Need some explanation of "Global`*"

Question

When I start a new notebook, I enter

Names["Global`*"]

I get this

{"list", "msgs", "rhs", "z"}

Then I enter,

mydummy[x_, y_, model_] := Module[
      {ans, j},
      ans = Sum[x[[j]], {j, 1, y}]

  ];
Names["Global`*"]

I get this:

{"ans", "ans$", "j", "j$", "list", "model", "model$", "msgs", "mydummy", "rhs", "x", "x$", "y", "y$", "z"}

I dont really know the difference between x and x$ here. I don't know any of the difference between the variables and the one with an extra $.

I check

?j
?j$

Ok, one of them is 'Temporary'.

Here are my questions:

1 - Are they all saved in RAM during the session? 2 - What's the point of saving these 'Temporary' (Global) variables? I thought when declaring them to be local using Module[], they would be thrown away after my execution.

3 - Why do we have x and y at first place? I only defined mydummy, which is a function. So I only want the 'final' value when it's evaluated.

4 - If the x and y are of any use, how do I access them? I tried

x

It does not tell me anything?

5 - If I define a new function,

mydummy2[x_, y_, model_] := Module[
  {ans, j},
  ans = Sum[x[[j]], {j, 1, y}]

]

Now

Names["Global`*"]

which 'x' is which?

6 - Sometimes, I get Global variables like

tmp$1
    tmp$20
tmp$300

To me, they are all 'local' to a Module. But it's in the list when I use 'Names["Global`*"]', why are they there? Can I remove them during a long calculation? How to remove and what's the downside of removing them?

7 - Do I need to declare $j$ within a Module, if it's a dummary index value, like this

ans=Table[Sum[j],{j,1,3}]
(* or *)
ans=Sum[x[[j]],{j,1,3}]

8 - Lastly, when i first started Mathematica, what are the "list,msgs,rhs,z" variables?

Sorry if this seems really silly. But I do want to understand this, as I have long codes, it seems sometimes it's using too much memory. I am not sure if it's caused by those 'local' variables.

Answer 1

First of all I suspect you are running Mathematica 10.0.0 and are experiencing these issues:

• Potential pollution of Global` context in fresh kernel
• Is garbage collection broken in version 10.0.0?

In version 10.0.1 I get:

Names["Global`*"]

{}

And then:

mydummy[x_, y_, model_] := Module[{ans, j}, ans = Sum[x[[j]], {j, 1, y}]];

Names["Global`*"]

{"ans", "ans$", "j", "j$", "model", "mydummy", "x", "y"}

The remaining names can all be explained as expected behavior. Every Symbol name that appears that does not correspond to an existing Symbol in the $ContextPath

is created in the current $Context. See:

• Local variables in Module leak into the Global context

This explains {"ans", "j", "model", "mydummy", "x", "y"}.

The remaining two: {"ans$", "j$"} are more tricky; I believe they are created by the automatic renaming mechanism that applies to nested scoping constructs, here SetDelayed and Module. See:

• Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs

I shall try to address all of your question on a point-by-point basis if I have time. I think those links should give you plenty to read for the moment, and right now it is time for me to eat. :-)