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Re: Problems with easy simplifications

• To: mathgroup at smc.vnet.net
• Subject: [mg54188] Re: Problems with easy simplifications
• From: Peter Pein <petsie at arcor.de>
• Date: Sat, 12 Feb 2005 01:59:10 -0500 (EST)
• References: <cuhsm1$9j1$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Antonio González wrote:
> I have found some weird behaviors of Mathematica (5.0) related to the 
> simplifications of easy expressions.
> 
> Take, for instance the function
> 
>    H[x_, a_, b_] = If[x < a, a + b, a - b]
> 
> If I try now to evaluate
> 
>    H[x,0,0]
> 
> the result
> 
>   If[x < 0, 0 + 0, 0 - 0]
> 
> (the values of a and b are irrelevat, a similar result is obtained, for 
> instance, with a=1, b= 2, or any integer, real or complex values). I 
> cannot force (at least in a simple way) Mathematica to make the addition 
> or the substraction. The action of Simplify or FullSimplify leaves the 
> expression unchanged while a Map of Simplify
> 
>    MapAll[Simplify, H[x, 0, 0]]
> 
> produces
> 
>    If[x < 0,
>      Simplify[Simplify[0] + Simplify[0]], Simplify[Simplify[
>        0] + Simplify[Simplify[-1] Simplify[0]]]]
> 
> Something even worse happens if a use values already defined. For instance
> 
>    c = 0; d = 0; H[x_] = If[x < c, c + d, c - d]
> 
> produces
> 
>   If[x < 0, c + d, c - d]
> 
> In this case, the addition is not necessary.
> 
>    c = 0; d = 0; H[x_] = If[x < c, c, d]
> 
> leads to
> 
>   If[x < 0, c, d]
> 
> Similar problems arise using the function Which.
> 
> Any explanation or help with this malfunction would be welcome.
> 

Hi,

the function If has the attribute HoldRest. So

H[x_, a_, b_] := If[x < a, Evaluate[a + b], Evaluate[a - b]]
/* do not forget the colon */

gives the desired result.

-- 
Peter Pein
Berlin