# Question:Nonlinear system of 14 equations/unknowns, 9 parameters: eliminate

## Question:Nonlinear system of 14 equations/unknowns, 9 parameters: eliminate

Maple 16

Hello,

this is the second time I'm writing.

I posted this question in June http://www.mapleprimes.com/questions/201781-System-Of-Parametric-Equations.

This time I have  a similar problem because I'm trying to find a solution for a parametric system of equations but the number of equations and parameters is much bigger and using the tips you gave me last time I couldn't reach any result.

Here is the system:

1) alpha=v*a*u*b ;
2) alpha=v*a*u*(1-b);
3) alpha= v*z*c*(1-a) ;
4) alpha=v*z*(1-a)*(1-c) ;
5) alpha=1/2*v*a* u* b* (-p*u*b+p*u*b*a+b*g-g);
6) alpha=1/2*v*a*u*(1-b)* (p u b-p u b a-b g-p u+p u a);
7) alpha =1/2*v*c*z*(1-a)* (c* (-z*p*a+q)-q);
8) alpha=1/2*v*z*((1-a)*(1-c)* (c*z*p*a-z*p*a-q*c);
9) alpha=v*a*u*b*(1- b)*(-p*u+p*u*a+g) ;
10) alpha=v*a*u*b*z*c*p*(1-a) ;
11) alpha=a*u*b*z*(1-a)*(1-c) ;
12) alpha=a*u*z*c*(1-a)*(1-b);
13) alpha=v*a*u*z*p*(1-a)*(1-b)*(1-c);
14) alpha= v*c*z*(1-a)*(1-c)*(-z*p*a+q);

I have 14 equations/unknowns and 8 parameters (a, b, c, u, v, z, p, q).

I would like to write this system only in terms of alphas. In order to do so, I usually try to find the value for the parameters and the substitute them into the equations (and I have already found b,c,g,q using this technique) but I couldn't manage to find all of them.

Howveer, as you suggested me, with Maple there is the command "eliminate" that implement exactly what I'm looking for but I can't make it work.

This is my code:

> sys := {alpha = v*a*u*(1-b), alpha = v*a*u*b, alpha = v*z*c*(1-a), alpha = v*z*(1-a)*(1-c), alpha = (1/2)*v*a*u*(1-b)*(p*u*b-p*u*b*a-b*g-p*u+p*u*a), alpha = v*a*u*b*(1-b)*(-p*u+p*u*a+g), alpha =      z*c*a*u*(1-a)*(1-b), alpha = v*z*a*u*p*(1-a)*(1-b)*(1-c), alpha = (1/2)*v*a*u*b*(-p*u*b+p*u*b*a+b*g-g), alpha = v*z*c*a*u*b*p*(1-a), alpha = z*a*u*b*(1-a)*(1-c), alpha = (1/2)*v*c*z*(1-a)*(c*(-z*p*a+q)-q), alpha = v*c*z*(1-a)*(1-c)*(-z*p*a+q), alpha = (1/2)*v*z*(1-a)*(1-c)*(c*z*p*a-z*p*a-q*c)};

> eliminate(sys, {a,b,c, p, q, u, v, z});

> simplify(%, size);

I also tries to substitute in the system the four parameters I already found but still I can't find a solution.

What am I doing wrong? Or the problem is that it is too complicated? 