Nonlinear systems of equations

[n0rbed]

From this discourse post:

@variables e_x[1:3]
heading = 0.01

eqs = [
    atan(-e_x[2]/-e_x[1]) ~ heading
    norm(e_x) ~ 1.0
    e_x[2] ~ 1.0
]

Equations: Equation[atan(e_x[2] / e_x[1]) ~ 0.01, sqrt(abs2(e_x[3]) + abs2(e_x[1]) + abs2(e_x[2])) ~ 1.0, e_x[2] ~ e_x[1]]
┌ Warning: Solve can not solve this input currently
└ @ Symbolics ~/.julia/packages/Symbolics/GYV9b/src/solver/main.jl:169

We can actually solve this system with our current solvers. First solve eqs[3], sub into 1, solve eqs[1], sub into [2], solve eqs[2]. I guess a general algorithm would be to brute force all the equations we can solve using our solvers, and then sub the found variables into the other equations. This can also be done by recursively calling ia_solve.

check if all equations of a system is a poly ? groebner solver : attempt other techniques