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Re: Re: Mathematica scoping / contexts / variable localization

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  • Subject: [mg105154] Re: [mg105135] Re: Mathematica scoping / contexts / variable localization
  • From: "David Park" <djmpark at comcast.net>
  • Date: Mon, 23 Nov 2009 06:48:57 -0500 (EST)
  • References: <32142906.1258547432910.JavaMail.root@n11> <he36g8$efk$1@smc.vnet.net> <he88nu$prb$1@smc.vnet.net> <31695084.1258894017394.JavaMail.root@n11>

It's called SubValues. One advantage is that it cleanly separates parameters
from variables. Another is that you can write expressions such as:

f[a, b]'[x]

You can also use it conveniently as a postfix operator:

x//f[a, b]

There would be many operations in Mathematica that would be easier to use if
they were defined with SubValues. For example the various
GeometricTransformations are inconvenient in their present form because they
have to be wrapped around a piece of graphics. Postfix operation would be
more convenient. (In Presentations I do provide alternative postfix forms of
all these operators because we always have the primitive form of graphics
available to operate on and it is convenient to define a basic form and then
move it to its proper place.)

But SubValues seems to be the poor orphan of Mathematica "Values". There is
a usage message but no documentation page. I don't know of any tutorial for
it. Command completion for SubValues definitions doesn't give the entire
expression, which I think it should. And DocuTools doesn't handle it
properly. WRI seems to avoid SubValues in any of their basic functions. I
don't know if there is a good reason for this.

You can type SubValues in the DC SEARCH box and then use "Try your search on
all Wolfram sites" to get a fair amount of MathGroup discussion about
SubValues.

The saying is: "Give a hungry man a fish and he'll be back the next day.
Teach a hungry man to fish and you won't see him again for two or three days
- if he hasn't drowned in the meantime."


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: AES [mailto:siegman at stanford.edu] 


> > Clear[a, b]
> >
> > ClearAll[f]
> > f[a_, b_][x_] := Exp[-a x] Sin[b x]

I've seen this more complex form of function definition go by once or 
twice in the past, but never used it or learned about it myself.  

Pointers to tutorial explanations?

[Or, more challenging, an explanation, in classic "teach a man to fish" 
mode, of how a mythical "ordinary user" might go about quickly and 
efficiently _finding_ such tutorial explanations, for this specific 
case, in Mathematica documentation.]




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