Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

I want to create the functions $even[f]$ and $odd[f]$ which will apply the formula $even[f(x)] = \frac{f(x)+f(-x)}{2}$ and $odd[f(x)]=\frac{f(x)-f(-x)}{2}$ for an arbitrary $f$.

I tried using

even[ff, x_] := (ff[x] + ff[-x])/2

But that doesn't seem to work. What would the correct approach to this be?

share|improve this question
    
even[f_[x_]] := (f[x] + f[-x])/2 and odd[f_[x_]] := (f[x] - f[-x])/2 –  RunnyKine Feb 18 at 4:38
1  
or like this: even[f_] := (f[#] + f[-#])/2 &; odd[f_] := (f[#] - f[-#])/2 & –  Szabolcs Feb 18 at 4:39
    
Neither approach is working for me at the moment. In the first approach mathematica doesn't evaluate anything, just leaving the even function with whatever its argument is, and in the second approach I have a lot of #'s that are left unevaluated as well. –  R R Feb 18 at 4:46
    
When I boot mathematica fresh and enter it in this is what I get:In[28]:= ClearAll[f, ff, even, x] In[29]:= even[f_[x_]] := (f[x] + f[-x])/2 In[30]:= f[x_] := x^2 + x In[35]:= even[f] even[f[x]] even[f[x_]] even[f[#]] Out[35]= even[f] Out[36]= even[x + x^2] Out[37]= even[x_ + x_^2] Out[38]= even[#1 + #1^2] –  R R Feb 18 at 5:12
1  
Did you SetAttributes like I did? –  RunnyKine Feb 18 at 5:23

2 Answers 2

up vote 11 down vote accepted
SetAttributes[{even, odd}, HoldAll];
even[f_[x_]] := (f[x] + f[-x])/2;
odd[f_[x_]] := (f[x] - f[-x])/2;

Usage

g[x_] := x + x^2;

even[g[x]]

x^2

OR as Szabolcs suggested using pure functions:

even[f_] := (f[#] + f[-#])/2 &;
odd[f_] := (f[#] - f[-#])/2 &

Usage

Using the same g as above

even[g][x]

x^2

share|improve this answer
3  
It might be helpful to mention that Szabolcs' method requires calling even[g][x] instead of even[g[x]]. Also it doesn't require HoldAll. –  Rahul Feb 18 at 10:19

You said you tried using

even[ff, x_] := (ff[x] + ff[-x])/2

but I guess you forgot to put the underscore on the first argument. If you do

even[ff_, x_] := (ff[x] + ff[-x])/2

instead, then it works.

g[x_] := x + x^2;
even[g, x]

x^2

P.S. No SetAttributes necessary using this method.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.