
Re: [mg5355] Problem with If[] and %
Posted:
Dec 6, 1996 11:46 PM


hans.steffani@etechnik.tuchemnitz.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 f[x,y z] 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
f'[x,y,z] (where f' is the value of f). (1)
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)
If[ % >15,15,%] (2)
Then the rules for evaluating (2) are used. the value of % >15, that is i^2+v^2 > 15, is examined since this is neither True nor False, (1) is returned. With the change suggested, the HE step in the evaluation of If[ Evaluate[% >15],15,Evaluate[%]] gives
If[ i^2+v^2 > 15, 15, i^2+v^2 ] (3)
Then the rules for evaluating (3) are used: the value of i^2+v^2 > 15, that is i^2+v^2 > 15, is examined since this is neither True nor False, (3) is returned. 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
If[ % >15,15,Evaluate[%]] 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@haystack.demon.co.uk http://www.haystack.demon.co.uk

