I have a piecewise function and I'm trying to extract the different functions for different values of the parameter. I use:


This gives be back the different functions except the last piece which is the function when the else or True condition holds. How can I extract the function at True?


1 Answer 1


In Mathematica everything is specified via patterns. So are, of course, Piecewise functions. To obtain a standardized form for nested Piecewise functions you were right to apply PiecewiseExpand first. So let's take a look at an example of a nested Piecewise function:

pw = Piecewise[{{g[x],x > 5}, {Piecewise[{{h1[x],x < 1}, 
{h2[x],x > 2}}, h3[x]], x < 3}}, f[x]];
pwe = PiecewiseExpand[pw];

Remember my remark about patterns before. Let's take a look at the underlying pattern (form) of the expanded Piecewise function:

pwe // FullForm

This gives you a clue on how to extract all the functions via using the Part operator, here is one possibility to do it:

Flatten[{pwe[[1, ;; , 1]], pwe[[2]]}]

{f[x], g[x], h1[x], h2[x], h3[x]}

Have fun playing around with this.

  • $\begingroup$ Thank you. I also tried to do it with Union, but it takes more time than Flatten. Any idea why? $\endgroup$
    – Rby
    Commented Sep 17, 2016 at 14:21
  • $\begingroup$ Union should be slower because it creates a new object, while Flatten does not do that. Also important to note is that according to Mathematica help Union "gives a sorted list of all the distinct elements", so additional sorting is applied, which costs time. For lists containing only a few elements you should not really notice a difference, of course this looks different for large lists. $\endgroup$
    – Wizard
    Commented Sep 17, 2016 at 14:28

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