sign of an expression resulting from solve()

[Alexander Tille]

Hi guys,

I want to calculate the steady states of a system of differential equations:

   

    from sympy import *

    X,Y,Z = symbols("X,Y,Z")
    variables_dimless = [X,Y,Z]
    Rxy,Rxz, Ry,Ryx,Ryz, Rz,Rzy,Rzz = symbols("Rxy,Rxz,  Ry,Ryx,Ryz,  Rz,Rzy,Rzz",positive=True)
    dimensionless_DES_list = [X*(1-X),
                              Ry *(Y* (1 - Y) + Rzy * Z *Y ),
                              Rz *(Z*(1-Z)+Rxz*X*Z+Ryz*Y*Z)]
    equilibria = solve( dimensionless_DES_list,(variables_dimless))

     Out[2]:
     [(0, 0, 0),
      (0, 0, 1),
      (0, 1, 0),
      (0, -(Rzy + 1)/(Ryz*Rzy - 1), -(Ryz + 1)/(Ryz*Rzy - 1)),
      (1, 0, 0),
      (1, 0, Rxz + 1),
      (1, 1, 0),
      (1, -(Rxz*Rzy + Rzy + 1)/(Ryz*Rzy - 1), -(Rxz + Ryz + 1)/(Ryz*Rzy - 1))]

My problem are the negative signs of the results for example solution 4:

    (0, -(Rzy + 1)/(Ryz*Rzy - 1), -(Ryz + 1)/(Ryz*Rzy - 1)),

For future calculation it is important that all solutions of the variables have a positive sign. The solution should look like:

    (0, (Rzy + 1)/(1 - Ryz*Rzy), (Ryz + 1)/(1 - Ryz*Rzy )),

I do not know how to manipulate the output. If I define the variables as following

    X,Y,Z = symbols("X,Y,Z",positive=True)

The solver just finds the one solution were X,Y,Z are positive.

Do you have any ideas?

Thank you in advance

Alex

[Alexander Tille]

I also tried

X,Y,Z = symbols("X,Y,Z",nonnegative=True) 

Well solve() finds all solutions in this case but the solutions look the same