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Re: Interaction of Remove and Global variables in a Module

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120102] Re: Interaction of Remove and Global variables in a Module
  • From: David Bailey <dave at removedbailey.co.uk>
  • Date: Fri, 8 Jul 2011 04:54:06 -0400 (EDT)
  • References: <iv45c7$et1$1@smc.vnet.net>

On 07/07/2011 12:30, blamm64 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.
>

Here is a simpler example of the same phenomenon:

In[7]:= f[] := (a = 2)

In[8]:= ?f

Global`f

f[]:=a=2


In[9]:= Remove[a]

In[10]:= ?f

Global`f

f[]:=Removed[a]=2

In[11]:= a

Out[11]= a

In[13]:= f[]

Out[13]= 2

In[14]:= a

Out[14]= a

As you can see, by removing 'a', you effectively trash the function f - 
so reintroducing 'a' doesn't put you back where you were before. If it 
had, the Remove operation would have done nothing!

Removing symbols is a fairly unusual thing to do - it might help to 
explain why you want to do this.

David Bailey
http://www.dbaileyconsultancy.co.uk



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