Solving a system of equations fails

[Uwe Fechner]

Hello,

I try to calculate the tangent of a circle. This is a quite simple system of equations (one is quadratic),
but sympy fails (empty solution set). Any idea why?

from __future__ import division
from sympy import *
from sympy.solvers import solve

init_printing(use_latex = True)
r, phi_0, phi_1, phi_2, beta_0, beta_1, beta_2= symbols('r phi_0, phi_1, phi_2, \
     beta_0, beta_1, beta_2')

if True:
    if True:
        phi_0 = 0
        beta_0 = 0
        phi_1 = 1.
        beta_1 = 1.
        r=1.
    eq1 = Eq((phi_2 - phi_1) * (phi_2 - phi_1) + (beta_2 - beta_1) * (beta_2 - beta_1) - r*r)
    eq2 = Eq((phi_2 - phi_0) * (phi_2 - phi_1) + (beta_2 - beta_0) * (beta_2 - beta_1))
    result = solve([eq1, eq2], phi_2)
    print result

The result is an empty list. Any idea, how to fix this?
Expected result: phi_2 = 1.

Any hints appreciated!

U. Fechner, TU Delft

[Aaron Meurer]

If you don't tell solve() that beta_2 is a parameter, it assumes that
it is a constant. It then returns no solutions because it solves eq1
and eq2 each for phi_2 and sees that they look different, because they
are only equal for certain values of beta_2 (at least, I'm fairly sure
this is what is happening).

You can get the solutions by telling solve that beta_2 is a parameter

In [14]: solve([eq1, eq2], [phi_2, beta_2])
Out[14]: [(0.0, 1.0), (1.0, 0.0)]

Aaron Meurer

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[Uwe Fechner]

Thank you very much, that did the trick.

Uwe