Question: ALgebraic equation

I am trying to solve the system of equation by maple but its not giving the correct answer.

> e1 := (1/2)*alpha*alpha[3]^2*q[2]^3-V*alpha[4]*q[2]^2-V*alpha[0]+(1/2)*alpha*alpha[0]^2+(1/2)*alpha*alpha[1]^2*q[2]+(1/2)*alpha*alpha[2]^2*q[2]^2+(1/2)*alpha*alpha[4]^2*q[2]^4-V*alpha[2]*q[2]+C+alpha*alpha[3]*q[2]^2*alpha[1]+alpha*alpha[4]*q[2]^3*alpha[2]+alpha*alpha[4]*q[2]^2*alpha[0]+alpha*alpha[2]*q[2]*alpha[0];
> e2 := -gamma*alpha[2]*q[3]*q[2]^2+2*beta*alpha[4]*q[2]^2*q[3]+(3/2)*alpha*alpha[3]^2*q[2]^2*q[3]+2*alpha*alpha[4]^2*q[2]^3*q[3]+(1/2)*alpha*alpha[1]^2*q[3]+alpha*alpha[2]*q[3]*alpha[0]+2*alpha*alpha[3]*q[2]*alpha[1]*q[3]+beta*alpha[2]*q[3]*q[2]-2*gamma*alpha[4]*q[3]*q[2]^3+3*alpha*alpha[4]*q[2]^2*alpha[2]*q[3]+2*alpha*alpha[4]*q[2]*q[3]*alpha[0]+alpha*alpha[2]^2*q[2]*q[3]-2*V*alpha[4]*q[2]*q[3]-V*alpha[2]*q[3];
> e3 := -16*gamma*alpha[2]*q[4]*q[2]^2+(3/2)*alpha*alpha[3]^2*q[2]^2*q[4]+8*beta*alpha[4]*q[2]^2*q[4]+(3/2)*alpha*alpha[3]^2*q[2]*q[3]^2+alpha*alpha[4]*q[3]^2*alpha[0]-(15/2)*gamma*alpha[2]*q[3]^2*q[2]+(3/2)*beta*alpha[2]*q[3]^2+2*alpha*alpha[4]^2*q[2]^3*q[4]+3*alpha*alpha[4]^2*q[2]^2*q[3]^2+(1/2)*alpha*alpha[1]^2*q[4]-31*gamma*alpha[4]*q[3]^2*q[2]^2+7*beta*alpha[4]*q[2]*q[3]^2+alpha*alpha[2]*q[4]*alpha[0]+2*alpha*alpha[3]*q[2]*alpha[1]*q[4]+alpha*alpha[3]*q[3]^2*alpha[1]-32*gamma*alpha[4]*q[4]*q[2]^3+3*alpha*alpha[4]*q[2]*q[3]^2*alpha[2]+alpha*alpha[2]^2*q[2]*q[4]+2*alpha*alpha[4]*q[2]*q[4]*alpha[0]+3*alpha*alpha[4]*q[2]^2*alpha[2]*q[4]+4*beta*alpha[2]*q[4]*q[2]+4*beta*alpha[2]*q[4]*q[2]-V*alpha[4]*q[3]^2-V*alpha[2]*q[4]+(1/2)*alpha*alpha[2]^2*q[3]^2;
> e4 := 6*alpha*alpha[4]*q[2]*q[3]*alpha[2]*q[4]+(1/2)*alpha*alpha[3]^2*q[3]^3+7*beta*alpha[2]*q[3]*q[4]-85*gamma*alpha[2]*q[3]*q[4]*q[2]+5*beta*alpha[4]*q[3]^3-(15/2)*gamma*alpha[2]*q[3]^3-332*gamma*alpha[4]*q[3]*q[2]^2*q[4]+alpha*alpha[2]^2*q[3]*q[4]+3*alpha*alpha[3]^2*q[2]*q[3]*q[4]+2*alpha*alpha[3]*q[4]*alpha[1]*q[3]+6*alpha*alpha[4]^2*q[2]^2*q[3]*q[4]+2*alpha*alpha[4]*q[3]*q[4]*alpha[0]-2*V*alpha[4]*q[3]*q[4]+alpha*alpha[4]*q[3]^3*alpha[2]+32*beta*alpha[4]*q[2]*q[3]*q[4]+2*alpha*alpha[4]^2*q[2]*q[3]^3-80*gamma*alpha[4]*q[3]^3*q[2];
> e5 := (3/2)*alpha*alpha[3]^2*q[2]*q[4]^2+(3/2)*alpha*alpha[3]^2*q[3]^2*q[4]+alpha*alpha[4]*q[4]^2*alpha[0]-120*gamma*alpha[2]*q[4]^2*q[2]-496*gamma*alpha[4]*q[4]^2*q[2]^2-(165/2)*gamma*alpha[2]*q[3]^2*q[4]+6*beta*alpha[2]*q[4]^2-(105/2)*gamma*alpha[4]*q[3]^4+3*alpha*alpha[4]*q[3]^2*alpha[2]*q[4]+28*beta*alpha[4]*q[2]*q[4]^2+27*beta*alpha[4]*q[3]^2*q[4]+alpha*alpha[3]*q[4]^2*alpha[1]-810*gamma*alpha[4]*q[3]^2*q[2]*q[4]+3*alpha*alpha[4]*q[2]*q[4]^2*alpha[2]+6*alpha*alpha[4]^2*q[2]*q[3]^2*q[4]-V*alpha[4]*q[4]^2+(1/2)*alpha*alpha[2]^2*q[4]^2+(1/2)*alpha*alpha[4]^2*q[3]^4+3*alpha*alpha[4]^2*q[2]^2*q[4]^2;
> e6 := (3/2)*alpha*alpha[3]^2*q[3]*q[4]^2-192*gamma*alpha[2]*q[3]*q[4]^2-1938*gamma*alpha[4]*q[3]*q[2]*q[4]^2-546*gamma*alpha[4]*q[3]^3*q[4]+6*alpha*alpha[4]^2*q[2]*q[3]*q[4]^2+42*beta*alpha[4]*q[3]*q[4]^2+2*alpha*alpha[4]^2*q[3]^3*q[4]+3*alpha*alpha[4]*q[3]*q[4]^2*alpha[2];
> e7 := (1/2)*alpha*alpha[3]^2*q[4]^3+alpha*alpha[4]*q[4]^3*alpha[2]-1280*gamma*alpha[4]*q[4]^3*q[2]+20*beta*alpha[4]*q[4]^3-120*gamma*alpha[2]*q[4]^3-1695*gamma*alpha[4]*q[3]^2*q[4]^2+3*alpha*alpha[4]^2*q[3]^2*q[4]^2+2*alpha*alpha[4]^2*q[2]*q[4]^3;
> e8 := 2*alpha*alpha[4]^2*q[3]*q[4]^3-2040*gamma*alpha[4]*q[3]*q[4]^3;
> e9 := -840*gamma*alpha[4]*q[4]^4+(1/2)*alpha*alpha[4]^2*q[4]^4;
> e10 := (1/2)*beta*alpha[1]*q[3]-(1/2)*gamma*alpha[1]*q[3]*q[2]-(3/2)*gamma*alpha[3]*q[3]*q[2]^2+3*alpha*alpha[4]*q[2]^2*alpha[3]*q[3]+2*alpha*alpha[4]*q[2]*q[3]*alpha[1]+2*alpha*alpha[3]*q[2]*alpha[2]*q[3]+alpha*alpha[3]*q[3]*alpha[0]+alpha*alpha[2]*q[3]*alpha[1]+(3/2)*beta*alpha[3]*q[2]*q[3]-V*alpha[3]*q[3];
> e11 := 2*alpha*alpha[4]*q[2]*q[4]*alpha[1]+3*alpha*alpha[4]*q[2]*q[3]^2*alpha[3]+3*alpha*alpha[4]*q[2]^2*alpha[3]*q[4]+2*alpha*alpha[3]*q[2]*alpha[2]*q[4]-(3/2)*gamma*alpha[1]*q[3]^2+alpha*alpha[2]*q[4]*alpha[1]+alpha*alpha[3]*q[3]^2*alpha[2]+3*beta*alpha[3]*q[3]^2+2*beta*alpha[1]*q[4]-8*gamma*alpha[1]*q[4]*q[2]+6*beta*alpha[3]*q[2]*q[4]-V*alpha[3]*q[4]+alpha*alpha[3]*q[4]*alpha[0]-(33/2)*gamma*alpha[3]*q[3]^2*q[2]-24*gamma*alpha[3]*q[4]*q[2]^2+alpha*alpha[4]*q[3]^2*alpha[1];
> e12 := 2*alpha*alpha[4]*q[3]*q[4]*alpha[1]+2*alpha*alpha[3]*q[3]*alpha[2]*q[4]-18*gamma*alpha[1]*q[3]*q[4]-(351/2)*gamma*alpha[3]*q[3]*q[4]*q[2]+6*alpha*alpha[4]*q[2]*q[3]*alpha[3]*q[4]+alpha*alpha[4]*q[3]^3*alpha[3]+(27/2)*beta*alpha[3]*q[3]*q[4]-(45/2)*gamma*alpha[3]*q[3]^3;
> e13 := 3*alpha*alpha[4]*q[2]*q[4]^2*alpha[3]+3*alpha*alpha[4]*q[3]^2*alpha[3]*q[4]+12*beta*alpha[3]*q[4]^2-24*gamma*alpha[1]*q[4]^2+alpha*alpha[4]*q[4]^2*alpha[1]-264*gamma*alpha[3]*q[4]^2*q[2]+alpha*alpha[3]*q[4]^2*alpha[2]-225*gamma*alpha[3]*q[3]^2*q[4];
> e14 := 3*alpha*alpha[4]*q[3]*q[4]^2*alpha[3]-540*gamma*alpha[3]*q[3]*q[4]^2;
> e15 := alpha*alpha[4]*q[4]^3*alpha[3]-360*gamma*alpha[3]*q[4]^3;
> e16 := alpha*alpha[3]*q[2]^2*alpha[2]+alpha*alpha[1]*alpha[0]+alpha*alpha[4]*q[2]^3*alpha[3]+alpha*alpha[3]*q[2]*alpha[0]+alpha*alpha[4]*q[2]^2*alpha[1]-V*alpha[3]*q[2]+alpha*alpha[2]*q[2]*alpha[1]-V*alpha[1];

> solve({e1, e10, e11, e12, e13, e14, e15, e16, e2, e3, e4, e5, e6, e7, e8, e9}, [alpha[2], alpha[4], alpha[3], alpha[1], alpha[0], alpha, beta, C, V]);
[[                                                                             
[[alpha[2] = 0, alpha[4] = 0, alpha[3] = 0, alpha[1] = 0, alpha[0] = alpha[0], 
[[                                                                             

                                               1               2       ]]
  alpha = alpha, beta = beta, C = V alpha[0] - - alpha alpha[0] , V = V]]
                                               2                       ]]
> 

Please solve the problem.

Moderator: cleaned up posting