Hints for using subscripted variables in Mathematica packages


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

                            (* 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 

             ... (* 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.

Robert Kragler

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

5/23/2014 6:42:45 AM
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