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RE: Re: Operate on Heads

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87086] RE: [mg86661] Re: Operate on Heads
  • From: "Dr Andy D Kucar P2EE4 www.radio4u.com" <andy at radio4u.com>
  • Date: Mon, 31 Mar 2008 02:05:39 -0500 (EST)
  • Reply-to: <andy at radio4u.com>

I would like to thank to all respondents to my posted questions
on this, as well as on previous topics.

I would try to explain some of my desires?
on a rather simple example related to some natural events

I have a number of Modules (subroutines, functions, or whatever one prefer
to call it)
With (subject, object(s), event(s), action(s)) structure.

For example,
a subject is an Earth based location triad,
Objects are Sun and Moon,
Events are Rise and Set, ...

Based on interrelations of all of above,
Some unique action, based on the state of the system, should be
described/specified, and executed

One way to solve this problem is to have all logic in the main program and
have a possibly large number of small modules,
Each describing a unique but simple action.
The logic could, in principle, be implemented via combination of
If,Then,Else,Switch;   And,Or,... ; (pattern construction) Alternatives; or
something better ?

In this simple example we have (hidden/protected possibly someone else or
even Mathematica own) commands such as
Set (possibly the same name for two completely different commands), Rise,
Sun, Moon,
but also commands (modules, or whatever) SunRise, SunSet, MoonRise, MoonSet,
which name (Head) is a composite word.

I have dealt with such situations along the lines described by Januk, tnx,
and via


fun[A,B,C][a,b,c][t]
Polygon @@ Line

Type of structures. The last line Apply approach actually just replaces the
Head name.
In principal no problem when I have my own relatively simple structures,
however, ...

Some of my Modules are to often inside some loops (Table, Plot).
In complex interrelations between a larger number of objects and events,
logic is becoming cumbersome and all things are getting to slow.
Thus my imperative in those situations is getting under the hood, if I can
and if I have enough time,
And speed things up.

Now comes Mathematica's sentence

Operate is essentially a generalization of Apply, which allows you to apply
an operator to the head of an expression, rather than simply to replace the
head

What this really means?
This is what stimulated me, since I smell (possibilities toward) a number of
better, more elegant, more efficient, solutions to my problems ...
Of course there might be some Pandora Boxes in between ... (non)technical
issues, etc.

C pointers and list of all lists, the machine code list, and its 1:1 twin
called assembler are coming to mind ...

Thanks, andy

-----Original Message-----
From: Januk [mailto:ggroup at sarj.ca]
Sent: Monday, March 17, 2008 00 21
To: mathgroup at smc.vnet.net
Subject: [mg87086] [mg86661] Re: Operate on Heads

Hi Andy,

A basic approach would be to convert everything to strings, use
Mathematica's string manipulation commands to create the expression
you'd like evaluated, then convert back to an expression.  See below
for a simple example.

f[something_, x__] := Module[{strArgs, strHeads},
  strHeads = ToString[something];
  strArgs = Riffle[ToString /@ {x}, ","];

  (* Manipulate your heads here *)
  strHeads = StringReplace[strHeads, "p" -> "P"];

  StringJoin[strHeads, "[", strArgs, "]" ] // ToExpression
  ]

f[plus, 2, 3]

Hope that helps,
Januk

On Mar 16, 6:49 am, "Dr Andy D Kucar P2EE4 www.radio4u.com"
<a... at radio4u.com> wrote:
> Hi,
>
> Hi,
>
> I would like to be able to pass a composite name Head, e.g.,
> FirstSecondThird to a Module,
> and then, inside the module, use
>
> FirstSecondThird, First, Second, Third
>
> Heads, and/or make other Operate ions on Heads
>
> How could this be accomplished?
> Thank you
>
> Sincerely Andy




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