CODEWITHSUNDEEP
pythonsympy
user663721
user663721

Reputation: 13

How to express a system of equations in terms of another variable

I want to solve a system of equations symbolically such as A = ax + by and B = cx + dy, for x and y explicitly on sympy.

I tried the solve function of sympy as solve([A, B], [x, y]), but isn't working. It's returning an empty list, [].

How can I solve it using sympy?

This is the actual equation I'm trying to solve:

from sympy import*
i,j,phi, p, e_phi, e_rho =     symbols(r'\hat{i} \hat{j} \phi \rho e_\phi     e_\rho')
e_rho = cos(phi)*i + sin(phi)*j
e_phi = -p*sin(phi)*i + p*cos(phi)*j
solve([e_rho,e_phi], [i,j])

Upvotes: 0

Views: 207

Answers (1)

Oscar Benjamin
Oscar Benjamin

Reputation: 14530

I don't know what version of SymPy you're using but I just tried with the latest version and I get an answer:

In [4]: from sympy import*
   ...: i,j,phi, p, e_phi, e_rho =     symbols(r'i j phi rho e_phi e_rho')
   ...: e_rho = cos(phi)*i + sin(phi)*j
   ...: e_phi = -p*sin(phi)*i + p*cos(phi)*j
   ...: solve([e_rho,e_phi], [i,j])
Out[4]: {i: 0, j: 0}

That's the correct answer to your equations (provided rho is nonzero):

In [5]: e_rho
Out[5]: i⋅cos(φ) + j⋅sin(φ)

In [6]: e_phi
Out[6]: -i⋅ρ⋅sin(φ) + j⋅ρ⋅cos(φ)

If you meant to solve for e_rho and e_phi to be equal to something other than zero then you should include a right hand side either by subtracting it from the expressions or by using Eq:

In [2]: A, B = symbols('A, B')

In [3]: solve([Eq(e_rho, A), Eq(e_phi, B)], [i, j])
Out[3]: 
⎧         A⋅ρ⋅cos(φ)               B⋅sin(φ)                 A⋅ρ⋅sin(φ)               B⋅cos(φ)      ⎫
⎪i: ───────────────────── - ─────────────────────, j: ───────────────────── + ─────────────────────⎪
⎨        2           2           2           2             2           2           2           2   ⎬
⎪   ρ⋅sin (φ) + ρ⋅cos (φ)   ρ⋅sin (φ) + ρ⋅cos (φ)     ρ⋅sin (φ) + ρ⋅cos (φ)   ρ⋅sin (φ) + ρ⋅cos (φ)⎪
⎩                                                                                                  ⎭

In [4]: solve([Eq(e_rho, A), Eq(e_phi, B)], [i, j], simplify=True)
Out[4]: 
⎧              B⋅sin(φ)                B⋅cos(φ)⎫
⎨i: A⋅cos(φ) - ────────, j: A⋅sin(φ) + ────────⎬
⎩                 ρ                       ρ    ⎭

Again that's the correct answer (assuming rho != 0).

Upvotes: 1

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