Subscript and the Sorcerer's Apprentice

*To*: mathgroup at smc.vnet.net*Subject*: [mg13530] Subscript and the Sorcerer's Apprentice*From*: Tom Burton <tburton at brahea.com>*Date*: Fri, 31 Jul 1998 04:33:39 -0400*Sender*: owner-wri-mathgroup at wolfram.com

The Players The Sorcerer: Mathematica The Apprentice: me The Broom: Subscript Act I I frequently subscript symbols to mimic common mathematical notation. A subscripted symbol x\_a in the Front End becomes the expression Subscript[x,a] in the Kernel. Set (=) and SetDelayed (:=) assign a definition of Subscript[x,a] to the System symbol Subscript (System`Subscript). Within a Module, I declare x and a to be local to the Module. Every time I execute this Module, another definition is assigned to Subscript. Thus, after three executions of \!\(Module[{x, a}, x\_a = 1]\) I might see the following three DownValues added to Subscript: \!\({HoldPattern[x$3\_a$3] \[RuleDelayed] 1, HoldPattern[x$4\_a$4] \[RuleDelayed] 1, HoldPattern[x$5\_a$5] \[RuleDelayed] 1}\) assuming that $ModuleNumber was 3, 4, and 5 when this module was executed. These DownValues do not disappear when the Module goes out of scope. Version 3.0 provides a neat way to avoid these useless DownValues: Utilities`Notation`Symbolize, whereby x\_a is translated not into Subscript[x,a] but instead a single symbol (like x_a but with a fancier underscore). Alas, I am addicted to the ability to manipulate subscripts, and I am (true to my role!) stubborn besides, so I don't use Symbolize much. These useless DownValues of Subscript can accumulate quickly. From time to time, I amuse myself with the awful response from the Kernel when asked ??Subscript Act II I am running larger problems. The Kernel is awash in these useless subscripts. From time to time, it abruptly quits, proclaiming "Out of memory", owing, I suspect, to these subscripts. I am no longer amused. These foul subscripts must go! The simplest step, Clear[Subscript], would be too drastic. Instead, I execute the following function from time to time cleanSubscript[] := DownValues[Subscript] = DeleteCases[DownValues[Subscript], HoldPattern[L_ :> R_] /; StringMatchQ[ToString[L], "*$*"]] to clear out DownValues that appear to be useless. If I fail to call this function often enough, I'm in trouble. This function is imperfect. Interlude I would like Act III to be more agreeable. How to avoid this mountain of subscripts in the first place? One approach is to have each module clean up after itself: \!\(x\_a =. \) Alas, this solution is tedious when there many subscripted symbols, and I am (again, true to my role) lazy. So I don't do this much. Another approach is ask Mathematica to assign the definition to the local variable x. Neither of the following Modules leaves subscripts behind. \!\(Module[{x, a}, x /: x\_a = 1]\) \!\(Module[{x, a}, x\_a ^= 1]\) Alas, this approach often unavailable, because x and a are too far "Down": In[26]:= \!\(x /: x\_a[1] = 2\) TagSet::tagpos: Tag x in x [1] is too deep for an assigned rule to be a found. The same error occurs when assigning a list or matrix of subscripted symbols. Set and SetDelayed assign such definitions to Subscript, but not as any kind of Value that I recognize. They show up in response to ??: ??Subscript System`Subscript InputForm[Subscript[x, a][1] = 2] but I cannot interact with this output. Would anyone out there care to write me a happy Act III? Thanks!