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Re: Simplifying If expressions

• To: mathgroup at smc.vnet.net
• Subject: [mg102969] Re: Simplifying If expressions
• From: pfalloon <pfalloon at gmail.com>
• Date: Thu, 3 Sep 2009 05:41:01 -0400 (EDT)
• References: <287030.1251791777166.JavaMail.root@n11> <h7l91h$3cj$1@smc.vnet.net>

On Sep 2, 6:06 pm, "David Park" <djmp... at comcast.net> wrote:
> If[x == 0, x, 0];
> FullSimplify[%]
> 0
>
> Piecewise[{{x, x == 0}}, 0];
> FullSimplify[%]
> 0
>
> David Park
> djmp... at comcast.nethttp://home.comcast.net/~djmpark/
>
> From: beep.beep [mailto:meph... at gmail.com]
>
> Hi,
>
> When I try to Simplify[If[x==0,x,0]] Mathematica returns If[x==0,=
x,0] rather
> than 0. It seems that it does not take into account that left and right
> if-branches should be simplified using ($Assumptions)&&if-condition and
> ($Assumptions)&&!if-condition respectively. Is there a way to force that
> behaviour?
>
> Best regards,
> Ilya

I don't know about anyone else, but I was surprised and troubled to
see the following result (as pointed out by others in this thread):

In[3]:= If[x==0,x,0] // FullSimplify
Out[3]= 0

To me this seems simply incorrect. For example, what about the
following cases:

In[5]:= With[{x=0.}, If[x==0,x,0]]
Out[5]= 0.

In[11]:= With[{x=1`20-1}, If[x==0,x,0]]
Out[11]= 0.*10^-20

Is this intentional?

• Follow-Ups:
  • Re: Re: Simplifying If expressions
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>