title: Passing predetermined parameters to scipy.optimize.fsolve
body: <p>I'm trying to use python to solve a system of 6 nonlinear equations. There are 9 variables, and 3 of them are predetermined (leaving a system of 6 equations with 6 unknowns). The problem is, it could be any 3, I have no way of knowing beforehand.</p>
  
  <p>Here are the equations (if you're interested).</p>
  
  <p>c11*c12 + c21*c22 + c31*c32 = 0</p>
  
  <p>c11*c13 + c21*c23 + c31*c33 = 0</p>
  
  <p>c12*c13 + c22*c23 + c32*c33 = 0</p>
  
  <p>c11*c21 + c12*c22 + c13*c23 = 0</p>
  
  <p>c11*c31 + c12*c32 + c13*c33 = 0</p>
  
  <p>c21*c31 + c22*c32 + c23*c33 = 0</p>
  
  <hr>
  
  <p>Note: This is the way I assumed would be quickest/easiest to solve. Another possible expression is:</p>
  
  <pre><code>    |c11 c21 c31|
  A = |c12 c22 c32|
      |c13 c23 c33|
  
      |c11 c12 c13|
  B = |c21 c22 c23|
      |c31 c32 c33|
  
        |1 0 0|
  A*B = |0 1 0|
        |0 0 1|
  </code></pre>
  
  <hr>
  
  <p><strong>My question is: is there anyway to set 3 of these as fixed, and have scipy.optimize.fsolve (or a more appropriate module?) solve for the remaining parameters?</strong></p>