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MathGroup Archive 2007

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Re: Picking Arguments

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74157] Re: Picking Arguments
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Tue, 13 Mar 2007 03:35:07 -0500 (EST)
  • References: <esdka9$ou3$1@smc.vnet.net>

As a second thought to your query I would suggest you to read
carefully the reply of
Andrzej Kozlowski to the recent thread with the title: "Map function
which adds last two numbers of a list".
Not very relevant at first glance but I think it talks about the right
"attitude" for attacking a "real" problem.

http://groups.google.gr/group/comp.soft-sys.math.mathematica/browse_thread/=
thread/3b38366201665b24/9c76eb8c939ce75d?lnk=st&q=&rnum=28&hl=el#9c=
76eb8c939ce75d


Anyway...

You have many ways to do what you want. You found by yourself (well
done!) that Cases gives your desired output.

So why hanging around with Select?

You could say for programming practise. But (at least!) for me the
important thing is to understand that Select is not "designed" for
doing things like what you desire. Cases is the key here (or other
built in functions suggested in the replies you got by some of the
gurus of this beautiful forum; no I don't talk about myself! I talk
about Bob Hanlon and Jean-Marc Gulliet!) . Not Select; except if you
just want to end with an extravagant code! So what? What's the deal?)

As regards myself, Understanding the (BIG!) Difference between Select
and Cases is the most important thing.

I copy directly from M. Trott's Guidebook for Programming...

Select picks the arguments according to the truth value, and it
delivers the result with the same head as the selected expression.
Cases chooses according to patterns, and it gives a result in the form
of a list. The optional third argument in the two functions also has a
completely different role. In Select, it defines the number of objects
to be selected, whereas in Cases, it gives the level specification at
which the first argument is to be tested.

Another issue which you should be more aware of (in my point of view
of course!) is why RuleDelayed is
unnessary here.

A = {f[x], g[p, q, r, s], h[u, v, w]}
{f[x], g[p, q, r, s], h[u, v, w]}

Cases[A, _[args__] :> {args}]
{{x}, {p, q, r, s}, {u, v, w}}

Cases[A, _[args__] -> {args}]
{{x}, {p, q, r, s}, {u, v, w}}

Trace[Cases[A, _[args__] :> {args}]]
{{HoldForm[A], HoldForm[{f[x], g[p, q, r, s], h[u, v, w]}]},
  HoldForm[Cases[{f[x], g[p, q, r, s], h[u, v, w]}, _[args__] :>
{args}]], HoldForm[{{x}, {p, q, r, s}, {u, v, w}}]}

Trace[Cases[A, _[args__] -> {args}]]
{{HoldForm[A], HoldForm[{f[x], g[p, q, r, s], h[u, v, w]}]},
  HoldForm[Cases[{f[x], g[p, q, r, s], h[u, v, w]}, _[args__] ->
{args}]], HoldForm[{{x}, {p, q, r, s}, {u, v, w}}]}


What about here?

sols = Solve[x^3 == 1]
{{x -> 1}, {x -> -(-1)^(1/3)}, {x -> (-1)^(2/3)}}

sols /. (a_ -> b_) -> a -> ComplexExpand[b]
{{x -> 1}, {x -> -(-1)^(1/3)}, {x -> (-1)^(2/3)}}

sols /. (a_ -> b_) :> a -> ComplexExpand[b]
{{x -> 1}, {x -> -(1/2) - (I*Sqrt[3])/2}, {x -> -(1/2) +
(I*Sqrt[3])/
2}}


If you have finished the relevant material in the Help Browser about
(the so much!) useful Built-in Symbols
like Select, Cases, Fold, Nest, Map, Apply of Functional Progarmming
and you want more things to read/practise (and avoid unnessary hanging
around...) trying

http://verbeia.com/mathematica/tips/Tricks.html
http://verbeia.com/mathematica/tips/GraphicsTricks.html

that is the (very famous and so properly called) Suplementary Help
Browser of Ted Ersek!
As notebooks see here:

http://library.wolfram.com/infocenter/MathSource/4557/

Very challenging material!


And here is something truly amazing!

http://documents.wolfram.com/flash/

See also here

http://library.wolfram.com/infocenter/MathSource/4286/

and here

http://www.mathematica.co.kr/


Best Regards
Dimitris



=CF/=C7 Mr Ajit Sen =DD=E3=F1=E1=F8=E5:
> Dear MathGroup,
>
>   Given a list of functions
>
>   A={f[x],g[p,q,r,s],h[u,v,w]},
>
>  I'd like to pick out their arguments as a list.
>
>    Cases[A,_[args__]:>{args}]
>
>  works fine returning  {{x}, {p,q,r,s}, {u,v,w}}.
>
>   How do I achieve the same thing with Select ?
>
>
> Thanks for your help.
>
>   Ajit Sen
>
>
>
>
>
> ___________________________________________________________
> Yahoo! Messenger - NEW crystal clear PC to PC calling worldwide with voic=
email http://uk.messenger.yahoo.com



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