def test_solve_biquadratic():
    x0, y0, x1, y1, r = symbols('x0 y0 x1 y1 r')

    f_1 = (x - 1)**2 + (y - 1)**2 - r**2
    f_2 = (x - 2)**2 + (y - 2)**2 - r**2

    assert solve_poly_system([f_1, f_2], x, y) == \
        [(S(3)/2 - sqrt(-1 + 2*r**2)/2, S(3)/2 + sqrt(-1 + 2*r**2)/2),
         (S(3)/2 + sqrt(-1 + 2*r**2)/2, S(3)/2 - sqrt(-1 + 2*r**2)/2)]

    f_1 = (x - 1)**2 + (y - 2)**2 - r**2
    f_2 = (x - 1)**2 + (y - 1)**2 - r**2

    assert solve_poly_system([f_1, f_2], x, y) == \
        [(1 - sqrt(((2*r - 1)*(2*r + 1)))/2, S(3)/2),
         (1 + sqrt(((2*r - 1)*(2*r + 1)))/2, S(3)/2)]

    query = lambda expr: expr.is_Pow and expr.exp is S.Half

    f_1 = (x - 1 )**2 + (y - 2)**2 - r**2
    f_2 = (x - x1)**2 + (y - 1)**2 - r**2

    result = solve_poly_system([f_1, f_2], x, y)

    assert len(result) == 2 and all(len(r) == 2 for r in result)
    assert all(r.count(query) == 1 for r in flatten(result))

    f_1 = (x - x0)**2 + (y - y0)**2 - r**2
    f_2 = (x - x1)**2 + (y - y1)**2 - r**2

    result = solve_poly_system([f_1, f_2], x, y)

    assert len(result) == 2 and all(len(r) == 2 for r in result)
    assert all(len(r.find(query)) == 1 for r in flatten(result))
dataset/ETHPy150Open sympy/sympy/sympy/solvers/tests/test_polysys.py/test_solve_biquadratic/original