How to define a global variable when giving each notebook its own Context?

Question

I have restricted the context of my notebooks to each individual notebook. So variables in each notebook are local and are not seen in another notebook.

But in two of my notebooks I have two functions that I want to plot simultaneously with the command Show. Please note that I want variables of each notebook to be local except for those two functions. So I need to define two global variables and then plot that two functions in Show. How can I define global variables in Mathematica?

Answer 1

You can explicitly define variables in the global context by prefixing their name with Global`, for example, Global`i = 3 or Global`f[x_]:=x^2. However if you have set the notebook to have private context, you don't have Global` in your $ContextPath (in order to prevent interference from other notebooks with non-private context). Therefore in your notebooks the context Global` isn't really special, you can use any context, like myShared`. Indeed, that's desirable because that way you know that a third notebook will be unlikely to interfere.

So you would write in your first notebook

myShared`function[x_]:=x^2

and then could access that function from the other notebook as

myShared`function[3]
(*
==> 9
*)

Note that you can add your context to the context path by using

AppendTo[$ContextPath, "myShared`"]

This then allows you to refer to the function above without the prefix, e.g.

function[3]
(*
==> 9
*)

However note that with this, your local symbols may shadow the shared ones (however access as myShared`function still works even then), so you have to make sure that you don't use the unprefixed symbol in any way before the prefixed one was created.

You might consider avoiding the issue by using PrependTo instead of AppendTo, but then you are vulnerable to variable injection (including accidental one) from the other notebook. For example, imagine that you have the definitions

a = 3;
PrependTo[$ContextPath, "myShared`"]

and then you do in your other notebook

Begin["myShared`"]
function[a_] := a^2
other[a_] := 5
End[]

Let's assume the symbol a had not yet been used in that notebook, then it is created, together with the symbols function and other, in the context myShared`, and therefore in your first notebook now hides the local definition of a. That is, if you now evaluate a in your first notebook, the kernel will find myShared`a (without a value) first, and therefore use that instead of the local a; of course it won't evaluate to 3.

Yet another way to access the symbol without prefix would be the definition

function := myShared`function

which however only works in a context with evaluation. Especially it should not be used for shared variables because after

variable := myShared`variable

a subsequent assignment like

variable = 42

does not change the shared variable, but only the local one (which no longer refers to the shared one).

Therefore I think it is a better idea to not do either, but always use the prefixed version.

Note that the PrependTo scenario is also an argument against using Begin["myShared`"] … End[] to simplify definitions in this case: It's too easy to accidentally introduce new symbols in that context which were not intended to be there.

Note that another way of sharing functions is to make them into a package and use that package from both notebooks. Ultimately this also boils down to having a shared context, as rcollyer noted in the comments. However a properly written package protects against or at least warns about most problems with hiding. Of course, writing a package might be overkill for your specific situation.

Answer 2

Globally define as follows $Assumptions = b >= 0 && c >= 0 && {u11, u13, u14} [Element] Reals then use globally defined variables as follows Simplify[expression with global variables]