title: How to set up equations in python
body: <p>I have a list with coefficients which define a system of equations I would like to solve. The first term in my list of coefficients is always 1 and the first variable in the solution is also assumed to be 1. </p>
  
  <p>If</p>
  
  <pre><code>coeffs = [1,2,3,4]
  </code></pre>
  
  <p>then system of equations I would like to solve are the circular convolution of <code>coeffs</code> with the variables <code>[1, x[3], x[2], x[1]]</code>. In this way we get</p>
  
  <pre><code>1*1 + 2*x[3] + 3*x[2] + 4*x[1] = 0
  
  1*x[3] + 2*x[2] + 3*x[1] + 4*1  = 0
  
  1*x[2] + 2*x[1] + 3*1 + 4*x[3] = 0
  
  1*x[1] + 2*1 + 3*x[3] + 4*x[2] = 0
  </code></pre>
  
  <p>Given <code>coeffs</code>, how can I set up this system of equations in numpy so I can solve for <code>x</code>? In practical cases <code>coeffs</code> will have length in the hundreds.</p>