I'm trying to solve the following nonlinear system
g = 1;b = 1;a = b+1;syms x y zeqn1 = 0 == -x^2/g-2*a*x-y^2/g+2*b*y+1;eqn2 = 0 == a*x-a*y-b*y+b*z-x*y/g-y*z/g;eqn3 = 0 == -y^2/g+2*a*y-z^2/g-2*b*z+1;[x,y,z] = solve([eqn1, eqn2, eqn3], [x, y, z])
When running the code I was expecting to get numeric solutions, but instead each one of them contain z1, which I think is linked to the variable z (maybe it has to do with real or complex parts?). If I write z1 in the command window and press Enter, the error "Unrecognized function or variable 'z1'." appears.
These are the solutions:
x = (230*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 1)^2)/361 + (100*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 1)^3)/361 + (21*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 1))/361 - 101/361 (230*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 2)^2)/361 + (100*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 2)^3)/361 + (21*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 2))/361 - 101/361 (230*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 3)^2)/361 + (100*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 3)^3)/361 + (21*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 3))/361 - 101/361 (230*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 4)^2)/361 + (100*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 4)^3)/361 + (21*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 4))/361 - 101/361 y = (42*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 1)^2)/19 + (10*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 1)^3)/19 + (4*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 1))/19 - 31/19 (42*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 2)^2)/19 + (10*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 2)^3)/19 + (4*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 2))/19 - 31/19 (42*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 3)^2)/19 + (10*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 3)^3)/19 + (4*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 3))/19 - 31/19 (42*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 4)^2)/19 + (10*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 4)^3)/19 + (4*root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 4))/19 - 31/19 z = root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 1) root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 2) root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 3) root(z1^4 + (32*z1^3)/5 + (241*z1^2)/25 - (103*z1)/25 - 739/100, z1, 4)
The code above corresponds to the following system:
Best Answer