title: Non-sequential substitution in SymPy
body: <p>I'm trying to use [SymPy][1] to substitute multiple terms in an expression at the same time. I tried the [subs function][2] with a dictionary as parameter, but found out that it substitutes sequentially.</p>
  
  <pre><code>In : a.subs({a:b, b:c})
  Out: c
  </code></pre>
  
  <p>The problem is the first substitution resulted in a term that can be substituted by the second substitution, but it should not (for my cause). </p>
  
  <p>Any idea on how to perform the substitutions simultaneously, without them interfering with each other?</p>
  
  <p><b>Edit:</b>
  This is a real example</p>
  
  <pre><code>In [1]: I_x, I_y, I_z = Symbol("I_x"), Symbol("I_y"), Symbol("I_z")
  
  In [2]: S_x, S_y, S_z = Symbol("S_x"), Symbol("S_y"), Symbol("S_z")
  
  In [3]: J_is = Symbol("J_IS")
  
  In [4]: t = Symbol("t")
  
  In [5]: substitutions = (
  (2 * I_x * S_z, 2 * I_x * S_z * cos(2 * pi * J_is * t) + I_y * sin(2 * pi * J_is * t)),
  (I_x,  I_x * cos(2 * pi * J_is * t) + 2 * I_x * S_z * sin(2 * pi * J_is * t)),
  (I_y,  I_y * cos(2 * pi * J_is * t) - 2 * I_x * S_z * sin(2 * pi * J_is * t))
  )
  
  In [6]: (2 * I_x * S_z).subs(substitutions)
  Out[7]: (I_y*cos(2*pi*J_IS*t) - 2*I_x*S_z*sin(2*pi*J_IS*t))*sin(2*pi*J_IS*t) + 2*S_z*(I_x*cos(2*pi*J_IS*t) + 2*I_x*S_z*sin(2*pi*J_IS*t))*cos(2*pi*J_IS*t)
  </code></pre>
  
  <p>Only the appropriate substitution should happen, in this case only the first one. So the expected output should be the following:</p>
  
  <pre><code>In [6]: (2 * I_x * S_z).subs(substitutions)
  Out[7]: I_y*sin(2*pi*J_IS*t) + 2*I_x*S_z*cos(2*pi*J_IS*t)
  </code></pre>