Hints for using subscripted variables in Mathematica packages

[Dr. Robert Kragler]

Hi,

perhaps some of you have 'struggled' in the past with subscripted or
subsuperscripted variables. To my opinion and observation most Mathematica users
do not exploit the potential of the Mathematica notation. As I had noticed
Mathematica code and output would (sometimes) look much nicer and more readable
if one uses the FrontEnd features provided by Mathematica's notation features.
The Notation package was introduced in Mathematica long ago (10-15 years) by
Jason Harris from WRI; with the help of this package one is able to create very
sophisticated notations quite common in scientific notation, for example, in
mathematics or physics .

However, the correct usage of subscripted variables has its price. If one
introduces on the FrontEnd level subscripted variables only by Subscript[a, b]
these quantities do not have (required) type 'Symbol' but are treated as
expressions with head 'Subscript'. Only loading Notation package a *Notation
Palette* pops up with several buttons, e.g. *Notation[... <=> ...]* . Important
in this context for the definition of subscripted symbols is *Symbolize[
\[SelectionPlaceholder] ].* Instead of the placeholder one may define
*Symbolize[ **Subscript[a_, b_] ] * with the effect that each subsequently
defined subscripted variable will be considered as a symbol. If *FullForm* is
applied to, say *Subscript[A, 1]*, then the internal representation
*A\[UnderBracket]Subscript\[UnderBracket]1* is shown (which gives rise to head
Symbol so that this subscripted quantity is treated as any other symbol such as
x, y1, ... in Mathematica).

Of course, this is nothing new. However, there are some pitfalls if subscripted
variables are used inside user-defined Mathematica *packages*. I struggled with
this problem for some time and - thanks to the help of Jason Harris / WRI (who
is the expert for these kind of questions) - I found a solution which I would
like to share with other Mathematica users.

If you want to define a Mathematica package *ABC.m *(with _context_, say *XYZ*)
making usage of subscripted variables one has to do the following (I will only
give the skeleton of the relevant commands) :

BeginPackage["XYZ`","Notation`"]; (* import of
Notation package which is autoloaded *)

Unprotect[Evaluate[Context[ ]<>"*"]];

(*
--------------------------------------------------------------------------------------------
declaration part of XYZ
----------------------------------------------------------------------------------------
*)

(*
-------------------------------------------------------------------------------------------------------------------------------------
*)
Off[General::spell1];
Off[Symbolize::boxSymbolExists]; (* subscripted
symbols : *)
Symbolize[ParsedBoxWrapper[SubscriptBox["_","_"]]]; (* this is the internal
representation of Symbolize suggested by Jason Harris for Mma package*)
On[Symbolize::boxSymbolExists];

(* makes a subscripted variable to a quantity with
head Symbol *)
Subscript[a_,b_]:= SubscriptBox[ ToBoxes[a], ToBoxes[b] ]//ToExpression

varList = { u, v, w, x, y, z }; (* define some subscripted variables
Subscript[A,u] etc. *)
subscriptList = Table[ Subscript[ A,varList[[k]] ],{k,varList//Length}];
(*
------------------------------------------------------------------------------------------------------------------------------------
*)

(* myToString[a_List] inserts lists with subscripted symbols into a usage string
(suggested by Jason Harris/WRI *)

myToString @ a_List := StringJoin[Riffle[myToString /@ a, ", "]]
myToString @ a_Symbol /; (Head@ToBoxes@a == SubscriptBox) := myToStringBoxes @
ToBoxes @ a
myToString @ a_ := ToString @ a
myToStringBoxes @ SubscriptBox[a_, b_] := StringJoin[{"\<\!\(\*SubscriptBox[",
a, ",", b, "]\)\>"}]

(*
------------------------------------------------------------------------------------------------------------------------------------
*)

varList::usage= "varList=List of variables : varList={u,v,w,x,y,z} default; or
{" <> *myToString[VList]* <> "} is a modified list of variables. Both lists may
be modified by the user to change variables and deduced quantities but ONLY
after the Notation package has been invoked.";
... (* further usage messages *)

(*
--------------------------------------------------------------------------------------
Implementation part of XYZ
--------------------------------------------------------------------------------------------
*)

Begin["`Private`"];
... (* procedures etc. defined in context Private` *)

End[ ]; (* end of private
context *)

Protect[Evaluate[Context[ ]<>"*"]];
EndPackage[ ]; (* end of package context *)


I hope that this skeleton example of a package will help to clarify the question
how subscripted variables may be used in the framework of a user-defined
Mathematica package. I should mention that Mathematica V9 has been used.

Regards
Robert Kragler

--
Prof. Dr. Robert Kragler
Hasenweg 5
D-88090 Immenstaad, Germany
Phone : +49 (7545) 2833 or 3500
Email : kra...@hs-weingarten.de
URL : http://portal.hs-weingarten.de/web/kragler