I have a long list of generated values from which I want to remove "weird" ones like Sin[Sin[1]] and Pi^2/4. However, trying to remove the powers of Pi fails on this value:

MatchQ[Sqrt[2 Pi], (_ Pi)^_] (* False *)

The FullForm of the expression is

Power[Times[2, Pi], Rational[1, 2]]

I can only match the expression when I explicitly specify the 2:

 (_Integer Pi)^_  (* False *)
 (2 Pi)^_         (* True *)

What's going on here?

  • $\begingroup$ I found out what's happening, but I don't know why it's happening. Points to anyone who can explain. $\endgroup$ – 2012rcampion Feb 22 '15 at 21:08
  • $\begingroup$ An interesting question would be: when does (x y)^power automatically split into x^power y^power and when does it stay together? $\endgroup$ – Szabolcs Feb 22 '15 at 21:59

A little more digging resulted in the answer: my pattern is being evaluated to


Using HoldPattern prevents this behavior and gives the expected result:

MatchQ[Sqrt[2 Pi], HoldPattern[(_ Pi)^_]] (* True *)
  • $\begingroup$ Interesting! I would not have hit me, that the Power-rules are applied even for patterns. Good find! $\endgroup$ – Jinxed Feb 23 '15 at 1:00

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