Re: Picking Arguments

*To*: mathgroup at smc.vnet.net*Subject*: [mg74298] Re: Picking Arguments*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sat, 17 Mar 2007 02:09:51 -0500 (EST)*References*: <esdka9$ou3$1@smc.vnet.net><et5npe$jij$1@smc.vnet.net>

Very informative post Drago! Cheers Dimitris P=2ES. Greetings from Greece! =CF/=C7 Drago Ganic =DD=E3=F1=E1=F8=E5: > Hi, > I just want to add to the difference of Select and Case. I think they > represent two important functions for a different domain of programming: > semantic Select > syntax Cases > > which sometimes can be used for the same problem but usually one method is > better that the other for a certain problem. > > If you look at all the List manipulation functions we have only three acc= ess > methods to the elements of lists: > 1. postion => via an integer number, eg. Part[] > 2. pattern => via a syntactical pattern, eg. Cases[] > 3. logical => via a logical boolean expression, eg. Select[] > > Here is a example: > > In[1]:= Select[ {1, 2.3, a}, # \[Element] Reals &] > Out[1]= {1, 2.3} > > In[2]:= Cases[{ 1, 2.3, a}, _Real ] > Out[2]= {2.3} > > In[3]:= Cases[{ 1, 2.3, a}, _Integer | _Rational | _Real] > Out[3]= {1, 2.3} > > It's a nice example for thinking about what OO inheritance might be in > Mathematica. > > I would says that Mathematica defines "types" in a syntactical way (head = of > expression) and uses them in pattern matching function (e.g. Cases), and > defines "domain" in a more semantical (logical/mathematical) way and uses > them in other functions (like Select). > > Of course types in Mathematica are more something like IntegerQ[] and not > _Integer and hence are a semantical "thing" and not just syntactical. > > Greeting from Croatia, > Drago > > "dimitris" <dimmechan at yahoo.com> wrote in message > news:et5npe$jij$1 at 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_thr= ead/= > > thread/3b38366201665b24/9c76eb8c939ce75d?lnk=st&q=&rnum=28&hl=e= l#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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