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May 23, 2014, 2:42:45 AM5/23/14

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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

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