulty varies from very easy even for a novice, up to very hard even for a professional mathematician.

You may go to the exercise with a simple choice of the level of difficulty: 1 ( very easy) , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ( a real challenge)

If you are expert, you can choose these parameters one by one.
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