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MathGroup Archive 1999

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Re: Subscript Variable

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20315] Re: [mg20188] Subscript Variable
  • From: "David Park" <djmp at earthlink.net>
  • Date: Fri, 15 Oct 1999 20:20:44 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Michel,

A couple of months ago Carl Woll posted one solution to this problem. Essentially he
changed the Attributes of Subscript to HoldFirst, and added SubscriptInformation and
ClearSubscripts routines. I liked his routine so much I made a little package of it
and extended it slightly. Here are examples of it's use.

< Algebra`WollSubscripts`

?Algebra`WollSubscripts
"WollSubscripts sets the attributes of Subscript to HoldFirst so that it can \
be used like a symbol. Subscript definitions can be defined. The additional \
routines ClearSubscripts and SubscriptInformation are also provided."

?ClearSubscripts
"ClearSubscripts[sym1, sym2,...] will clear all Subscript definitions based \
on the symbols."

?SubscriptInformation
"SubscriptInformation[sym1, sym2,...] will print the Subscript definitions \
based on the symbols."

Here I use InputFormat so it will be readable in email.

Subscript[f, 1][x_] = x^2 + 1;
Subscript[f, 2][x_] = x^3 - 1;

SubscriptInformation[f]
Subscript[f, 1][x_] = 1 + x^2
Subscript[f, 2][x_] = -1 + x^3

?? Subscript
"Subscript has been given the Attribute HoldFirst so that it can be \
used like a symbol and be given definitions."
Attributes["Subscript"] = {HoldFirst}
Subscript[f, 1][x_] = 1 + x^2
Subscript[f, 2][x_] = -1 + x^3

Subscript[f, 2][y] - Subscript[f, 1][y]
-2 - y^2 + y^3

ClearSubscripts[f]
SubscriptInformation[f]
(none)

?? Subscript
"Subscript has been given the Attribute HoldFirst so that it can be \
used like a symbol and be given definitions."
Attributes["Subscript"] = {HoldFirst}

I am pasting the notebook that creates the package at the end of the email. The
package should be placed in the AddOns/ExtraPackages/Algebra directory.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

>Hello,
>
>I have a problem about subscript variables.
>
>First Question :
>
>If I use a variable named Subscript[x,1] ,
>(typed in with Ctrl _)
>
>I can affect a value to this variable, get value of expressions
>involving this variable, clear this variable with . but not with Clear[]
>!
>
>This variable is not given when I ask Names["x*"] and I cannot get
>information on it with ?.
>
>
>Second Question :
>
>If I use such a variable in order to define a function with
>  f1[x_]=x^2+1
>I cannot clear the variable with f1=.
>(of course, just above f1 means Subscript[f,1])
>
>
>Thanks a lot for any help
>
>
>J.Michel CORNIL
>


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Cell[CellGroupData[{
Cell["Algebra`WollSubscripts` Package", "Title"],

Cell[CellGroupData[{

Cell["Implementation", "Section",
  InitializationCell->True],

Cell[BoxData[{
    \(ClearAll[Subscript]\), "\[IndentingNewLine]",
    \(\(Subscript::usage = "\<Subscript has been given the Attribute \
HoldFirst so that it can be used like a symbol and be given \
definitions.\>";\)\), "\[IndentingNewLine]",
    \(SetAttributes[Subscript, {HoldFirst}]\)}], "Input",
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    \(BeginPackage["\<Algebra`WollSubscripts`\>"]\)], "Input",
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  InitializationCell->True],

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    \(\(SubscriptInformation::usage = "\<SubscriptInformation[sym1, sym2,...] \
will print the Subscript definitions based on the symbols.\>";\)\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(Begin["\<`Private`\>"]\)], "Input",
  InitializationCell->True],

Cell[BoxData[{
    \(\(SetAttributes[
        ClearSubscripts, {HoldAll}];\)\), "\[IndentingNewLine]",
    \(ClearSubscripts[a__]\  := \[IndentingNewLine]\
      Module[{b}, \[IndentingNewLine]DownValues[Subscript]\  =
          Cases[DownValues[Subscript], \((b_\  :> \ _)\)\  /; \
              FreeQ[b,
                HoldPattern[
                  Subscript[
                    Alternatives[a], \ __]]]]; \[IndentingNewLine]SubValues[
            Subscript]\  =
          Cases[SubValues[Subscript], \((b_\  :> \ _)\)\  /; \
              FreeQ[b,
                HoldPattern[
                  Subscript[
                    Alternatives[
                      a], \ __]]]];\[IndentingNewLine]]\)}], "Input",
  InitializationCell->True],

Cell[BoxData[{
    StyleBox[\(SetAttributes[SubscriptInformation, \ {HoldAll}];\),
      FormatType->StandardForm], "\n",
    StyleBox[\(SubscriptInformation[syms__]\  := \[IndentingNewLine]\
        Module[{PrintDownValue}, \[IndentingNewLine]PrintDownValue[\(Verbatim[
                    HoldPattern]\)[a_]\  :> \ b_]\  := \
            Print[HoldForm[
                a\  = \
                  b]]; \[IndentingNewLine]PrintDownValue\  /@ \((DeleteCases[
                Join[DownValues[Subscript],
                  SubValues[Subscript]], \ \((b_\  :> \ _)\)\  /; \
                  FreeQ[b,
                    HoldPattern[
                      Subscript[
                        Alternatives[
                          syms], \ __]]]])\);\[IndentingNewLine]]\),
      FormatType->StandardForm]}], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(End[]\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(Protect[ClearSubscripts, SubscriptInformation]\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(EndPackage[]\)], "Input",
  InitializationCell->True]
}, Open  ]]
}, Open  ]]
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WindowSize->{591, 571},
WindowMargins->{{Automatic, 94}, {Automatic, 21}}
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