Hello everyone! I am (trying <https://github.com/jessegrabowski/gEconpy>) to use Sympy to automatically derive first order conditions and a log-linear approximation to non-linear systems of equations from user provided problem descriptions. An example system might look something like this:
-C_t - I_t + K_t-1*r_t + L_t*w_t I_t - K_t + K_t-1*(1 - delta) -lambda_t + C_t**(-sigma_C) -L_t**sigma_L + lambda_t*w_t beta*(lambda_t+1*r_t+1 + lambda_t+1*(1 - delta)) - lambda_t A_t*K_t-1**alpha*L_t**(1 - alpha) - Y_t alpha*A_t*K_t-1**(alpha - 1)*L_t**(1 - alpha) - r_t A_t*K_t-1**alpha*(1 - alpha)/L_t**alpha - w_t rho_A*log(A_t-1) + epsilon_A_t - log(A_t) A priori I know that this particular system can be written in reduced form in only two state variables, A_t and K_t. At the bare minimum, many equations can be eliminated via substitution. For example, we clearly see that lambda_t = C_t ** (-sigma_C), and we could make that substitutions everywhere to eliminate the equation. Less obviously, I can combine equations -4, -3 and -2 to get a single expression for w_t as a function of r_t, eliminating that variable. If the system were linear, I could easily obtain the reduced form in Sympy with something like this: A, b = sp.linear_eq_to_matrix(system) sp.rref(sp.hstack(A, b)) But in the non-linear case I understand there is no "nice" way to do this. I guess I am asking if anyone knows of tricks (or better yet algorithms) to attack a problem like this? I currently use a big stack of heuristics, for example looking for equations with only 2 non-parameter atoms in the form y = f(x), then recursively making substitutions. These heuristics are quite flaky though, because I'm quite out of my depth. Thank you to everyone for such a marvelous open source tool! Jesse -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/146998fa-c6e5-4c5b-8c8a-76861b7c7446n%40googlegroups.com.
