Re: Interaction of Remove and Global variables in a Module

*To*: mathgroup at smc.vnet.net*Subject*: [mg120193] Re: Interaction of Remove and Global variables in a Module*From*: Gianluca Gorni <gianluca.gorni at uniud.it>*Date*: Tue, 12 Jul 2011 06:59:57 -0400 (EDT)*References*: <201107091132.HAA13513@smc.vnet.net>

Suppose I define a recursive sequence a[0] = 1; a[n_] := a[n] = 2 a[n - 1] If I evaluate a[2], then its value will be kept in memory. When I need to clear and reuse the symbol a, I use Clear[a]. Suppose now that I do it more traditional-looking: Subscript[a, 0] = 1; Subscript[a, n_] := Subscript[a, n] = 2 Subscript[a, n - 1]; If I call Subscript[a, 2], its value will be remembered. What can I do to clear the values? Clear[a] and ClearAll[a] do not work. Remove[a] does work. Is there a better alternative? Best regards, Gianluca On 09/lug/2011, at 13.32, DrMajorBob wrote: > So far, I haven't heard a purpose for Remove that ClearAll does not serve > just as well... without the side-effect of "spoiling" other symbols. > > Bobby > > On Fri, 08 Jul 2011 03:53:55 -0500, Leonid Shifrin <lshifr at gmail.com> > wrote: > >> Brian, >> >> The problem you encountered is actually more subtle. Remember that when >> you >> use Remove (as compared to Clear or ClearAll), the symbol is completely >> removed >> from the system. This is a pretty disruptive operation. Now, what should >> the system do if the symbol you are removing is referenced by some other >> symbols? >> Keeping it there unchanged would mean that the symbol has not been >> really removed >> from the system. The solution used in Mathematica is to change a >> reference to a >> symbol >> (say "a") to Removed[a]. In practice, this means that, even when you >> re-introduce >> the symbol, those definitions that were involving it are still "spoiled" >> and >> can not >> be used. IMO, this is a very sensible design, but this is what leads to >> the >> behavior >> that puzzled you. Have a look: >> >> f[b_]:=Module[{t},a[t_]=b*t^2;] >> Remove[a]; >> ?f >> >> Global`f >> f[b_]:=Module[{t},Removed[a][t_]=b t^2;] >> >> What you have to do in your approach is to re-run the definition for >> "f", to >> be able to >> use it. This is however pretty error-prone. You can cure this by calling >> Clear or ClearAll >> instead of Remove, but even this approach I don't consider a good >> practice. >> Even though >> you use "a" as a function, calling Clear or Remove on it means that in a >> way, you use >> it as a global variable. In this post: >> >> = http://stackoverflow.com/questions/6236458/plot-using-with-versus-plot-using-block-mathematica/6236808#6236808 >> >> there is a lengthy discussion why making implicit dependencies on global >> variables is a >> bad practice. >> >> Here are a few ways out. What you seem to want is to generate a function >> with embedded >> parameters (a closure). One way is to generate a pure function and return >> it: >> >> In[31]:= Clear[f]; >> f[b_]:=Function[t,b*t^2]; >> a = f[3]; >> a[t] >> a=f[4]; >> a[t] >> Remove[a]; >> a = f[5]; >> a[t] >> >> Out[34]= 3 t^2 >> Out[36]= 4 t^2 >> Out[39]= 5 t^2 >> >> Another way is to explicitly pass to "f" the symbol to which you want to >> assign >> the definition: >> >> In[40]:= Clear[ff,a]; >> ff[fname_Symbol,b_]:=Module[{t},fname[t_]=b*t^2;]; >> ff[a,3]; >> a[t] >> ff[a,4]; >> a[t] >> Remove[a]; >> ff[a,5]; >> a[t] >> >> Out[43]= 3 t^2 >> Out[45]= 4 t^2 >> Out[48]= 5 t^2 >> >> By making the function name an explicit parameter to "ff", you make the >> problematic >> situation above impossible to happen. >> >> HTH >> >> Regards, >> Leonid >> >> >> >> >> >> On Thu, Jul 7, 2011 at 3:28 PM, blamm64 <blamm64 at charter.net> wrote: >> >>> This is what I get for querying SetDelayed >>> >>> In[1]:= ?SetDelayed >>> lhs:=rhs assigns rhs to be the delayed value of lhs. rhs is maintained >>> in an unevaluated form. When lhs appears, it is replaced by rhs, >>> evaluated afresh each time. >> >>> >>> Note particularly the above reads AFRESH EACH time. It appears then >>> the following is inconsistent behavior based on the above description: >>> >>> In[2]:= f[b_]:=Module[{t},a[t_]=b*t^2;] >>> In[3]:= a[t] >>> Out[3]= a[t] >>> In[4]:= f[3] >>> In[5]:= a[t]//InputForm >>> Out[5]//InputForm= >>> 3*t^2 >>> In[6]:= f[5] >>> In[7]:= a[t]//InputForm >>> Out[7]//InputForm= >>> 5*t^2 >>> In[8]:= Remove[a] >>> In[9]:= f[4] >>> In[10]:= a[t]//InputForm >>> Out[10]//InputForm= >>> a[t] >>> >>> Apparently AFRESH is not an accurate description of how SetDelayed >>> operates in this case, or I am missing something about this particular >>> interaction of Module, Remove, and global variables inside Modules. >>> >>> However, if I go back, after executing the last line above (<a> has >>> been Removed), and place the cursor in the input line where <f> is >>> defined and hit Enter, which I thought would be identical to just >>> evaluating <f> AFRESH again, and then execute the <f[4]> line again, >>> then the global <a> definition is re-constituted. >>> >>> The documentation for Remove reads the name is no longer recognized by >>> Mathematica. My understanding is that if the same name is defined >>> AFRESH, it will once again be recognized. >>> >>> So if anyone would let me know what I am missing, regarding why the >>> definition of <a> is not created AFRESH each time <f> is evaluated, I >>> would appreciate it. >>> >>> Please don't construe the definition of <f> as my way of >>> 'parameterizing' a function definition, I just use that definition to >>> convey the apparent inconsistency. >>> >>> -Brian L. >>> >>> > > > -- > DrMajorBob at yahoo.com >

**Follow-Ups**:**Re: Interaction of Remove and Global variables in a Module***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**Re: Interaction of Remove and Global variables in a Module***From:*DrMajorBob <btreat1@austin.rr.com>

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