Question: How to find this solution using Maple?

Hello,

I have several sets of nonlinear equations that need to be solved for certain unknowns. In many cases, the equations admit more than one solution, and Maple is sometimes able to find different solutions by changing the order of the unknowns.

However, in one particular case, I haven't been able to get Maple to find a known solution that was obtained elsewhere.

Below are the equations, the list of unknowns, the solution returned by Maple, and the alternative solution I'm trying to obtain.

Is there a way to guide Maple to find this other solution?

eqjerkAB:=[-alpha[9, 1, 1] - alpha[9, 2, 2] - alpha[9, 3, 3] = -alpha[14, 1, 1] - alpha[14, 2, 2] - alpha[14, 3, 3], alpha[9, 1, 1] + alpha[9, 2, 2] = alpha[14, 1, 1] + alpha[14, 2, 2], -alpha[9, 2, 6]*alpha[9, 3, 5] = -alpha[14, 2, 6]*alpha[14, 3, 5], alpha[9, 1, 1]*alpha[9, 3, 3] + alpha[9, 2, 2]*alpha[9, 3, 3] = alpha[14, 1, 1]*alpha[14, 3, 3] + alpha[14, 2, 2]*alpha[14, 3, 3], alpha[9, 1, 1]*alpha[9, 2, 6]*alpha[9, 3, 5] - alpha[9, 1, 2]*alpha[9, 2, 6]*alpha[9, 3, 4] = alpha[14, 1, 1]*alpha[14, 2, 6]*alpha[14, 3, 5], -alpha[9, 1, 1]*alpha[9, 2, 2]*alpha[9, 3, 3] - alpha[9, 1, 2]*alpha[9, 2, 6]*alpha[9, 3, 0] = -alpha[14, 1, 1]*alpha[14, 2, 2]*alpha[14, 3, 3] + alpha[14, 1, 2]*alpha[14, 2, 1]*alpha[14, 3, 3]]:

incA:={alpha[9, 1, 1], alpha[9, 1, 2], alpha[9, 2, 2], alpha[9, 2, 6], alpha[9, 3, 0], alpha[9, 3, 3], alpha[9, 3, 4], alpha[9, 3, 5]}:

solM:=[alpha[9, 1, 1] = (alpha[9, 1, 2]*alpha[9, 2, 6]*alpha[9, 3, 4] + alpha[14, 1, 1]*alpha[14, 2, 6]*alpha[14, 3, 5])/(alpha[14, 2, 6]*alpha[14, 3, 5]), alpha[9, 1, 2] = alpha[9, 1, 2], alpha[9, 2, 2] = (-alpha[9, 1, 2]*alpha[9, 2, 6]*alpha[9, 3, 4] + alpha[14, 2, 2]*alpha[14, 2, 6]*alpha[14, 3, 5])/(alpha[14, 2, 6]*alpha[14, 3, 5]), alpha[9, 2, 6] = alpha[9, 2, 6], alpha[9, 3, 0] = alpha[14, 3, 3]*(-alpha[14, 1, 2]*alpha[14, 2, 1]*alpha[14, 2, 6]^2*alpha[14, 3, 5]^2 + alpha[9, 1, 2]*alpha[14, 3, 5]*alpha[9, 2, 6]*alpha[9, 3, 4]*(alpha[14, 1, 1] - alpha[14, 2, 2])*alpha[14, 2, 6] + alpha[9, 1, 2]^2*alpha[9, 2, 6]^2*alpha[9, 3, 4]^2)/(alpha[9, 1, 2]*alpha[9, 2, 6]*alpha[14, 3, 5]^2*alpha[14, 2, 6]^2), alpha[9, 3, 3] = alpha[14, 3, 3], alpha[9, 3, 4] = alpha[9, 3, 4], alpha[9, 3, 5] = alpha[14, 2, 6]*alpha[14, 3, 5]/alpha[9, 2, 6]]:

solother:={alpha[9,2,2]=-alpha[9,1,1] + alpha[14,1,1] + alpha[14,2,2],
alpha[9,3,0] = (((alpha[9,1,1] - alpha[14,1,1])*(alpha[9,1,1] - alpha[14,2,2]) - alpha[14,1,2]*alpha[14,2,1])*alpha[14,3,3])/(alpha[9,1,2]*alpha[9,2,6]),
alpha[9,3,3] = alpha[14,3,3],
alpha[9,3,4] = (alpha[9,1,1] - alpha[14,1,1])*alpha[14,2,6]*alpha[14,3,5]/(alpha[9,1,2]*alpha[9,2,6]),
alpha[9,3,5] = alpha[14,2,6]*alpha[14,3,5]/alpha[9,2,6]}:

Many thanks.

Ed