10 years, 7 days

## Nonlinear system of 14 equations/unknown...

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[1]=v*a*u*b ;
2) alpha[2]=v*a*u*(1-b);
3) alpha[3]= v*z*c*(1-a) ;
4) alpha[4]=v*z*(1-a)*(1-c) ;
5) alpha[11]=1/2*v*a* u* b* (-p*u*b+p*u*b*a+b*g-g);
6) alpha[22]=1/2*v*a*u*(1-b)* (p u b-p u b a-b g-p u+p u a);
7) alpha[33] =1/2*v*c*z*(1-a)* (c* (-z*p*a+q)-q);
8) alpha[44]=1/2*v*z*((1-a)*(1-c)* (c*z*p*a-z*p*a-q*c);
9) alpha[12]=v*a*u*b*(1- b)*(-p*u+p*u*a+g) ;
10) alpha[13]=v*a*u*b*z*c*p*(1-a) ;
11) alpha[14]=a*u*b*z*(1-a)*(1-c) ;
12) alpha[23]=a*u*z*c*(1-a)*(1-b);
13) alpha[24]=v*a*u*z*p*(1-a)*(1-b)*(1-c);
14) alpha[34]= 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[1] = v*a*u*(1-b), alpha[2] = v*a*u*b, alpha[3] = v*z*c*(1-a), alpha[4] = v*z*(1-a)*(1-c), alpha[11] = (1/2)*v*a*u*(1-b)*(p*u*b-p*u*b*a-b*g-p*u+p*u*a), alpha[12] = v*a*u*b*(1-b)*(-p*u+p*u*a+g), alpha[13] =      z*c*a*u*(1-a)*(1-b), alpha[14] = v*z*a*u*p*(1-a)*(1-b)*(1-c), alpha[22] = (1/2)*v*a*u*b*(-p*u*b+p*u*b*a+b*g-g), alpha[23] = v*z*c*a*u*b*p*(1-a), alpha[24] = z*a*u*b*(1-a)*(1-c), alpha[33] = (1/2)*v*c*z*(1-a)*(c*(-z*p*a+q)-q), alpha[34] = v*c*z*(1-a)*(1-c)*(-z*p*a+q), alpha[44] = (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?

Elena

## System of parametric equations...

Maple

Hello,

I'm quite new to Maple and I have a serious problem when I'm trying to solve this system of equations for (a,b,p,v,u,g):

1) alpha[1]= v a u (1- b)
2) alpha[2]= v a ub
3) alpha[3]= v (1-a)=v-va
4) alpha[11]= 1/(2) auv (-1+b) (-b u p+b a u p+b g+p u-u p a)
5) alpha[22]= 1/(2) a u v b (-b u p+b a u p+b g-g)
6) alpha[33]= 1/(2)(a- 1)apv
7) alpha[12]= -a u v b(pu-pua-g - bup +baup +bg)
8) alpha[13]= (a-1) (b-1)ap vu
9) alpha[23]= (1-a) a p v ub

I tried this command:

solve({v*(1-a) = alpha[3], a*u*v*b = alpha[2], v*a*u*(1-b) = alpha[1], (1/2*(-1+a))*a*p*v = alpha[33], (-1+a)*(-1+b)*a*p*v*u = alpha[13], (1-a)*a*p*v*u*b = alpha[23], (1/2)*a*u*v*b*(-b*u*p+b*a*u*p+b*g-g) = alpha[22], -a*u*v*b*(p*u-u*p*a-g-b*u*p+b*a*u*p+b*g) = alpha[12], (1/2)*a*u*v*(-1+b)*(-b*u*p+b*a*u*p+b*g+p*u-u*p*a) = alpha[11]}, {a, b, g, p, u, v}, 'parametric' = 'full', 'parameters' = {alpha[1], alpha[2], alpha[3], alpha[11], alpha[12], alpha[13], alpha[22], alpha[23], alpha[33]})

but the Maple output is [ ]. I can find a solution manually but I don't understand why I cannot do it with Maple. It's very important that I find a solution as I have a much more complicated system to solve in a similar manner.

Thank you very much for your help!!

Elena

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