       Re: Problems with easy simplifications

• To: mathgroup at smc.vnet.net
• Subject: [mg54175] Re: [mg54143] Problems with easy simplifications
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sat, 12 Feb 2005 01:58:04 -0500 (EST)
• References: <200502110834.DAA09274@smc.vnet.net>
• Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

```The problem is that there is a type of hold on the function that isn't
showing itself. I found it when I checked the attributes of the If
command.

The following commands do what you want globally, but I haven't been
able to selectively mute the HoldRest.

H[x_, a_, b_] = If[x < a, a + b, a - b]

If[x < a, a + b, a - b]

Attributes[If]

{HoldRest, Protected}

Unprotect[If]

{If}

ClearAttributes[If, HoldRest]

H[x, 0, 0]

If[x < 0, 0, 0]

On Fri, 11 Feb 2005 03:34:47 -0500 (EST), Antonio González
<gonferh2o at esi.us.es> 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 + Simplify], Simplify[Simplify[
>        0] + Simplify[Simplify[-1] Simplify]]]
>
> 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]
>
>
>   If[x < 0, c, d]
>
> Similar problems arise using the function Which.
>
> Any explanation or help with this malfunction would be welcome.
>
> --
>
>    Antonio
>
> (Eliminar el agua para responder por e-mail - Remove water to reply by
> e-mail)
>
>

--
Chris Chiasson
Kettering University
Mechanical Engineering