System of equations in GSL

  1. 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?
  2. jcsd
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