#include <iostream>
#include <ginac/ginac.h>
using namespace std;
using namespace GiNaC;

    

int main()
     {
       symbol a_0("a_0"), a_1("a_1"), a_2("a_2"), a_3("a_3"), a_4("a_4"), a_5("a_5"),a_6("a_6"),a_7("a_7"),a_8("a_8"),a_9("a_9"),a_10("a_{10}"),a_11("a_{11}"),a_12("a_{12}"),a_13("a_{13}");
       symbol u("u");
       int i,j;
       ex w=a_0*pow(u,-1)+a_1+a_2*pow(u,1)+a_3*pow(u,2)+a_4*pow(u,3)+a_5*pow(u,4)+a_6*pow(u,5)+a_7*pow(u,6)+a_8*pow(u,7)+a_9*pow(u,8)+a_10*pow(u,9)+a_11*pow(u,10)+a_12*pow(u,11)+a_13*pow(u,12);  
   ex dw=diff(w,u);
   ex ddw=diff(dw,u);
   ex EOM=(expand(ddw+w*w*w)); 

   
      EOM=EOM.subs(a_0==pow(-2,numeric(1,2)),subs_options::algebraic);
      EOM=EOM.subs(a_1==0);
      EOM=EOM.subs(a_2==0);
      EOM=EOM.subs(a_3==0);
      EOM=EOM.subs(a_5==0);
      EOM=EOM.subs(a_6==0);
      EOM=EOM.subs(a_7==0);
      EOM=EOM.subs(a_9==0);
      EOM=EOM.subs(a_10==0);
      EOM=EOM.subs(a_11==0);
      

  
  
   cout<<latex;
 cout<<"\\documentclass[12pt]{article} \n";
  cout<<"\\topmargin -0.5in \n";
  cout<<"\\oddsidemargin -0.5in \n";
  cout<<"\\evensidemargin -0.5in \n";
  cout<<"\\textheight 9in \n";
  cout<<"\\textwidth 6.5in \n";
  cout<<"\\begin{document} \n";
  cout<<"\\begin{tabular}{|c|c|}\\hline \n";
  cout<<"\\multicolumn{2}{|c|}{\\bf $\\ddot{w}=-w^3$}\\\\\\hline \n";
  cout<<"$u^{-3}$"<<"&"<<"$"<<EOM.coeff(u,-3)<<"$\\\\\n";
  cout<<"$u^{-2}$"<<"&"<<"$"<<EOM.coeff(u,-2)<<"$\\\\\n";
  cout<<"$u^{-1}$"<<"&"<<"$"<<EOM.coeff(u,-1)<<"$\\\\\n";
  cout<<"$u^{0}$"<<"&"<<"$"<<EOM.coeff(u,0)<<"$\\\\\n";
  cout<<"$u^{1}$"<<"&"<<"$"<<EOM.coeff(u,1)<<"$\\\\\n";
  cout<<"$u^{2}$"<<"&"<<"$"<<EOM.coeff(u,2)<<"$\\\\\n";
  cout<<"$u^{3}$"<<"&"<<"$"<<EOM.coeff(u,3)<<"$\\\\\n";
  cout<<"$u^{4}$"<<"&"<<"$"<<EOM.coeff(u,4)<<"$\\\\\n";
  cout<<"$u^{5}$"<<"&"<<"$"<<EOM.coeff(u,5)<<"$\\\\\n";
  cout<<"$u^{6}$"<<"&"<<"$"<<EOM.coeff(u,6)<<"$\\\\\n";
  cout<<"$u^{7}$"<<"&"<<"$"<<EOM.coeff(u,7)<<"$\\\\\n";
  cout<<"$u^{8}$"<<"&"<<"$"<<EOM.coeff(u,8)<<"$\\\\\n";
  cout<<"$u^{9}$"<<"&"<<"$"<<EOM.coeff(u,9)<<"$\\\\\n";
  cout<<"$u^{10}$"<<"&"<<"$"<<EOM.coeff(u,10)<<"$\\\\\n";
  cout<<"\\hline\n";
  cout<<"\\end{tabular}\n";
  cout<<"\\end{document}\n";
         return 0;
     }