I want to know that if you are given a very complex equation g(x)=A(T). How could you solve for x, which is a function of variable T. To be more specific, I encounter a polylogarithmic function I need to solve numerically..
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I guess by complex equation you don't mean equation with complex variables but a polynomial. I have a solution for you. Take a value of T and find out A(T)=y. Now get x solving g(x)-y=0 using a bisection method (or some root finding algorithm). Do that for every x on the parameter space. Choose your initial values carefully. You may use some plotting software to decide them.