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Re: Assuming odd/even functions

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  • Subject: [mg98674] Re: Assuming odd/even functions
  • From: dh <dh at>
  • Date: Thu, 16 Apr 2009 04:12:50 -0400 (EDT)
  • References: <gs47hn$7l1$>

Hi Martin,

there is an options of Simplify: TransformationFunctions, that tells 

Simplify what to try. You may e.g.  specify a function that transforms 

f[-x] into -f[x] for an odd function. Here is an example:

t[e_] := e /. f[-x] -> -f[x];

Simplify[f[x] + f[-x], TransformationFunctions -> {Automatic, t}]

hope this helps, Daniel

Martin Schönecker wrote:

> How can we give Mathematica the information of a function being odd or even, and have it applied automatically or in a Simplify[]?


> Such that, if e.g. f[y] is odd, the sum f(a)+f(-a) yields zero, the 

> integral Integrate[f[y], {y, -a, a}] vanishes?


> --Martin


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