title: Python non linear equation with lagrangian multipliers estimation
body: <p>i 've been struggling for days on this thing....but to no avail. I'm not very good at difficult math let alone this kind of level of difficulty.</p>
  
  <p>I was trying to implement the maximum entropy application for the lottery in python for my graduation assignment, altough the focus of the project was to implement a number of data mining techinques (Decision trees,Apriori,kmeans) something alreadey finished, i just could not pass the opportunity to do something more advanced....but i guess this is too advanced for me.</p>
  
  <p>So, my question is how can i solve the non linear equation (8) from the following paper</p>
  
  <p>reference1: <a href="http://eprints.ecs.soton.ac.uk/901/01/paper05.pdf" rel="nofollow">http://eprints.ecs.soton.ac.uk/901/01/paper05.pdf</a></p>
  
  <p>the method is based in the following paper</p>
  
  <p>reference2: <a href="http://www.stanford.edu/~cover/papers/paper91.pdf" rel="nofollow">http://www.stanford.edu/~cover/papers/paper91.pdf</a></p>
  
  <p>any help (theoritical or othwerwise) will be deeply appreciated.
  thanks</p>