System of equations in GSL

csopi

Hi,
I need to solve the following system of equations:

qa = fa (qa, qb, qc, qd)
qb = fb (qa, qb, qc, qd)
qc = fc (qa, qb, qc, qd)
qd = fd (qa, qb, qc, qd)

where all the variables and functions are complex. However, there are some additional constraints for the variables, lets call them

na (qa, qb, qc, qd) = 1
nb (qa, qb, qc, qd) = 1
nc (qa, qb, qc, qd) = 1
nd (qa, qb, qc, qd) = 1

My problem is, that if I take into account the constraints, the system will be overdetermined (4 variables, 8 equations). However, it is known, that it still has a lot of solutions.

I am quite new to GSL (GNU Scientific Library), and I do not know, how to solve overdetermined systems and I cannot find anything in the manual either.

Do you have any suggestions?