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MathGroup Archive 1996

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Re: Problem with If[] and %

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5462] Re: [mg5355] Problem with If[] and %
  • From: Allan Hayes <hay at haystack>
  • Date: Sat, 7 Dec 1996 00:26:41 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

hans.steffani at e-technik.tu-chemnitz.de (Hans Steffani)
[mg5355] Problem with If[] and %
writes

> i^2+v^2
> If[ % >15,15,%]
> Plot3D[ %,{i,-5,5},{v,-5,5}]
>
>... leads to several errors.

Hans,

In version 2.2 you can get what you want by replacing
If[ % >15,15,%]
with
If[ Evaluate[% >15],15,Evaluate[%]];
In version 3.0 you can use this or If[ % >15,15,Evaluate[%]]

Here is what lies behind this in version 2.2 (version3.0 is  
slightly different - I'll deal with this after).

In evaluating an expression
the first step (the HE step)is, * subject to any attributes of f *,  
to evaluate the head and the entries,  f,x,y,z, in turn.
This means that, if f has the attribute HoldAll (as If has in  
version 2.2), then the entries x,y,z are held unevaluated, and we  
get


Then the *rules* for evaluating (1) are used.

In the evaluation of your original code the HE step in the  
evaluation of If[ % >15,15,%] simply gives (because If has the  
attribute Hold all an the value of If is If)


Then the rules for evaluating (2) are used.
With the change suggested, the HE step in the evaluation of
If[ Evaluate[% >15],15,Evaluate[%]] gives


Then the rules for evaluating (3) are used:
In version 3.0 If has the attribute HoldRest (so in the HE step the  
first entry is evaluated). This is the reason that you can use

Incidentally, you get the same picture with

i^2+v^2
Plot3D[ %,{i,-5,5},{v,-5,5}, PlotRange -> {0,5}]

and you can modify the clipped part with the option ClipFill.


Allan Hayes
hay at haystack.demon.co.uk
http://www.haystack.demon.co.uk


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