How to solve a function and get x, y and z?

[TheZenMan]

Hi, I'm fairly new to python and was wondering how to solve this.

So I have the following:

sigma_x=2
sigma_y=2
sigma_z=2
curr_location_x1=3
curr_location_y1=3
curr_location_z1=3

curr_location_x2=4
curr_location_y2=4
curr_location_z2=4

curr_location_x3=5
curr_location_y3=5
curr_location_z3=5
    
f_1=0.3
f_2=0.25
f_3=0.2
    
f = math.exp(-((((curr_location_x - x_my) * (curr_location_x - x_my)) / (2*sigma_x * sigma_x)) + (((curr_location_y - y_my) *(curr_location_y - y_my)) / (2 * sigma_y * sigma_y)) + (((curr_location_z - z_my) *(curr_location_z - z_my)) / (2 * sigma_z * sigma_z))))

What I want to do is subsitute f for f_1, f_2 and f_3 to get x_my, y_my and z_my. Since there are three unknowns and three equations this should be solvable. I tried using scipy but had no luck since the equations have to equal 0 and didn't find the way that I could apply my problem on it. Does anyone know how to solve this?

[micseydel]

Have you tried sympy?

[scidam]

Applying natural logarithm to these equations, you will get three equations, where each equation represents an ellipsoid. So, you will need to find intersection of three ellipsoids in R^3; that, probably, could be solved analytically.