Solving a system of polynomial equations

[Jason Moore]

I have been working on a problem and end up needing to solve a system of nonlinear equations that are polynomials wrt to the variables of interest. There are six equations and six unknowns and only two of the variables are related non-linearly. This is the basic form:

[-c3 + 55.3719398861938],
[-c2 - 3*c3 + 1524.09472216942],
[-c1 - 3*c2 - 100*c3 - 111.682822870417*k_delta*k_phi + 16670.819288228]
[-c0 - 3*c1 - 100*c2 - 8153.56338281556*k_delta*k_phi + 3891.45616272381*k_delta + 55610.0242428841]
[-3*c0 - 100*c1 - 90978.6714602982*k_delta*k_phi + 276475.776481344]
[-100*c0 - 38237.9055133813*k_delta + 84011.44228978]

But more generally, I have symbolic coefficients. SymPy solve solves this correctly! Which is cool, but it took 4 hours to solve on my machine. I haven't tried to solve the above numerical form yet.

I'm curious if there is something I should be doing with SymPy to help it solve this faster. If I change some of the symbols to specific rationals I've had it solve as quickly as 20 minutes.

The full example is here: http://nbviewer.jupyter.org/gist/moorepants/0e85508f1b0753b01e4d9ced83e3519c/solve_inner_loop_gains.ipynb

Jason
moorepants.info
+01 530-601-9791

[Denis Akhiyarov]

if you define k_delta*k_phi as another terms, e.g. c4, then k_phi disappears and the equations are linear.

[Jason Moore]

Thank you. How nice an simple.

Sounds like a strategy that could be baked into solve().

Jason
moorepants.info
+01 530-601-9791

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