CODEWITHSUNDEEP
pythonsympy
Gabe Morris
Gabe Morris

Reputation: 872

How to solve a non-linear system in sympy with respect to a specified variable

I would like to know how to solve a non-linear system of equations with respect to a certain variable. Consider this example:

import sympy as sp
from sympy.solvers import solve

t2, t3, c = sp.symbols('theta_2 theta_3 c')

f1 = 2*sp.cos(t2) - 10*sp.cos(t3) - c
f2 = 2*sp.sin(t2) - 10*sp.sin(t3)

solve([f1, f2], c)[c]

enter image description here

Any ideas?

Upvotes: 0

Views: 283

Answers (1)

Oscar Benjamin
Oscar Benjamin

Reputation: 14530

If you specify theta3 as an unknown then solve will eliminate it from the solution for c:

In [9]: solve([f1, f2], [c, t3], dict=True)
Out[9]: 
⎡⎧          _______________                               ⎫  ⎧        _______________                                   ⎫⎤
⎢⎪         ╱    2                                ⎛sin(θ₂)⎞⎪  ⎪       ╱    2                                    ⎛sin(θ₂)⎞⎪⎥
⎢⎨c: - 2⋅╲╱  cos (θ₂) + 24  + 2⋅cos(θ₂), θ₃: asin⎜───────⎟⎬, ⎨c: 2⋅╲╱  cos (θ₂) + 24  + 2⋅cos(θ₂), θ₃: π - asin⎜───────⎟⎬⎥
⎢⎪                                               ⎝   5   ⎠⎪  ⎪                                                 ⎝   5   ⎠⎪⎥
⎣⎩                                                        ⎭  ⎩                                                          ⎭⎦

Now you can extract the solutions for c only:

In [10]: sol = solve([f1, f2], [c, t3], dict=True)

In [11]: [s[c] for s in sol]
Out[11]: 
⎡       _______________                   _______________            ⎤
⎢      ╱    2                            ╱    2                      ⎥
⎣- 2⋅╲╱  cos (θ₂) + 24  + 2⋅cos(θ₂), 2⋅╲╱  cos (θ₂) + 24  + 2⋅cos(θ₂)⎦

The output that I show here is from isympy which can print nicely if you use a unicode capable terminal making code and output that can be copy-pasted into something like SO. That's better and quicker than using screenshots.

Upvotes: 1

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